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Background Re-randomisation trials involve re-enrolling and re-randomising patients for each new treatment episode they experience. They are often used when interest lies in the average effect of an intervention across all the episodes for which it would be used in practice. Re-randomisation trials are often analysed using independence estimators, where a working independence correlation structure is used. However, research into independence estimators in the context of re-randomisation has been limited. Methods We performed a simulation study to evaluate the use of independence estimators in re-randomisation trials. We focussed on a continuous outcome, and the setting where treatment allocation does not affect occurrence of subsequent episodes. We evaluated different treatment effect mechanisms (e.g. by allowing the treatment effect to vary across episodes, or to become less effective on re-use, etc), and different non-enrolment mechanisms (e.g. where patients who experience a poor outcome are less likely to re-enrol for their second episode). We evaluated four different independence estimators, each corresponding to a different estimand (per-episode and per-patient approaches, and added-benefit and policy-benefit approaches). Results We found that independence estimators were unbiased for the per-episode added-benefit estimand in all scenarios we considered. We found independence estimators targeting other estimands (per-patient or policy-benefit) were unbiased, except when there was differential non-enrolment between treatment groups (i.e. when different types of patients from each treatment group decide to re-enrol for subsequent episodes). We found the use of robust standard errors provided close to nominal coverage in all settings where the estimator was unbiased. Conclusions Careful choice of estimand can ensure re-randomisation trials are addressing clinically relevant questions. Independence estimators are a useful approach, and should be considered as the default estimator until the statistical properties of alternative estimators are thoroughly evaluated.

Background\ud \ud Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy.\ud \ud \ud Methods\ud \ud We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets.\ud \ud \ud Results\ud \ud Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall.\ud \ud \ud Conclusions\ud \ud For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt.

Background Recruitment to clinical trials is often problematic, with many trials failing to recruit to their target sample size. As a result, patient care may be based on suboptimal evidence from underpowered trials or non-randomised studies. Methods For many conditions patients will require treatment on several occasions, for example, to treat symptoms of an underlying chronic condition (such as migraines, where treatment is required each time a new episode occurs), or until they achieve treatment success (such as fertility, where patients undergo treatment on multiple occasions until they become pregnant). We describe a re-randomisation design for these scenarios, which allows each patient to be independently randomised on multiple occasions. We discuss the circumstances in which this design can be used. Results The re-randomisation design will give asymptotically unbiased estimates of treatment effect and correct type I error rates under the following conditions: (a) patients are only re-randomised after the follow-up period from their previous randomisation is complete; (b) randomisations for the same patient are performed independently; and (c) the treatment effect is constant across all randomisations. Provided the analysis accounts for correlation between observations from the same patient, this design will typically have higher power than a parallel group trial with an equivalent number of observations. Conclusions If used appropriately, the re-randomisation design can increase the recruitment rate for clinical trials while still providing an unbiased estimate of treatment effect and correct type I error rates. In many situations, it can increase the power compared to a parallel group design with an equivalent number of observations. Electronic supplementary material The online version of this article (doi:10.1186/s12874-015-0082-2) contains supplementary material, which is available to authorized users.

Background Sensitivity analyses are an important tool for understanding the extent to which the results of randomised trials depend upon the assumptions of the analysis. There is currently no guidance governing the choice of sensitivity analyses. Discussion We provide a principled approach to choosing sensitivity analyses through the consideration of the following questions: 1) Does the proposed sensitivity analysis address the same question as the primary analysis? 2) Is it possible for the proposed sensitivity analysis to return a different result to the primary analysis? 3) If the results do differ, is there any uncertainty as to which will be believed? Answering all of these questions in the affirmative will help researchers to identify relevant sensitivity analyses. Treating analyses as sensitivity analyses when one or more of the answers are negative can be misleading and confuse the interpretation of studies. The value of these questions is illustrated with several examples. Summary By removing unreasonable analyses that might have been performed, these questions will lead to relevant sensitivity analyses, which help to assess the robustness of trial results.

Background When multiple prognostic factors are adjusted for in the analysis of a randomised trial, it is unclear (1) whether it is necessary to account for each of the strata, formed by all combinations of the prognostic factors (stratified analysis), when randomisation has been balanced within each stratum (stratified randomisation), or whether adjusting for the main effects alone will suffice, and (2) the best method of adjustment in terms of type I error rate and power, irrespective of the randomisation method. Methods We used simulation to (1) determine if a stratified analysis is necessary after stratified randomisation, and (2) to compare different methods of adjustment in terms of power and type I error rate. We considered the following methods of analysis: adjusting for covariates in a regression model, adjusting for each stratum using either fixed or random effects, and Mantel-Haenszel or a stratified Cox model depending on outcome. Results Stratified analysis is required after stratified randomisation to maintain correct type I error rates when (a) there are strong interactions between prognostic factors, and (b) there are approximately equal number of patients in each stratum. However, simulations based on real trial data found that type I error rates were unaffected by the method of analysis (stratified vs unstratified), indicating these conditions were not met in real datasets. Comparison of different analysis methods found that with small sample sizes and a binary or time-to-event outcome, most analysis methods lead to either inflated type I error rates or a reduction in power; the lone exception was a stratified analysis using random effects for strata, which gave nominal type I error rates and adequate power. Conclusions It is unlikely that a stratified analysis is necessary after stratified randomisation except in extreme scenarios. Therefore, the method of analysis (accounting for the strata, or adjusting only for the covariates) will not generally need to depend on the method of randomisation used. Most methods of analysis work well with large sample sizes, however treating strata as random effects should be the analysis method of choice with binary or time-to-event outcomes and a small sample size.

Background It is often desirable to account for centre-effects in the analysis of multicentre randomised trials, however it is unclear which analysis methods are best in trials with a binary outcome. Methods We compared the performance of four methods of analysis (fixed-effects models, random-effects models, generalised estimating equations (GEE), and Mantel-Haenszel) using a re-analysis of a previously reported randomised trial (MIST2) and a large simulation study. Results The re-analysis of MIST2 found that fixed-effects and Mantel-Haenszel led to many patients being dropped from the analysis due to over-stratification (up to 69% dropped for Mantel-Haenszel, and up to 33% dropped for fixed-effects). Conversely, random-effects and GEE included all patients in the analysis, however GEE did not reach convergence. Estimated treatment effects and p-values were highly variable across different analysis methods. The simulation study found that most methods of analysis performed well with a small number of centres. With a large number of centres, fixed-effects led to biased estimates and inflated type I error rates in many situations, and Mantel-Haenszel lost power compared to other analysis methods in some situations. Conversely, both random-effects and GEE gave nominal type I error rates and good power across all scenarios, and were usually as good as or better than either fixed-effects or Mantel-Haenszel. However, this was only true for GEEs with non-robust standard errors (SEs); using a robust ‘sandwich’ estimator led to inflated type I error rates across most scenarios. Conclusions With a small number of centres, we recommend the use of fixed-effects, random-effects, or GEE with non-robust SEs. Random-effects and GEE with non-robust SEs should be used with a moderate or large number of centres.

Background Recent reviews have shown that while clustering is extremely common in individually randomised trials (for example, clustering within centre, therapist, or surgeon), it is rarely accounted for in the trial analysis. Our aim is to develop a general framework for assessing whether potential sources of clustering must be accounted for in the trial analysis to obtain valid type I error rates (non-ignorable clustering), with a particular focus on individually randomised trials. Methods A general framework for assessing clustering is developed based on theoretical results and a case study of a recently published trial is used to illustrate the concepts. A simulation study is used to explore the impact of not accounting for non-ignorable clustering in practice. Results Clustering is non-ignorable when there is both correlation between patient outcomes within clusters, and correlation between treatment assignments within clusters. This occurs when the intraclass correlation coefficient is non-zero, and when the cluster has been used in the randomisation process (e.g. stratified blocks within centre) or when patients are assigned to clusters after randomisation with different probabilities (e.g. a surgery trial in which surgeons treat patients in only one arm). A case study of an individually randomised trial found multiple sources of clustering, including centre of recruitment, attending surgeon, and site of rehabilitation class. Simulations show that failure to account for non-ignorable clustering in trial analyses can lead to type I error rates over 20% in certain cases; conversely, adjusting for the clustering in the trial analysis gave correct type I error rates. Conclusions Clustering is common in individually randomised trials. Trialists should assess potential sources of clustering during the planning stages of a trial, and account for any sources of non-ignorable clustering in the trial analysis.