design analysis and presentation of crossover trials

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Research Article

The Use and Reporting of the Cross-Over Study Design in Clinical Trials and Systematic Reviews: A Systematic Assessment

* E-mail: [email protected]

Affiliations Department of Biostatistics, University of Liverpool, Liverpool, United Kingdom, Cochrane Cystic Fibrosis and Genetic Disorders Group, Liverpool, United Kingdom

Affiliations Cochrane Cystic Fibrosis and Genetic Disorders Group, Liverpool, United Kingdom, Chronic Disease Research Centre, The University of the West Indies, Barbados, West Indies

Affiliation Cochrane Editorial Unit, London, United Kingdom

Sarah Jane Nolan,
Ian Hambleton,

Published: July 13, 2016
https://doi.org/10.1371/journal.pone.0159014
Reader Comments

Systematic reviews of treatment interventions in stable or chronic conditions often require the synthesis of clinical trials with a cross-over design. Previous work has indicated that methodology for analysing cross-over data is inadequate in trial reports and in systematic reviews assessing trials with this design.

We assessed systematic review methodology for synthesising cross-over trials among Cochrane Cystic Fibrosis and Genetic Disorders Group reviews published to July 2015, and assessed the quality of reporting among the cross-over trials included in these reviews.

Methodology

We performed data extraction of methodology and reporting in reviews, trials identified and trials included within reviews.

Principal Findings

We reviewed a total of 142 Cochrane systematic reviews including 53 reviews which synthesised evidence from 218 cross-over trials. Thirty-three (63%) Cochrane reviews described a clear and appropriate method for the inclusion of cross-over data, and of these 19 (56%) used the same method to analyse results. 145 cross-over trials were described narratively or treated as parallel trials in reviews but in 30 (21%) of these trials data existed in the trial reports to account for the cross-over design. At the trial level, the analysis and presentation of results were often inappropriate or unclear, with only 69 (32%) trials presenting results that could be included in meta-analysis.

Conclusions

Despite development of accessible, technical guidance and training for Cochrane systematic reviewers, statistical analysis and reporting of cross-over data is inadequate at both the systematic review and the trial level. Plain language and practical guidance for the inclusion of cross-over data in meta-analysis would benefit systematic reviewers, who come from a wide range of health specialties. Minimum reporting standards for cross-over trials are needed.

Citation: Nolan SJ, Hambleton I, Dwan K (2016) The Use and Reporting of the Cross-Over Study Design in Clinical Trials and Systematic Reviews: A Systematic Assessment. PLoS ONE 11(7): e0159014. https://doi.org/10.1371/journal.pone.0159014

Editor: Andre Scherag, University Hospital Jena, GERMANY

Received: March 24, 2016; Accepted: June 24, 2016; Published: July 13, 2016

Copyright: © 2016 Nolan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files. The data underlying S1 Table is available on Figshare: https://dx.doi.org/10.6084/m9.figshare.3466946.v2 .

Funding: The time of SJN and KD was partly supported by the National Institute for Health Research, via Cochrane Infrastructure funding to the Cochrane Cystic Fibrosis and Genetic Disorders Group [ http://www.nihr.ac.uk/research/systematic-reviews.htm ], [ http://cfgd.cochrane.org/funding-and-support ]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. IH received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

A cross-over trial is a design in which participants receive two or more sequential interventions in a random order in separate treatment periods, often separated by a washout period to avoid a ‘carry-over’ intervention effect from one treatment period into the next [ 1 ]. Such a design has advantages over a parallel design in which participants are allocated to a single intervention for comparison with other interventions. In a cross-over trial, each participant can act as their own control in the trial [ 2 , 3 ], reducing the sample size required for the same statistical power, which is advantageous for assessing interventions for rare diseases. Cross-over designs are suitable for evaluating interventions with a temporary effect on stable or chronic conditions, such as arthritis, asthma or epilepsy [ 4 ]. Therefore, systematic reviews in these clinical areas often require the synthesis of intervention trials with a cross-over design.

Elbourne et al [ 5 ] reported that systematic review descriptions of cross-over trial synthesis were insufficient, and recommendations were made for improvement. Based on these recommendations, the Cochrane Handbook for Systematic Reviews of Interventions [ 6 ] has proposed a “three stage” decision process for including cross-over data in meta-analysis.

Ideally (first stage), the results from paired analyses, which adjust for within-individual comparisons, should be used. If the first stage approach is not possible, the second stage would be to include data from the first cross-over period, treating this period as a randomised parallel trial. Such an approach that requires trials to report data by treatment period and would result in a loss of statistical power from analysing only half of the available information from the trial. The third stage, the least desirable and most conservative approach, would be to assume the treatment arms are independent, which ignores the cross-over design and will likely overestimate variability of the within-study treatment effect. Despite the development of the recommendations in Elbourne et al [ 5 ], and subsequent guidance on meta-analyses combining parallel and cross-over data [ 7 – 9 ], it remains unclear whether these recommendations have been widely adopted in systematic reviews and meta-analyses, or how commonly the use of such ideal approaches is feasible from information reported in publications of cross-over trials.

For an appropriate trial synthesis, a systematic review needs access to methodological details of a trial and either individual level data or appropriately summarised data. Recent work found that cross-over trial reports often omit important methodological issues in design, presentation and analysis [ 4 ]. While Consolidated Standards of Reporting Trials (CONSORT) guidelines for randomised controlled trials in general have existed for nearly 20 years [ 10 , 11 ], as yet the CONSORT reporting guidelines have not been extended specifically for cross-over trials.

Our objectives in this study were to assess review methodology for including cross-over trials in reviews published by the Cochrane Cystic Fibrosis and Genetic Disorders (CFGD) Group based on the “three stage” approach as described in Elbourne et al [ 5 ]. Our aims were to assess the quality of reporting of cross-over trials within the trial reports themselves and subsequently, within the Cochrane CFGD reviews and to establish the basis of practical guidelines for how cross-over data should be included in systematic reviews, in line with Methodological Expectations of Cochrane Intervention Reviews (MECIR) standards.

Selection of reviews and cross-over trials

We accessed the most recently published version of all Cochrane Cystic Fibrosis and Genetic Disorders (CFGD) reviews (published to July 2015) and recorded the number and designs of included studies in each systematic review. We excluded reviews that explicitly considered the cross-over trial design to be inappropriate given the review question, usually because an intervention effect was not considered to be temporary, making a washout period ineffectual. For 17 reviews it was unclear whether cross-over studies would be included, and we contacted the corresponding author of these reviews for clarification.

For all included systematic reviews, we recorded how review authors planned to synthesise cross-over trial data. If a review included at least one cross-over trial, we compared the actual synthesis method to the intended method.

We accessed reports of all included cross-over trials and recorded trial characteristics, analysis details and presentation of all trial results. For review primary outcomes, we compared the relevant trial level results to the data included in the review(s).

Data extraction and presentation of results

Information extracted from included systematic reviews and cross-over trials are described in S1 Table , with data items extracted from cross-over trials based on a previous review of cross-over trial quality [ 4 ].

Two authors (SJN and KD) extracted information from reviews and trials using pre-designed data extraction forms. The third author (IH) independently double data extracted from a random sample of trials with uncertainties or discrepancies resolved by discussion.

Results of assessments at review and trial level are summarised narratively. Frequency data are presented as numbers and percentages.

See Fig 1 for flow diagram of selection of reviews and cross-over trials, S1 File for reference list of included Cochrane CFGD reviews and S2 File for reference list of included cross-over trials.

PPT PowerPoint slide
PNG larger image
TIFF original image

Flow diagram of selection of Cochrane Cystic Fibrosis and Genetic Disorders (CFGD) reviews and included cross-over trials a-d . a All numbers in Fig 1 refer to number of trials, some of which were published across multiple reports. Where this was the case, we extracted only from the primary reference as stated in the Cochrane review or according to our judgement of which reference was the most relevant. b In one review, review level and included trial level data was extracted following initial identification of reviews and trials up to January 2015. An update of this review was published in May 2015 in which five cross-over trials previously included were excluded (for reasons not due to cross-over design). These excluded cross-over trials were retained in the data extraction and results. c Note: in forty reviews which did not consider cross-over trials to be an eligible design; 13 cross-over trials were listed as “Excluded Studies” in these reviews due to design (one of which was included in another review). d Note: in the 102 reviews where cross-over designs were eligible, 10 unique trials listed as ‘Ongoing’ had a cross-over design and 35 unique trials listed as ‘Awaiting Assessment’ had a cross-over design (three of which were included in other reviews).

https://doi.org/10.1371/journal.pone.0159014.g001

Up to July 2015, 142 published CFGD reviews included a total of 684 trials of different designs. Cross-over designs were considered eligible in 102 reviews, and these reviews included 607 trials of any design. At least one cross-over trial was included in 53 reviews; twenty reviews included one cross-over trial, 11 reviews included two cross-over trials, 14 reviews included 3 to 10 cross-over trials and 8 reviews included 11 to 20 cross-over trials. A total of 218 unique cross-over trials; published between 1966 and 2012, were included in one or more of these 53 reviews. Less than 50% of the trials included were cross-over trials in 22 reviews, 50 to 99% of the included trials were cross-over trials in 21 reviews and in 10 reviews, all included trials were cross-over trials.

Systematic review methods

Table 1 and Fig 2 summarise the methods planned and the methods used in CFGD reviews for the inclusion of cross-over data.

Methods planned compared to methods used for and the inclusion of results from cross-over (CO) trials in meta-analysis for 53 reviews.

https://doi.org/10.1371/journal.pone.0159014.g002

https://doi.org/10.1371/journal.pone.0159014.t001

No methods or vague methods such as “consult a statistician” were described in 17 out of the 102 reviews (17%); but only two of these reviews actually included at least one cross-over trial. Fifty-three of the 102 reviews cite Elbourne et al [ 5 ], with 20 out of these 53 reviews (37%) giving no further description of their intended methods. Only a single review planned to include cross-over results narratively in the review only. The remaining 64 reviews described one or more of the “three stages” from Elbourne et al [ 5 ] for selecting and analysis approach, with 18 reviews intending to include first period data only and 4 reviews intending to conservatively analyse cross-over trials as parallel trials.

In the 53 reviews which included cross-over trials, 16 reviews with more than one cross-over trial included used more than one approach to analysing the trials ( Table 1 ). Twenty seven out of the 53 reviews used the method described in the ‘Methods’ section of the review; three were provided with extra data by the original trialists. The other 24 reviews which described a method of paired analyses or analysis of first period data actually included studies narratively or analysed as parallel studies ( Fig 2 ); it was mostly unclear whether authors had chosen not to use the analysis method described or if it was not feasible to use the method due to presentation of results.

Cross-over trial reporting

Table 2 , Fig 3 and Fig 4 summarise the characteristics, analysis details and presentation of the results in the 218 cross-over studies.

Analysis and reporting of results in 218 cross-over trials, and the incorporation of results in 53 systematic reviews.

https://doi.org/10.1371/journal.pone.0159014.g003

How many cross-over trials could be been included in meta-analysis?

https://doi.org/10.1371/journal.pone.0159014.g004

https://doi.org/10.1371/journal.pone.0159014.t002

The trials were of mostly small sample size ranging from 4 to 116 participants (median sample size 18). The majority of trials (72%) had an AB/BA design (i.e. participants randomised to one of two interventions and then order reversed). The use of a washout period was clearly described in 60 trials (27.5%), and assessment for a carry-over or period effect was clearly described in 48 trials (22%; Table 2 ).

Forty-five trials (20%) described no or unclear statistical methods and in a further 23 trials (11%), an inappropriate method of statistical analysis was described for the cross-over design (i.e. a statistical test for independent groups). The other 150 trials (69%) described an appropriate method of statistical analysis for the paired design ( Fig 3 ).

In 69 (32%) trials, sufficient information was presented to include some or all results in meta-analysis; either adjusted results, individual participant data or results according to treatment period ( Fig 3 ). In the remaining 149 (68%) trials, the presentation of the results would not allow the inclusion in meta-analysis; most trials presented results narratively or as a parallel trial.

How cross-over trials were included in systematic reviews

S2 Table , Fig 3 and Fig 4 summarise reporting of cross-over trial data in publications and how published results were included in the CFGD reviews.

One hundred and ninety trials were included in a single review, 26 trials were included in two reviews and two trials were included in three reviews; a full description of how trials were included in meta-analysis is given in S2 Table .

Twenty-three trials (11%) were not included in the results of the reviews due to no outcomes of interest to the review reported or ongoing information requests to original trial authors. A further 86 trials (39%) were included narratively in the review but not in meta-analysis; 19 of which could have been included in meta-analysis from published information provided ( Fig 4 ).

Thirty-two trials (15%) were included correctly accounting for design in meta-analysis via the analysis of adjusted results or analysis of first period data ( Fig 4 ). In seven of these trials, sufficient information was not presented in the trial reports; it was stated for three trials that extra data was provided by trialists but for the other four trials, results seemed to have been adjusted for inclusion in the review but it was not stated that extra information was provided.

Fifty-nine trials (27%) were included in reviews as parallel trials; 11 of which could have been included correctly accounting for design in meta-analysis ( Fig 4 ). The remaining 18 trials (8%) were included in two or more reviews and different approaches to the inclusion of the same results were taken across the reviews ( S2 Table ).

Statement of principal findings

The cross-over trial design is commonly used in chronic, stable, and rare disorders. Out of the 684 unique trials included in 142 reviews published by the Cochrane Cystic Fibrosis and Genetic Disorders (CFGD) Group up to July 2015, around a third (218 unique trials) had a cross-over design.

Despite the wide use of such designs in this area, only around 60% of CFGD reviews describe a clear and appropriate method for the inclusion of cross-over data in the review and only around half of these reviews eventually used their proposed synthesis methodology.

The analysis and presentation of results in cross-over trial reports were often inappropriate or unclear. Around 70% of trials clearly described appropriate statistical methodology but only 30% presented results that could be included in meta-analysis. Nearly 80% of studies failed to acknowledge or assess the presence of carry-over or period effect; biases which if present must be accounted for when interpreting results and performing future meta-analyses

Cross-over trials were most commonly included narratively in CFGD reviews, rather than in meta-analysis; however 30% of cross-over trials were included in meta-analysis incorrectly for design as parallel trials. In addition to ignoring carryover and period effects, the conservative assumption of parallel treatment arms over-estimates the variability between the treatment groups, artificially widening confidence intervals of the pooled treatment effect in meta-analysis. For the 28 cross-over trials which were included in more than one review, different approaches were taken for 18 of these trials (64%) by review authors to including the same results.

Strengths and limitations of the study

The strength of this study is the systematic, detailed assessment of all published reviews of a Cochrane Review Group and all cross-over trials within them.

We took the approach of assessing the most recently published version of reviews and made the assumption that methods described reflected an a priori analysis plan of cross-over data. However, it is possible that originally planned methods had been updated over time as Cochrane reviews were updated or adapted to reflect the approach actually taken in the review or in accordance with changes in Cochrane reporting standards over time. To know originally planned methods an assessment of original review protocols would be required. Such a protocol assessment had its own drawbacks, with some of the included reviews initiated up to 20 years ago, before the initiation of current format and current guidelines for Cochrane review protocols. Therefore this study does not provide an assessment of a change in reporting standards over time, but does highlight some reporting inconsistencies between methods and results sections of the most up to date version of each review.

We also note that the scientific aims of a review may influence the proposed methodology; for example, analysis of first period data may be preferable to analysis of paired results if carry-over is a particular concern for review authors. It was out of the scope of this work to examine clinical objectives of reviews in detail; however we encourage systematic reviewers to clearly state and justify use of particular methodology to address review specific clinical objectives.

When reviewing the inclusion of cross-over trials in systematic reviews, we only considered primary endpoints of Cochrane reviews. It would be inadvisable for Cochrane systematic reviews to vary synthesis methodology according to whether an endpoint is considered as primary or secondary. Therefore it is likely that if secondary review outcomes had also been considered, results would be similar.

Comparison to other studies

The poor reporting of cross-over trials in this assessment broadly agrees with the work of Mills et al [ 4 ], which considered all cross-over trials published within an 18 month period and concluded that cross-over trials “frequently omit important methodological issues in design, analysis, and presentation. “The sample of cross-over trials included in this current assessment is from specific disease areas, in contrast to Mills’ wide inclusion [ 4 ]. Nevertheless, our results highlight similarly poor reporting and in some areas, such as the use of inappropriate or unclear statistical methods and lack of clarity regarding use of washout period, are worse.

Elbourne et al [ 5 ] concluded that “poor reporting of cross-over trials will often impede attempts to perform a meta-analysis using the available methods.” This study shows that the reporting of cross-over trials still impedes their inclusion in meta-analysis, with inadequate presentation of results preventing data inclusion in meta-analysis for nearly 70% of cross-over trials assessed.

The methods of Elbourne et al [ 5 ] were cited in over half of the CFGD reviews which considered cross-over trials to be eligible, indicating some level of awareness of methodology for meta-analysis involving cross-over trials. However, it was not demonstrated in a large proportion of the reviews citing Elbourne et al [ 5 ] that the authors understood the methodology or how to implement the described approaches.

The results of this study are also largely comparable to the review of Lathrytis et al [ 17 ]; evaluating the analysis and results of cross-over trial data in a sample of Cochrane review meta-analyses compared to parallel design trials. The authors report variability in the approach to analysis of cross-over data and a paucity of clear methodological information regarding analysis approach. Our results suggest that despite nearly ten years of development of accessible guidance and training for Cochrane systematic reviewers, reporting of methodology related to cross-over data has not improved.

Recommendations and future research

This study has important implications for future research at both the level of systematic reviews and trial level. Current guidance available to systematic review authors on the meta-analysis of cross-over data is often statistically technical and published in specialised journals [ 5 , 7 – 9 ] and even in the Cochrane Handbook for Systematic Reviews of Interventions [ 6 ], analysis of cross-over data is covered under the chapter of “Special Topics in Statistics” [ 18 ]. The inconsistency and lack of detail in described methodology, and the variability in approaches to the inclusion of results in CFGD reviews suggests that review authors require more practical, plain language guidance for the inclusion of cross-over data in systematic reviews, to supplement the current statistical based guidance.

We note that while cross-over designs are appropriate for many systematic review questions within the scope of the CFGD review group, the proportion of cross-over trials included, and the review author guidance for the inclusion of cross-over data may vary by clinical area and by Cochrane Review Group. Therefore, it is important that guidance given to systematic review authors should be consistent when given at a review group level, but appropriate for the scope of the review group. An extension of this study could consider the review methodology for the inclusion of cross-over data and the quality of reporting of included cross-over trials of other Cochrane review groups.

Mills et al [ 4 ] called for development of “minimum standards for the transparent reporting of cross-over trials.” The present study emphasises the need for the development of reporting standards such as an extension of the CONSORT guidelines, for cross-over studies. The existence of minimum reporting standards at a trial level, in addition to supplementary guidance for systematic reviewers analysing cross-over data could increase the proportion of meta-analyses adequately conducted; which would be greatly beneficial to clinical decision making, particularly in clinical areas where cross-over designs are commonly used.

Statistical analysis and reporting of cross-over data is inadequate at both the systematic review and the individual trial level. Plain language and practical guidance for the inclusion of cross-over data in Cochrane meta-analyses at a review group level are needed. Minimum reporting guidelines, such as a CONSORT extension to cross-over trials are needed to ensure that results from trials of such design can be appropriately synthesised.

Supporting Information

S1 file. cochrane cystic fibrosis and genetic disorders group reviews..

Reference list of 142 Cochrane Cystic Fibrosis and Genetic Disorders reviews published to July 2015.

https://doi.org/10.1371/journal.pone.0159014.s001

S2 File. Cross-over trials included in Cochrane Cystic Fibrosis and Genetic Disorders Group reviews.

Reference list of 218 unique cross-over trials included in Cochrane Cystic Fibrosis and Genetic Disorders reviews published to July 2015.

https://doi.org/10.1371/journal.pone.0159014.s002

S1 Table. Data items extracted.

List of information extracted at the review level and at the study level.

https://doi.org/10.1371/journal.pone.0159014.s003

S2 Table. Inclusion of cross-over data in Cochrane Reviews.

Inclusion of cross-over trials for the primary outcomes (PO) of reviews of the Cochrane Cystic Fibrosis and Genetic Disorders Group.

https://doi.org/10.1371/journal.pone.0159014.s004

Acknowledgments

The authors would like to thank the authors of all included Cochrane CFGD group authors for further information on their reviews and the Cochrane CFGD group editorial team for their support.

Author Contributions

Conceived and designed the experiments: KD. Analyzed the data: SJN KD. Wrote the paper: SJN IH KD.

1. Senn SJ. Cross-over trials in clinical research. Chichester: John Wiley. 2002
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6. Higgins JPT, Green S, editors. Cochrane Handbook for Systematic Reviews of Interventions Version 5.1.0 [updated March 2011]. The Cochrane Collaboration, 2011. Available from www.cochrane-handbook.org .
18. Higgins JPT, Deeks JJ, Altman DG, editors. Chapter 16: Special topics in statistics. In: Higgins JPT, Green S (editors), Cochrane Handbook for Systematic Reviews of Interventions Version 5.1.0 (updated March 2011). The Cochrane Collaboration, 2011. Available from www.cochrane-handbook.org .

DOI: 10.2307/2532176
Corpus ID: 122318989

Design and Analysis of Cross-Over Trials

B. Jones , M. Kenward
Published 1 June 1989
Mathematics

1,278 Citations

Meta-analyses involving cross-over trials: methodological issues., mathematical analysis of a five periods crossover design for two treatments, choosing cross-over designs when few subjects are available, efficient crossover designs in the presence of interactions between direct and carry-over treatment effects, interim analyses in 2 x 2 crossover trials., comparison of statistical models for cross-over design, bayesian analysis of an optimal five period cross-over design, the construction of a williams design and randomization in cross-over clinical trials.

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CrossOver: an algorithm for the construction of efficient cross‐over designs

Analysis of 2 x 2 cross-over trials using an integrated macro package, 114 references, the construction of balanced designs for experiments involving sequences of treatments, the performance of the two-stage analysis of two-treatment, two-period crossover trials., optimal crossover designs in the presence of carryover effects., recent developments in crossover designs, tied-double-change-over designs, a variational approach to optimal two-treatment crossover designs: application to carryover-effect models, repeated measurements designs, cyclic change-over designs, the two-period change-over design an its use in clinical trials., experimental designs balanced for the estimation of residual effects of treatments, related papers.

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Design, Analysis, and Presentation of Crossover Trials

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Design, Analysis, and Reporting of Crossover Trials for Inclusion in a Meta-Analysis

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1 Center for Clinical Trials and Evidence Synthesis, Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, United States of America.
PMID: 26284684
PMCID: PMC4540315
DOI: 10.1371/journal.pone.0133023

Objective: To evaluate the characteristics of the design, analysis, and reporting of crossover trials for inclusion in a meta-analysis of treatment for primary open-angle glaucoma and to provide empirical evidence to inform the development of tools to assess the validity of the results from crossover trials and reporting guidelines.

Methods: We searched MEDLINE, EMBASE, and Cochrane's CENTRAL register for randomized crossover trials for a systematic review and network meta-analysis we are conducting. Two individuals independently screened the search results for eligibility and abstracted data from each included report.

Results: We identified 83 crossover trials eligible for inclusion. Issues affecting the risk of bias in crossover trials, such as carryover, period effects and missing data, were often ignored. Some trials failed to accommodate the within-individual differences in the analysis. For a large proportion of the trials, the authors tabulated the results as if they arose from a parallel design. Precision estimates properly accounting for the paired nature of the design were often unavailable from the study reports; consequently, to include trial findings in a meta-analysis would require further manipulation and assumptions.

Conclusions: The high proportion of poorly reported analyses and results has the potential to affect whether crossover data should or can be included in a meta-analysis. There is pressing need for reporting guidelines for crossover trials.

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Competing Interests: The authors have declared that no competing interests exist.

Fig 1. Illustration of the design and…

Fig 1. Illustration of the design and analysis of a crossover trial.

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Design and Analysis of Cross-Over Trials

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Design and Analysis of Cross-Over Trials is concerned with a specific kind of comparative trial known as the cross-over trial, in which subjects receive different sequences of treatments. Such trials are widely used in clinical and medical research, and in other diverse areas such as veterinary science, psychology, sports science, and agriculture.T

Chapter 1 | 10 pages, introduction, chapter 2 | 94 pages, the 2 × 2 cross-over trial, chapter 3 | 30 pages, : higher-order designs for two treatments, chapter 4 | 52 pages, designing cross-over trials for three or more treatments, chapter 5 | 94 pages, 7 example 5.1: innovo trial: dose–response study, chapter 6 | 38 pages, analysis of discrete data, chapter 7 | 12 pages, bioequivalence trials, chapter 8 | 12 pages, case study: phase i dose–response noninferiority trial, chapter 9 | 8 pages, case study: choosing a dose–response model, chapter 10 | 6 pages, case study: conditional power, chapter 11 | 8 pages, case study: proof of concept trial with sample size re-estimation, chapter 12 | 6 pages, case study: blinded sample size re-estimation in a bioequivalence study, chapter 13 | 6 pages, case study: unblinded sample size re-estimation in a bioequivalence study that has a group sequential design, chapter 14 | 4 pages, case study: various methods for an unblinded sample size re-estimation in a bioequivalence study.

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Crossover Trials: Design and Analysis

Oct 23, 2014

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Crossover Trials: Design and Analysis. Peter T. Donnan Professor of Epidemiology and Biostatistics. Objectives of session. Understand what is meant by a crossover trial design Understand the correlated nature of data

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Crossover Trials: Design and Analysis Peter T. Donnan Professor of Epidemiology and Biostatistics

Objectives of session Understand what is meant by a crossover trial design Understand the correlated nature of data Able to implement crossover analysis with continuous outcome in SPSS and SAS Interpret the output

Crossover designs • In this design each patient receives ALL treatments • Comparison of treatments is within-patient comparison • Removes all fixed within-patient factors e.g. gender • Essentially a matched design

Randomisation • Order of receipt is randomised • With 2-period, 2-treatments – AB or BA • With 3-preriod, 3-treatments – • ABC, ACB, BAC, BCA, CAB, CBA • Note above are balanced in the sense that every patient gets every treatment • Requires a wash-out period between treatments – to prevent CARRY-OVER

Crossover Trial Eligible subjects RANDOMISED Intervention Control Wash-out Wash-out Control Intervention

Efficiency of Crossover design • To estimate efficiency we can compare the variances • For a similar parallel trial design: • Total number M = 2N / (1 – rho) • Where M is the total size of the parallel trial and N is the number of subjects in the crossover design and rho is the correlation between measurements in Period I and II between a random subject • So a similar parallel trial design requires AT LEAST TWICE as many subjects

Strengths and Weaknesses of crossover design • Within patient characteristics remain same since matched analysis • Smaller sample size needed compared with parallel design - Very efficient design • Not suitable for intervention that ‘cures’ condition • Used for treatments of symptoms / control in chronic conditions; pain, asthma, COPD, diabetes, MS, hypertension, etc. • Fails if carry-over effect from previous period Senn S. (1993) Crossover trials in clinical research. Chichester, John Wiley

Simple Analysis Simple analysis makes use of the within-patient comparison: Paired t-test for continuous outcomes McNemar’s Chi-squared test for categorical data

Organisation of data Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 54 BA

Paired t-test Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 54 BA • t = Mean difference / Se (differences) • = 3.94 / 1.67 • = 2.36 • So with 108 df , p = 0.02 • So a statistically significant effect with drug A generally lower BP • Analysis assumes no PERIOD effect and • No CARRY-OVER effect

Paired t-test Then select two columns with the BP measurements for each drug • In SPSS: • Analyze • Compare Means • Paired-Samples t-test

Examining the assumptions We can test for a PERIOD x TREATMENT interaction i.e. Does the effect of the drug vary depending on whether it is given in the first period compared to the second period? Common reason is CARRY-OVER Test for interaction is independent t-test for continuous outcome

Period X Treatment interaction Independent t-test t = 0.77 which is not significant

Period X Treatment interaction Unfortunately the test is not very powerful and carry-over may not be detected with small sample size even if present (Solution: design study to be powerful enough!) If detected then the simple treatment analysis could be BIASED as the effect depends on which period the patients got which drug Then only use comparison in FIRST period for treatment effect (Grizzle two-step analysis).

Grizzle Two-stage analysis not recommended Senn (1994) says: Two-step approach does not remove potential bias and carry-over test is usually underpowered Test on period 1 is also underpowered Best approach is to make sure there is NO carry-over with an efficient wash-out! FDA recommend Washout ≥ 3 x half-life of drug

Senn’s advice Senn (1994) offers this advice: …my advice to the trialist is under no circumstances must the two-stage procedure be used.”

Senn’s proposed analysis Make use of the two baseline measures in a two period design so we have four measurements

Senn’s proposed analysis Use Generalised Linear Models (GLM) Fit simple SAS model as below: procglm; class ORDER; model OUTCOME = ORDER BASELINE; Estimate ‘TREATMENT’ intercept 1; run; Intercept value is the TREATMENT effect and p-value Baseline can be removed to assess the effect of baseline in results

Senn’s proposed analysis Generalized Linear Models (GLM) include both continuous and categorical data and can be fitted in SPSS Analyze Generalized Linear Model etc… n.b. SPSS offers Generalized Estimating Equations (GEE) for binary outcomes

Other pitfalls Patient drop-out in the first period can mean there are fewer in the second period and potentially with different characteristics Analysis of only complete data or ‘Per Protocol’ is likely to be BIASED and breaks the Intention-To-Treat (ITT) principle Consider Multiple Imputation but assumes data is Missing-At-Random (MAR) Alternatively use Mixed Models (also assumes MAR)

Summary Design is powerful and efficient Eliminates within-patient confounding Opportunity for head-to-head trials Problem of carry-over effect; test often underpowered Drop-outs break ITT principle and per protocol analysis could bias results

References Senn S. (2002) Crossover trials in clinical research. Chichester, John Wiley Mills JM, Chan A-W, Wu P, Vail A, Guyatt GH, Altman DG. Design, analysis and presentation of crossover trials. BMC Trials 2009; 10: 27 Schouten H and Kester A. A simple analysis of a simp[le crossover trial with a dichotomous outcome measure. Statist Med 2010; 29: 193-198 Senn S. The AB/BA crossover: past, present and future? Statistical Methods in Medical Research 1994; 3:303-324.

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Study protocol
Open access
Published: 31 July 2024

The combined effect of transcutaneous electrical nerve stimulation and transcutaneous auricular vagus nerve stimulation on pressure and heat pain thresholds in pain-free subjects: a randomized cross-over trial

Richard E. Liebano ORCID: orcid.org/0000-0003-4795-6723 1 ,
Noura Awad 1 ,
Christopher Bellino 1 ,
Katherine Bray 1 ,
Heidi Rosentrater 1 ,
Joshua Roy 1 &
Camryn Tate 1

Trials volume 25 , Article number: 516 ( 2024 ) Cite this article

Metrics details

Transcutaneous electrical nerve stimulation (TENS) is a non-invasive modality that utilizes electrical currents to modulate pain in populations with acute and chronic pain. TENS has been demonstrated to produce hypoalgesic effects in postoperative pain, fibromyalgia, knee osteoarthritis, and healthy subjects. Transcutaneous auricular vagus nerve stimulation (TaVNS) is a non-invasive modality that modulates the vagus nerve by stimulating its auricular branches. The effects of the combination of TENS and TaVNS on producing an analgesic response have not been studied. Considering that TENS and TaVNS both stimulate similar analgesic pathways but through different means of activation, we can hypothesize that a combination of both methods can produce a more pronounced analgesic response. Therefore, the objective of this study is to assess the hypoalgesic effect of a combination of TENS and TaVNS in pain-free subjects.

Methods/design

The study will be a simple crossover design conducted at the University of Hartford. Subjects will be recruited from the University of Hartford population via oral communication, digital flyers, and posters on campus. Thirty participants will undergo two sessions in a crossover manner with one week in between. During one session, the participants will receive TENS with active TaVNS and the other session will be a placebo procedure (TENS with placebo TaVNS). The order of these sessions will be randomized. Importantly, the pressure pain threshold (PPT) and heat pain threshold (HPT) assessors will be blinded to the treatment category. For active TaVNS, a frequency of 25 Hz will be applied with a pulse duration of 200 µs. For placebo TaVNS, the intensity will be increased to a sensory level and then decreased to 0 mA. High-frequency TENS of 100 Hz will be applied in both sessions, with a pulse duration of 200 µsec, asymmetrical biphasic square waveform, and intensity of maximal tolerance without pain. TENS and TaVNS will be turned on for 30 min after a baseline measurement of outcomes. TENS and TaVNS will then be turned off, but the electrodes will remain on until completion of post-treatment assessment. Pressure pain threshold, heat pain threshold, blood pressure, oxygen saturation, and heart rate will be tested 4 times: Once pre-intervention, once during intervention, once immediately after the intervention, and once 15 min post-intervention. Statistical analysis of the data obtained will consider a significance level of p < 0.05.

This study will provide evidence concerning the combined effects of TENS and TaVNS on pain threshold in pain-free participants. Based on the outcomes, a greater understanding of how TENS and TaVNS, when used in conjunction, can modulate pain pathways.

Trial registration

ClinicalTrials.gov NCT06361381. Registered on 09 April 2024.

Peer Review reports

Administrative information

Title {1}	The combined effect of transcutaneous electrical nerve stimulation and transcutaneous auricular vagus nerve stimulation on pressure and heat pain thresholds in pain-free subjects: a randomized cross-over trial
Trial registration {2a and 2b}	ClinicalTrials.gov (NCT06361381). Registered on 09 April 2024
Protocol version {3}	Version 1, February 6, 2024
Funding {4}	There is no funding. All necessary materials and facilities will be provided by the University of Hartford’s Physical Therapy program
Author details {5a}	Richard E Liebano , Noura Awad , Christopher Bellino , Katherine Bray , Heidi Rosentrater , Joshua Roy , Camryn Tate Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Author for correspondence. Tel.: + 1 860.768.5181. Department of Rehabilitation Sciences, University of Hartford
Name and contact information for the trial sponsor {5b}	Richard Liebano. Department of Rehabilitation Sciences, University of Hartford, 200 Bloomfield Avenue, West Hartford, CT 06117. E-mail: [email protected] Tel.: + 1 860.768.5181
Role of sponsor {5c}	The sponsor collaborated in developing the study design. He will oversee data collection, management, analysis, interpretation, and report writing. The sponsor will make decisions regarding submitting the report

Introduction

Background and rationale {6a}.

Transcutaneous electrical nerve stimulation (TENS) is a noninvasive modality that utilizes electrical currents to modulate pain in populations with acute and chronic pain [ 1 , 2 , 3 ]. TENS was created after the publication of the gate theory of pain. According to this theory, the activation of large-diameter afferent fibers (A-beta) stimulates local inhibitory circuits in the dorsal horn of the spinal cord, thereby impeding nociceptive signals transmitted by small-diameter fibers (C and A-delta) from reaching higher brain centers [ 4 ]. However, further studies have demonstrated TENS modulates pain via a pathway with projection neurons from the periaqueductal gray (PAG) to the rostral ventral medulla (RVM), and then subsequently to the dorsal horn where excitability of nociceptive neurons are inhibited [ 5 , 6 ]. Different frequencies of TENS will activate different opioid receptors, thus leading to a hypoalgesic effect. Frequencies above 50 Hz will activate δ-opioid and GABA receptors, and frequencies under 10 Hz will activate μ-opioid and serotonin receptors [ 6 , 7 ]. Due to these mechanisms, TENS has demonstrated an analgesic effect in different clinical populations such as postoperative pain [ 8 , 9 ], fibromyalgia [ 10 ], and knee osteoarthritis [ 11 ]. Previous studies have also shown a hypoalgesic response in healthy subjects [ 12 , 13 , 14 , 15 , 16 , 17 ].

Vagus nerve stimulation (VNS) was first approved by the US Food and Drug Association in 1997 and is currently approved for the treatment of drug-resistant epilepsy, morbid obesity, and depression [ 18 ]. Recent studies have demonstrated that VNS can provide positive results when treating chronic pain [ 19 ], hand osteoarthritis [ 11 ], anxiety disorders, Alzheimer’s disease, rheumatoid arthritis, and many other conditions [ 18 ]. VNS has also been found to alleviate chronic pain conditions and increase pain threshold for heat stimulation [ 12 , 20 ] and mechanical pressure [ 20 ]. The classic approach of VNS was originally through the use of a cervical implanted device which was an invasive technique and not only expensive but is also associated with adverse effects [ 11 ]. Some of the reported adverse effects were nausea, vomiting, skin irritation, headache, burning sensation, and dizziness [ 18 ]. Transcutaneous auricular vagus nerve stimulation (TaVNS) is a newer delivery system that uses transcutaneous electrical stimulation which eliminates the need for the implantation of a device [ 21 ]. TaVNS is a simple and non-invasive therapy that modulates the vagus nerve by stimulating its auricular branches with fewer side effects [ 21 ]. TaVNS can be used to stimulate the cymba, concha, or tragus of the ear which contains afferent branches of the vagus nerve. These afferent branches terminate in the brain stem nuclei of the vagal and trigeminal nerves [ 22 , 23 ]. The nucleii then project to the PAG and RVM, the same structures that are involved in the descending pain pathway affected by TENS [ 6 , 12 ]. In order to alter pain perception, TaVNS creates an analgesic effect through the activation of serotonergic and endorphinergic analgesic pathways [ 24 ]. Finding effective, non-invasive pain management options can improve the quality of life for individuals suffering from pain conditions. Professionals, such as physical therapists and pain management specialists, can benefit from understanding the combined effects of TENS and TaVNS, potentially leading to alternative and more effective treatment plans. These non-invasive modalities can reduce the reliance on pharmacological treatments, lowering healthcare costs and risks associated with long-term medication use. Both TaVNS and TENS create an analgesic effect using similar inhibitory pathways, but no research has investigated the effectiveness on pain thresholds when using both interventions in combination. Thus, the current study will investigate the combined effects of TENS and TaVNS on pain thresholds in healthy subjects.

Objectives {7}

This study aims to understand the combined effect of transcutaneous electrical nerve stimulation and transcutaneous auricular nerve stimulation on pressure and heat pain thresholds in pain-free subjects.

Trial design {8}

The study will be a simple crossover design and will be conducted at the University of Hartford. This protocol study was written following the recommendations of Standard Protocol Items: Recommendations for Interventions Trials (SPIRIT). The study protocol will be registered online on ClinicalTrials.gov, and reported according to CONSORT guidelines [ 25 ].

Methods: participants, interventions, and outcomes

Study setting {9}.

The study will be carried out at the Department of Rehabilitation Sciences of the University of Hartford, West Hartford, CT, USA.

Eligibility criteria {10}

Potential participants will be registered and screened to ensure that they meet the inclusion and exclusion criteria.

Inclusion criteria

Absence of pain

Men and women

Exclusion criteria

Neurological diseases

Severe cardiorespiratory disease

Skin infection or lesions or change in sensation at the TENS or TaVNS application site

Cardiac pacemaker

Allergy to electrodes

Chronic illness or pain

Use of drugs that affect pain or vagal tone in the past 48 h prior to data collection

Who will take informed consent? {26a}

Data collection will only start after the participants have signed an informed consent form, which the evaluator will explain.

Additional consent provisions for collection and use of participant data and biological specimens {26b}

N/A. No biological specimens will be collected as part of this trial.

Interventions

Explanation for the choice of comparators {6b}.

Previous studies have only looked at the effects of TaVNS or TENS independently of each other. Therefore, the proposed research will assess the combined effects of TaVNS and TENS regarding pain modulation.

Intervention description {11a}

Tens electrode placement.

A 5 × 5 cm electrode (ValuTrode®) will be placed 1 cm proximal to the elbow crease and 1 cm proximal to the wrist crease on the dorsum of the left upper limb [ 13 ]. These self-adhesive electrodes are commercially available and will be purchased for each subject.

TENS parameters

All subjects in all groups will rest in a supine position for the 30-min treatment period. Area of the forearm will be prepared with an alcohol wipe prior to the application of electrodes. High-frequency TENS (100 Hz) [ 13 ] (IBRAMED Neurodyn portable TENS/FES, Brazil) will be applied with a pulse duration of 200 µsec [ 12 , 23 , 24 , 26 ], waveform of an asymmetrical biphasic square wave, and intensity of maximal tolerable without pain [ 13 ]. TENS will be placed for 30 min after baseline testing and then turned off; the electrodes will remain on for the post-assessment test.

TaVNS electrode placement

Both conchas will be swabbed with an alcohol wipe before applying a thin layer of conductive gel. An ear clip electrode (Plafnio, China) will be placed in the concha of both ears [ 2 , 23 , 26 , 27 ].

Active TaVNS

An IBRAMED Neurodyn portable system unit will be used to deliver the active TaVNS intervention. A frequency of 25 Hz [ 19 , 20 , 21 ] will be applied with a pulse duration of 200 µs [ 12 , 23 , 24 , 26 ] at the maximum intensity tolerable without pain. Every 5 min, the subject will be asked if the intensity can be increased, decreased, or remain the same to maintain the same level of intensity.

Placebo TaVNS

For placebo TaVNS (IBRAMED Neurodyn portable system, Brazil), the intensity will be increased to a sensory level and then decreased to 0 mA.

Criteria for discontinuing or modifying allocated interventions {11b}

There will be no changes in the treatment allocation order. If participants discontinue treatment, recent data will be computed for the analyses according to the intention-to-treat principle, and the reason for the withdrawal from the study will be recorded.

Strategies to improve adherence to interventions {11c}

To minimize data loss, all participants will be guided when they sign the informed consent form and commit to attending on the scheduled treatment dates. An evaluator will be responsible for notifying and monitoring the participants weekly (via telephone contact, text message, and/or email) and accompanying them during the research. In cases of abandonment or impossibility of continuing the study, the data will be analyzed according to an intention-to-treat protocol.

Relevant concomitant care permitted or prohibited during the trial {11d}

Throughout the trial, participants will be asked not to start/use any other interventions or pain medications within 48 h of assessments as it may influence outcomes.

Provisions for post-trial care {30}

The interventions are designed to inflict minimal to no harm, and no compensation for harm is deemed necessary.

Outcomes {12}

The primary outcome will be pressure pain threshold (PPT). The secondary outcomes will be heat pain threshold (HPT) and autonomic function including heart rate, oxygen saturation, and blood pressure. These outcomes will be measured four times, once as a baseline testing, once at 15 min, once at 30 min, and once at 45 min (15 min after interventions have concluded) (Fig. 1 ).

Timeline for when outcome measures will be taken. There will first be a 30-min adaptation time prior to measuring their baseline Heat Pain Threshold, Pressure Pain Threshold, blood pressure, heart rate, and O 2 saturation. Measurements will be retaken after 15 and 30 min of treatment and then once again 15 min after treatment is turned off. Orange is when treatment is off, blue indicates that treatment is on

Pressure Pain Threshold (PPT)

A digital pressure algometer (Medoc AlgoMed FPIX, Israel) will measure the pain threshold to deep mechanical stimuli. The intra-rater and inter-rater reliability of measurement of PPT will be performed in 12 asymptomatic subjects by a single evaluator at 48-h intervals. Reliability will be estimated by calculating the intraclass correlation coefficients (ICCs). A 1-cm 2 algometer probe will apply pressure at 40 kPa/sec. Subjects will be instructed to activate a button when the sensation of pressure becomes one of painful pressure, and this value will be recorded. Three trials will be done on each region tested. This method will register the mean PPT of the forearm and anterior tibia region.

Measure on the forearm will be done over one point marked on the left arm (primary outcome) with a permanent marker located 3 cm distal to the elbow crease on the extensor mass [ 13 , 14 ]. Another point will be marked over the ipsilateral tibialis anterior muscle (secondary outcome) that is 5 cm from the tibial tuberosity [ 28 , 29 ].

Heat Pain Threshold (HPT)

Superficial heat pain sensitivity (secondary outcome) will be assessed using a handheld thermode (Medoc TSA-II, Israel) with a single 40 × 40 mm probe placed on a marked location on the left hand 5 cm distal to the elbow crease on extensor mass. The baseline temperature will be pre-set to 32 degrees Celsius (C). During testing, the temperature will increase at a rate of 1 °C/s until the participant reports the temperature as painful by pressing an indicator button. Maximum temperature will be pre-set at 50 °C, and if no pain had been elicited by then, this will be recorded as the heat pain threshold (HPT) [ 30 ]. Three trials will be done on each region tested with the average of these numbers being recorded.

All QST tests (PPT and HPT) will be performed with the patient in a supine position with their arm resting next to their body on the plinth. Before data collection, a test trial of each pain threshold assessment will be performed on the ventral forearm of the non-tested arm.

Autonomic measures

Heart rate and oxygen saturation will be measured using a pulse oximeter (Zacurate/500DL/ USA) on the right index finger. An automatic blood pressure cuff (Omron/BP5100/Japan) will measure the subject’s blood pressure using the brachial artery on the right arm.

Study blinding assessment

Each subject will receive both treatments: (1) TENS with TaVNS and (2) TENS with placebo TaVNS. The treatment order will be randomized via the website (randomization.com). Simple randomization results will be concealed in sealed envelopes with consecutive numbers. Subjects will be tested one time per week for 2 weeks. Importantly, the PPT and HPT assessors will be blinded to the treatment category. A different tester will administer the active or placebo TaVNS. The HPT and PPT assessors will also be asked if they believe it was placebo TaVNS or active TaVNS, and their responses will also be recorded.

Participant timeline {13}

Demographics of the participants will be subjectively collected during the recruitment process: this includes age, sex, weight, and height. Participants will be randomized to treatment group order after providing written consent. It will be decided if the participant receives TENS with active TaVNS or placebo TaVNS during their first session through a randomization process via the website (randomization.com). Simple randomization results will be concealed in sealed opaque envelopes with consecutive numbers and will not be available to the outcomes assessor. The envelopes will be signed, dated, and opened by the TENS and TaVNS allocator before the TENS and TaVNS application and after the outcomes assessor has left the room.

An overview of the study procedures is shown in Fig. 2 .

Schedule of enrolment, interventions, and assessments

Sample size {14}

The sample size was calculated considering a difference of 100 kPa between sessions and a standard deviation of 117 kPa obtained from previous data on pressure pain threshold (PPT) and TENS [ 15 ]. At a significance level of 0.05 and a power of 80%, the required sample size in each group was 23 participants (Minitab, v.17, State College, PA, USA). Allowing for attrition, a total of 30 participants will therefore be recruited: 15 men and 15 women.

Recruitment {15}

Participants will be invited to participate in the study through social media sites (e.g., Facebook and Instagram), paper and digital flyers, websites, and online news sources from the University of Hartford. After selecting the participants, a subjective interview will be conducted to assess the sample eligibility.

Assignment of interventions: allocation

Sequence generation {16a}.

The participant will receive TENS with active TaVNS or placebo TaVNS based on randomization via the website (randomization.com). Participants will then receive the other treatment in the following session (Fig. 3 ).

Flow chart indicating crossover study design. Subjects will be randomly assigned to the active or placebo transcutaneous auricular vagus nerve stimulation group for the first session, followed by a weeklong washout period. Subjects will then return and receive the other treatment for their second session. TENS, transcutaneous electrical nerve stimulation; TaVNS, transcutaneous auricular vagus nerve stimulation

Concealment mechanism {16b}

Concealment of the treatment order will be achieved using sequential numbering in sealed opaque envelopes, which will be stored in a secure cabinet and only be opened before the first session by the researcher responsible for the application of the TENS and TaVNS treatments.

Implementation {16c}

An independent researcher with no other role in this study will perform the randomization.

Assignment of interventions: blinding

Who will be blinded {17a}.

The evaluator, participants, and data analysts will be blinded to the randomization and intervention processes. The researchers responsible for the TaVNS treatment cannot be blinded due to the nature of the interventions.

Procedure for unblinding if needed {17b}

The outcome evaluator and data analysts will not be allowed to unblock the blinding. However, the researcher responsible for applying the treatments will not be blinded.

Data collection and management

Plans for assessment and collection of outcomes {18a}.

All researchers, including the person responsible for the interventions and the outcome evaluator, will undergo training before the experiment. Intra-examiner and inter-examiner reliability will be estimated for the pressure pain threshold by calculation of the intraclass correlation coefficient (ICC). All data will be anonymized and stored in a folder on the institutional One Drive cloud. Only the study team will have access to this study folder.

Plans to promote participant retention and complete follow-up {18b}

The researchers will be in weekly contact with the study participants. Twenty-four hours before treatment sessions, a researcher will send text messages or emails to remind participants of the treatment date and time. This procedure will ensure that participants receive the necessary attention and will assist in fully accompanying them during the research. If any subject fails to attend the appointment, the researchers will immediately call to inquire about the reasons for the no-show. If participants abandon the trial, the reasons will be recorded, the most recent data will be compiled, and analysis will be performed using the intention-to-treat principle.

Data management {19}

All the data will be collected weekly and stored on a secure computer server, with personal login access authorized by the principal investigator of the present study. All data collected in this trial will be restricted to the principal investigator and specific research team members.

Confidentiality {27}

The information collected will remain anonymous; participants will be assigned a participant number for identification purposes. The data will be stored on the institutional One Drive of the University of Hartford which only the research team can access.

Plans for collection, laboratory evaluation, and storage of biological specimens for genetic or molecular analysis in this trial/future use {33}

Statistical methods, statistical methods for primary and secondary outcomes {20a}.

An assessor blinded to the randomization and assessment processes will perform the data analysis. Descriptive statistics will be generated for all variables. The differences between the averages of the PPT and HPT scores between the baseline and the other moments (15, 30, and 15 min after the current is switched off) of each group will be used for the analysis. Normality will be evaluated using the Shapiro–Wilk test. Parametric and nonparametric analyses will be used for normally and non-normally distributed data, respectively. These analyses will be performed using the IBM SPSS Statistics v.28 statistical software (SPSS, Inc., IL, USA). Statistical significance will be considered at p < 0.05.

Interim analyses {21b}

No interim analyses were planned.

Methods for additional analyses (e.g., subgroup analyses) {20b}

Currently, there is no planned additional subgroup or adjusted analyses.

Methods in analysis to handle protocol non-adherence and any statistical methods to handle missing data {20c}

The intention-to-treat analysis will be used, and the missing data will be handled appropriately following established guidelines.

Plans to give access to the full protocol, participant-level data, and statistical code {31c}

Any data required to support the protocol can be supplied on reasonable request to the corresponding author to promote study transparency. However, only de-identified datasets will be supplied.

Oversight and monitoring

Composition of the coordinating center and trial steering committee {5d}.

The trial steering committee contains seven members: one principal investigator and six co-investigators. The duties that each member upholds are effective management of the trial and monitoring the study’s ongoing process. The committee also has the authority to consider and agree on modifications regarding this study’s protocol. The trial management committee has six co-investigators, who are doctoral physical therapy students, and one independent primary investigator. The management committee is responsible for planning day-to-day management for the trial. As a group, they are to monitor all aspects involving the conduct and progress of the trial, engage in the patient recruitment process, and ensure the protocol is adhered to. All members must take appropriate action to safeguard participants and the trial’s quality. The independent primary investigator will be responsible for generating the allocation sequences of the randomization. Meetings are held weekly.

Composition of the data monitoring committee, its role and reporting structure {21a}

We will conduct the study without a Data Monitoring Committee. The principal investigator will organize and monitor the data obtained in this research project.

Adverse event reporting and harms {22}

All participants will be carefully evaluated after each session, and all adverse events related to treatments will be reported, if any. The adverse events of this study will be classified by the evaluator according to their severity as mild, moderate, or severe.

Frequency and plans for auditing trial conduct {23}

The principal investigator will permit study-related audits, and inspections by the IRB and applicable granting agencies or regulatory bodies, including access to all study-related documents.

Plans for communicating important protocol amendments to relevant parties (e.g. trial participants, ethical committees) {25}

Any changes to the protocol will be reported to the IRB of the University of Hartford for approval.

Dissemination plans {31a}

This trial’s results will be presented at scientific conferences and published in a peer-reviewed medical journal.

TENS is a non-invasive modality used by healthcare professionals to produce analgesic effects in people experiencing acute and chronic pain. Varying frequencies of TENS activate different opioid receptors which produces hypoalgesic effects. TaVNS has been demonstrated to modulate pain through its stimulation of serotonergic and endorphinergic analgesic pathways. TENS and TaVNS activate similar pathways to produce hypoalgesic effects, however, the effect on pain perception with the combination of TENS and TaVNS has not been studied.

In this trial, we will examine the effects of maximal tolerable TENS and TaVNS on pain threshold in pain-free subjects. This will be measured using pressure-pain and heat-pain thresholds in participants without pain. We hypothesize that the combined effect of TENS and TaVNS on pain threshold will be greater than that of just TENS without TaVNS. This increase in pain threshold should occur immediately after TaVNS application, which distinguishes it from the outcomes of groups receiving the placebo intervention.

Trial status

The study protocol was approved by the IRB of the University of Hartford on January 25, 2024 (Prot. n. 24–01-281). This study was registered at ClinicalTrials.gov on April 4, 2024, with registration number NCT06361381. Recruitment of participants will start in May 2024 and is expected to be completed in August 2024.

Availability of data and materials {29}

The datasets used and/or analyzed will be available from the corresponding author upon reasonable request after the study is complete.

Abbreviations

Connecticut

Heat pain threshold

Pressure pain threshold

Intraclass correlation coefficient

Institutional Review Board

Transcutaneous auricular vagus nerve stimulation

Transcutaneous electrical nerve stimulation

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Richard E. Liebano, Noura Awad, Christopher Bellino, Katherine Bray, Heidi Rosentrater, Joshua Roy & Camryn Tate

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Richard Liebano was responsible for the initial conception of the trial. Richard Liebano, Noura Awad, Christopher Bellino, Katherine Bray, Heidi Rosentrater, Joshua Roy, and Camryn Tate contributed to the study design. Richard Liebano, Noura Awad, Christopher Bellino, Katherine Bray, Heidi Rosentrater, Joshua Roy, and Camryn Tate revised the manuscript. All authors have given final approval of the version to be published.

Corresponding author

Correspondence to Richard E. Liebano .

Ethics declarations

Ethics approval and consent to participate {24}.

This trial has been approved by the institutional review board of the University of Hartford, and consent for participation in the trial will be obtained from all participants.

Consent for publication {32}

Not applicable: no identifying images or other personal or clinical details of participants are presented here nor will be presented in reports of the trial results.

Competing interests {28}

The authors declare that they have no competing interests.

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Liebano, R.E., Awad, N., Bellino, C. et al. The combined effect of transcutaneous electrical nerve stimulation and transcutaneous auricular vagus nerve stimulation on pressure and heat pain thresholds in pain-free subjects: a randomized cross-over trial. Trials 25 , 516 (2024). https://doi.org/10.1186/s13063-024-08352-x

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Pressure pain

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The Use and Reporting of the Cross-Over Study Design in Clinical Trials and Systematic Reviews: A Systematic Assessment

Sarah jane nolan.

1 Department of Biostatistics, University of Liverpool, Liverpool, United Kingdom

2 Cochrane Cystic Fibrosis and Genetic Disorders Group, Liverpool, United Kingdom

Ian Hambleton

3 Chronic Disease Research Centre, The University of the West Indies, Barbados, West Indies

4 Cochrane Editorial Unit, London, United Kingdom

Conceived and designed the experiments: KD. Analyzed the data: SJN KD. Wrote the paper: SJN IH KD.

Associated Data

All relevant data are within the paper and its Supporting Information files. The data underlying S1 Table is available on Figshare: https://dx.doi.org/10.6084/m9.figshare.3466946.v2 .

Methodology

We performed data extraction of methodology and reporting in reviews, trials identified and trials included within reviews.

Principal Findings

Conclusions

Introduction

Selection of reviews and cross-over trials

Data extraction and presentation of results

Results of assessments at review and trial level are summarised narratively. Frequency data are presented as numbers and percentages.

See Fig 1 for flow diagram of selection of reviews and cross-over trials, S1 File for reference list of included Cochrane CFGD reviews and S2 File for reference list of included cross-over trials.

An external file that holds a picture, illustration, etc.
Object name is pone.0159014.g001.jpg

Systematic review methods

Table 1 and Fig 2 summarise the methods planned and the methods used in CFGD reviews for the inclusion of cross-over data.

An external file that holds a picture, illustration, etc.
Object name is pone.0159014.g002.jpg

Methods planned compared to methods used for and the inclusion of results from cross-over (CO) trials in meta-analysis for 53 reviews.

Methods described for the inclusion of cross-over (CO) trials in reviews	CO trials eligible (n = 102)	CO trials included (n = 53)
Describes “Three stages of Elbourne” approach [ ]	17 (17%)	8 (15%)
Use paired analyses (First stage of Elbourne)	16 (16%)	11 (21%)
Use generic inverse variance (GIV) meta-analysis (paired analysis)	6 (6%)	4 (7%)
Marginal probabilities of success method [ ] (paired analysis)	3 (3%)	1 (2%)
Include first period data only (Second stage of Elbourne)	18 (17%)	10 (19%)
Analyse as a parallel trial (Third stage of Elbourne)	4 (4%)	4 (7%)
Refers to "Elbourne," no specific details of methods.	20 (19%)	12 (23%)
Include narratively in the review only	1 (1%)	1 (2%)
Consult a statistician	1 (1%)	1 (2%)
No methods stated	14 (14%)	1 (2%)
Consult the Cochrane Handbook	1 (1%)	0 (0%)
“Depends on study”	1 (1%)	0 (0%)

:
Included narratively in the review		15 (28%)
Analysed as a parallel trial		8 (15%)
Included first period data only		6 (11%)
Paired analyses (analysed by GIV meta-analysis)		5 (9%)
Paired analyses (data provided from trialist)		2 (4%)
First period (data provided from trialist)		1 (2%)
:
Included narratively / analysed as a parallel trial		9 (17%)
First period only / analysed as parallel / Included narratively		5 (9%)
Paired analyses / first period only / analysed as parallel / Included narratively		2 (4%)

NA—No specific analysis method described		2 (4%)
No—A method of paired analysis was described but data was analysed as parallel or data was included narratively		24 (45%)
Yes—for some of the studies / outcomes included in the review		5 (9%)
Yes—but were provided with extra data from trial authors		3 (6%)
Yes—specified three stages of Elbourne [ ] and analysed data as parallel (third stage)		6 (11%)
Yes—method of including CO trial data used as described		13 (25%)

Legend: Methods planned compared to methods used for and the inclusion of results from cross-over (CO) trials in meta-analysis.

a See Introduction for further details.

Cross-over trial reporting

Table 2 , Fig 3 and Fig 4 summarise the characteristics, analysis details and presentation of the results in the 218 cross-over studies.

An external file that holds a picture, illustration, etc.
Object name is pone.0159014.g003.jpg

Analysis and reporting of results in 218 cross-over trials, and the incorporation of results in 53 systematic reviews.

An external file that holds a picture, illustration, etc.
Object name is pone.0159014.g004.jpg

How many cross-over trials could be been included in meta-analysis?

Trial design and characteristics (n = 218)

AB/ BA design (i.e. randomised to one of two interventions and then order reversed)	157 (72%)
More than two arms in a randomised order	44 (20%)
Other design	14 (7%)
Unclear	3 (1%)

Used	60 (27%)
Not used	28 (13%)
Not mentioned	119 (55%)
Unclear	11 (5%)
?
Not mentioned	203 (93%)
Control within-participant variability (participant acts as own control)	6 (3%)
States the measurement of participant preference is an objective	6 (3%)
Increase the statistical power of a small sample size (rare condition)	3 (1%)
?
Yes	42 (19%)
No	176 (81%)
?
No calculation specified	177 (81%)
The study is a pilot or exploratory so a sample size calculation is not necessary	6 (3%)
Sample size calculation described but no allowance for cross-over design	27 (12%)
Sample size calculation allows for paired / cross-over design	8 (4%)


Not mentioned	169 (77%)
Text regarding carry-over effect but no statistical test performed:	21 (10%)





Carry-over effect described as "significant" or "non-significant effect" but not stated which statistical test was used	9 (4%)
Statistical test for carry-over specified:	19 (9%)

]





Not mentioned	170 (78%)
Text regarding period effect but no statistical test performed:	9 (4%)




Period effect described as "significant" or "non-significant effect" but not stated which statistical test was used:	12 (6%)



Statistical test for period effect specified:	27 (12%)

]




:	27 (12%)



?
No statistical methods described	35 (16%)
Statistical methods not clear:	10 (4%)
,

,
Statistical analysis not appropriate:	23 (11%)




Analysis appropriate for paired design:	150 (69%)


]

]



]
]
?
Yes	69 (32%)
No	44 (20%)
Unclear if any participants have been excluded from analysis	105 (48%)
?
Yes	13 (6%)
No	205 (94%)

Published results could be included in meta-analysis	56 (26%)




Results for some outcomes could be included in meta-analysis	13 (6%)
,
,
,
Published results could not be included in meta-analysis accounting for cross-over design.	149 (68%)
. , ,

ANOVA: Analysis of variance, ANCOVA: Analysis of covariance

a Examples of other designs: participants received at least one of the interventions more than once (e.g. two treatment periods of each intervention).

b Examples of unclear designs: unclear how interventions were allocated or when cross-over occurred.

c Unclear washout period: for example, a gap between treatments is described (e.g. interventions were given on consecutive days) but unclear if this was intended to be a washout period.

d Statistical analyses considered appropriate a priori are described in S1 Table . Other methods considered on a case by case basis

e Statistical analysis section describes as mixture of paired and unpaired tests; e.g paired t-test if data is normally distributed and Wilcoxon Rank Sum test (not paired) if data is skewed.

f Non-parametric equivalent of repeated measures ANOVA.

g Data could be included in meta-analysis if results adjusted for the paired design could be extracted (e.g. mean difference and standard error (SE) of mean difference) or calculated (e.g. from individual participant data presented, from estimation of SE from exact p value reported or from correlation coefficient between treatment groups) or if data was presented by treatment period or first period only.

How cross-over trials were included in systematic reviews

S2 Table , Fig 3 and Fig 4 summarise reporting of cross-over trial data in publications and how published results were included in the CFGD reviews.

Statement of principal findings

Strengths and limitations of the study

The strength of this study is the systematic, detailed assessment of all published reviews of a Cochrane Review Group and all cross-over trials within them.

Comparison to other studies

Recommendations and future research

Supporting Information

Reference list of 142 Cochrane Cystic Fibrosis and Genetic Disorders reviews published to July 2015.

Reference list of 218 unique cross-over trials included in Cochrane Cystic Fibrosis and Genetic Disorders reviews published to July 2015.

List of information extracted at the review level and at the study level.

Inclusion of cross-over trials for the primary outcomes (PO) of reviews of the Cochrane Cystic Fibrosis and Genetic Disorders Group.

Acknowledgments

The authors would like to thank the authors of all included Cochrane CFGD group authors for further information on their reviews and the Cochrane CFGD group editorial team for their support.

Funding Statement

The time of SJN and KD was partly supported by the National Institute for Health Research, via Cochrane Infrastructure funding to the Cochrane Cystic Fibrosis and Genetic Disorders Group [ http://www.nihr.ac.uk/research/systematic-reviews.htm ], [ http://cfgd.cochrane.org/funding-and-support ]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. IH received no specific funding for this work.

Data Availability

COMMENTS

Design, analysis, and presentation of crossover trials
Objective: Although crossover trials enjoy wide use, standards for analysis and reporting have not been established. We reviewed methodological aspects and quality of reporting in a representative sample of published crossover trials. Methods: We searched MEDLINE for December 2000 and identified all randomized crossover trials. We abstracted data independently, in duplicate, on 14 design ...
Design, analysis, and presentation of crossover trials
Although crossover trials enjoy wide use, standards for analysis and reporting have not been established. We reviewed methodological aspects and quality of reporting in a representative sample of published crossover trials. We searched MEDLINE for December 2000 and identified all randomized crossover trials. We abstracted data independently, in duplicate, on 14 design criteria, 13 analysis ...
Design, analysis, and presentation of crossover trials
Only 29% presented CIs or SE so that data could be entered into a meta-analysis. Reports of crossover trials frequently omit important methodological issues in design, analysis, and presentation ...
Design, analysis, and presentation of crossover trials
Reports of crossover trials frequently omit important methodological issues in design, analysis, and presentation, which might improve the conduct and reporting of studies using this important trial design. ObjectiveAlthough crossover trials enjoy wide use, standards for analysis and reporting have not been established. We reviewed methodological aspects and quality of reporting in a ...
Design, Analysis, and Reporting of Crossover Trials for ...
Results. We identified 83 crossover trials eligible for inclusion. Issues affecting the risk of bias in crossover trials, such as carryover, period effects and missing data, were often ignored. Some trials failed to accommodate the within-individual differences in the analysis. For a large proportion of the trials, the authors tabulated the ...
Design, analysis, and presentation of crossover trials
Conclusion: Reports of crossover trials frequently omit important methodological issues in design, analysis, and presentation. Guidelines for the conduct and reporting of crossover trials might improve the conduct and reporting of studies using this important trial design. {\textcopyright} 2009 Mills et al; licensee BioMed Central Ltd.",
Design and analysis of crossover trials for ...
1. Introduction. In a randomized controlled trial, each study subject is randomized to receive an investigational treatment. Such designs of clinical trials are fundamental in clinical research [1].A crossover clinical trial, however, is designed such that each subject receives a sequence of investigational treatments, typically with the aim to compare the effects of these treatments, not the ...
Considerations for crossover design in clinical study
In a crossover study design, two or more treatments (e.g., drugs, procedures) are provided to subjects at different time periods, and the sequence of treatments is randomized for each subject. This design is applied to several fields such as bioequivalence clinical trials, and the simplest study design is a two-period, two-sequence crossover ...
15 Design and Analysis of Cross-Over Trials
Abstract. This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA.
On the Proper Use of the Crossover Design in Clinical Trials
Correct procedure for statistical analysis. The formal structure of a crossover trial for comparison of two treatments A and B is shown in Figure 1 (where A is placebo and B is CT-3). The two phases that each patient has to complete in the course of the trial are usually referred to as the two study periods ([], p. 79).The efficacy of A and B is assessed on the basis of the within-subject ...
Design, analysis, and presentation of crossover trials
Reports of crossover trials frequently omit important methodological issues in design, analysis, and presentation. Guidelines for the conduct and reporting of crossover trials might improve the conduct and reporting of studies using this important trial design. ... We defined randomized crossover trials as studies where an individual receives ...
The Use and Reporting of the Cross-Over Study Design in Clinical Trials
At the trial level, the analysis and presentation of results were often inappropriate or unclear, with only 69 (32%) trials presenting results that could be included in meta-analysis. ... Lehmacher W. Analysis of the crossover design in the presence of residual effects. Stat Med 1991; 10(6): 891-899. pmid:1876779 . View Article
Design and Analysis of Cross-Over Trials
The first edition of Design and Analysis of Cross-Over Trials quickly became the standard reference on the subject and has remained so for more than 12 years. In that time, however, the use of cross-over trials has grown rapidly, particularly in the pharmaceutical arena, and researchers have made a number of advances in both the theory and methods
PDF Design and Analysis of Cross-Over Trials (3rd ed.). Byron Jones and
Chapter 4 employs the R package Crossover, which was specifically developed to accompany this book, to facilitate the design of cross-over trials. The package Crossover pro vides a graphical user interface (GUI) and can calculate the efficiencies and variances of a design that is either user-defined or selected from a built-in (and expanding ...
Design and Analysis of Cross-Over Trials
B. Jones, M. Kenward. Published 1 June 1989. Mathematics. Abstract This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA.
Design, Analysis, and Presentation of Crossover Trials
Objective:Although crossover trials enjoy wide use, standards for analysis and reporting have notbeen established. We reviewed methodological aspects and quality of reporting in a representativesample of published crossover trials.Methods:We searched MEDLINE for December 2000 and identified all randomized crossovertrials. We abstracted data independently, in duplicate, on 14 design criteria ...
Design, Analysis, and Reporting of Crossover Trials for Inclusion in a
Illustration of the design and analysis of a crossover trial. Carryover effect: If A is an active intervention and B is a placebo, then the BA sequence is unlikely to be affected by a carryover ...
Design, Analysis, and Reporting of Crossover Trials for Inclusion in a
Objective: To evaluate the characteristics of the design, analysis, and reporting of crossover trials for inclusion in a meta-analysis of treatment for primary open-angle glaucoma and to provide empirical evidence to inform the development of tools to assess the validity of the results from crossover trials and reporting guidelines. Methods: We searched MEDLINE, EMBASE, and Cochrane's CENTRAL ...
Design and Analysis of Cross-Over Trials
ABSTRACT. Design and Analysis of Cross-Over Trials is concerned with a specific kind of comparative trial known as the cross-over trial, in which subjects receive different sequences of treatments. Such trials are widely used in clinical and medical research, and in other diverse areas such as veterinary science, psychology, sports science, and ...
Crossover Trials: Design and Analysis
References Senn S. (2002) Crossover trials in clinical research. Chichester, John Wiley Mills JM, Chan A-W, Wu P, Vail A, Guyatt GH, Altman DG. Design, analysis and presentation of crossover trials. BMC Trials 2009; 10: 27 Schouten H and Kester A. A simple analysis of a simp[le crossover trial with a dichotomous outcome measure.
Design, analysis, and presentation of crossover trials
Study cohort. Our study is nested within a larger analysis of RCTs [] where we used an extended version of the Cochrane search strategy (phase 1) to identify all randomized trials published in December 2000 and indexed on PubMed by July 2002 [].A randomized trial was defined as a prospective study assessing health-care interventions in human participants who were randomly allocated to study ...
Design, Analysis, and Reporting of Crossover Trials for Inclusion in a
Illustration of the design and analysis of a crossover trial. Carryover effect: If A is an active intervention and B is a placebo, then the BA sequence is unlikely to be affected by a carryover effect, but the AB sequence is potentially susceptible.In the AB sequence, when some effect of the active intervention A is carried over to the second period, placebo could demonstrate artificial ...
The combined effect of transcutaneous electrical nerve stimulation and
The study will be a simple crossover design conducted at the University of Hartford. Subjects will be recruited from the University of Hartford population via oral communication, digital flyers, and posters on campus. Thirty participants will undergo two sessions in a crossover manner with one week in between.
Design and analysis of crossover trials for investigating high-risk
In these applications, the sponsors design crossover clinical trials for the purpose of demonstrating the safety and effectiveness of an investigational device. In this article, we reviewed the crossover clinical trials reported in the premarket approvals (PMA) [ 5, 6] of high-risk medical devices in a period of 14 years from 2005 to 2018.
The Use and Reporting of the Cross-Over Study Design in Clinical Trials
The poor reporting of cross-over trials in this assessment broadly agrees with the work of Mills et al , which considered all cross-over trials published within an 18 month period and concluded that cross-over trials "frequently omit important methodological issues in design, analysis, and presentation.

The Use and Reporting of the Cross-Over Study Design in Clinical Trials and Systematic Reviews: A Systematic Assessment

Methodology

Principal Findings

Conclusions

Introduction

Selection of reviews and cross-over trials

Data extraction and presentation of results

Systematic review methods

Cross-over trial reporting

How cross-over trials were included in systematic reviews

Statement of principal findings

Strengths and limitations of the study

Comparison to other studies

Recommendations and future research

Supporting Information

S2 File. Cross-over trials included in Cochrane Cystic Fibrosis and Genetic Disorders Group reviews.

S1 Table. Data items extracted.

S2 Table. Inclusion of cross-over data in Cochrane Reviews.

Acknowledgments

Author Contributions

Design and Analysis of Cross-Over Trials

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CrossOver: an algorithm for the construction of efficient cross‐over designs

Design, Analysis, and Presentation of Crossover Trials

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Design, Analysis, and Reporting of Crossover Trials for Inclusion in a Meta-Analysis

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TABLE OF CONTENTS

Crossover Trials: Design and Analysis

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Introduction &amp; Flood Hydrologic Analysis

From Syllabus Design to Curriculum Design

Design and Analysis of Large Scale Log Studies A CHI 2011 course v11

Three Dimensional Static and Dynamic Analysis and Design of Buildings

Object-oriented Analysis and Design

Adaptive Design Methods in Clinical Trials

Systems Analysis and Design

Design and Analysis of Multi-Factored Experiments

Unresolved Issues in the Globalization of Clinical Trials

Design and Analysis of a Spiral Bevel Gear

Algorithm Design and Analysis (ADA)

Systems Analysis and Design : Project Planning

PRELIMINARY DESIGN REVIEW

OBJECT ORIENTED ANALYSIS AND DESIGN

Object-Oriented Analysis and Design

Object Oriented Analysis and Design using UML

Object-Oriented Analysis and Design with UML2 and Rational Software Modeler

Primer Design &amp; Restriction Analysis 2 nd April 2014

Chapter 5 Object Oriented Design

Primer Design &amp; Restriction Analysis 10 th April 2013

The combined effect of transcutaneous electrical nerve stimulation and transcutaneous auricular vagus nerve stimulation on pressure and heat pain thresholds in pain-free subjects: a randomized cross-over trial

Methods/design

Trial registration

Administrative information

Introduction

Objectives {7}

Trial design {8}

Methods: participants, interventions, and outcomes

Eligibility criteria {10}

Inclusion criteria

Exclusion criteria

Who will take informed consent? {26a}

Additional consent provisions for collection and use of participant data and biological specimens {26b}

Interventions

Intervention description {11a}

TENS parameters

TaVNS electrode placement

Active TaVNS

Placebo TaVNS

Criteria for discontinuing or modifying allocated interventions {11b}

Introduction & Flood Hydrologic Analysis

Primer Design & Restriction Analysis 2 nd April 2014

Primer Design & Restriction Analysis 10 th April 2013