Categorisation of continuous covariates for stratified randomisation: How should we adjust?

To obtain valid inference following stratified randomisation, treatment effects should be estimated with adjustment for stratification variables. Stratification sometimes requires categorisation of a continuous prognostic variable (eg, age), which raises the question: should adjustment be based on randomisation categories or underlying continuous values? In practice, adjustment for randomisation categories is more common. We reviewed trials published in general medical journals and found none of the 32 trials that stratified randomisation based on a continuous variable adjusted for continuous values in the primary analysis. Using data simulation, this article evaluates the performance of different adjustment strategies for continuous and binary outcomes where the covariate-outcome relationship (via the link function) was either linear or non-linear. Given the utility of covariate adjustment for addressing missing data, we also considered settings with complete or missing outcome data. Analysis methods included linear or logistic regression with no adjustment for the stratification variable, adjustment for randomisation categories, or adjustment for continuous values assuming a linear covariate-outcome relationship or allowing for non-linearity using fractional polynomials or restricted cubic splines. Unadjusted analysis performed poorly throughout. Adjustment approaches that misspecified the underlying covariate-outcome relationship were less powerful and, alarmingly, biased in settings where the stratification variable predicted missing outcome data. Adjustment for randomisation categories tends to involve the highest degree of misspecification, and so should be avoided in practice. To guard against misspecification, we recommend use of flexible approaches such as fractional polynomials and restricted cubic splines when adjusting for continuous stratification variables in randomised trials.

Reporting of Factorial Randomized Trials: Extension of the CONSORT 2010 Statement.

Importance: Transparent reporting of randomized trials is essential to facilitate critical appraisal and interpretation of results. Factorial trials, in which 2 or more interventions are assessed in the same set of participants, have unique methodological considerations. However, reporting of factorial trials is suboptimal. Objective: To develop a consensus-based extension to the Consolidated Standards of Reporting Trials (CONSORT) 2010 Statement for factorial trials. Design: Using the Enhancing the Quality and Transparency of Health Research (EQUATOR) methodological framework, the CONSORT extension for factorial trials was developed by (1) generating a list of reporting recommendations for factorial trials using a scoping review of methodological articles identified using a MEDLINE search (from inception to May 2019) and supplemented with relevant articles from the personal collections of the authors; (2) a 3-round Delphi survey between January and June 2022 to identify additional items and assess the importance of each item, completed by 104 panelists from 14 countries; and (3) a hybrid consensus meeting attended by 15 panelists to finalize the selection and wording of items for the checklist. Findings: This CONSORT extension for factorial trials modifies 16 of the 37 items in the CONSORT 2010 checklist and adds 1 new item. The rationale for the importance of each item is provided. Key recommendations are (1) the reason for using a factorial design should be reported, including whether an interaction is hypothesized, (2) the treatment groups that form the main comparisons should be clearly identified, and (3) for each main comparison, the estimated interaction effect and its precision should be reported. Conclusions and Relevance: This extension of the CONSORT 2010 Statement provides guidance on the reporting of factorial randomized trials and should facilitate greater understanding of and transparency in their reporting.

Consensus Statement for Protocols of Factorial Randomized Trials: Extension of the SPIRIT 2013 Statement.

Importance: Trial protocols outline a trial's objectives as well as the methods (design, conduct, and analysis) that will be used to meet those objectives, and transparent reporting of trial protocols ensures objectives are clear and facilitates appraisal regarding the suitability of study methods. Factorial trials, in which 2 or more interventions are assessed in the same set of participants, have unique methodological considerations. However, no extension of the Standard Protocol Items: Recommendations for Interventional Trials (SPIRIT) 2013 Statement, which provides guidance on reporting of trial protocols, for factorial trials is available. Objective: To develop a consensus-based extension to the SPIRIT 2013 Statement for factorial trials. Evidence Review: The SPIRIT extension for factorial trials was developed using the Enhancing the Quality and Transparency of Health Research (EQUATOR) methodological framework. First, a list of reporting recommendations was generated using a scoping review of methodological articles identified using a MEDLINE search (inception to May 2019), which was supplemented with relevant articles from the personal collections of the authors. Second, a 3-round Delphi survey (January to June 2022, completed by 104 panelists from 14 countries) was conducted to assess the importance of items and identify additional recommendations. Third, a hybrid consensus meeting was held, attended by 15 panelists to finalize selection and wording of the checklist. Findings: This SPIRIT extension for factorial trials modified 9 of the 33 items in the SPIRIT 2013 checklist. Key reporting recommendations were that the rationale for using a factorial design should be provided, including whether an interaction is hypothesized; the treatment groups that will form the main comparisons should be identified; and statistical methods for each main comparison should be provided, including how interactions will be assessed. Conclusions and Relevance: In this consensus statement, 9 factorial-specific items were provided that should be addressed in all protocols of factorial trials to increase the trial's utility and transparency.

Evaluating whether the proportional odds models to analyse ordinal outcomes in COVID-19 clinical trials is providing clinically interpretable treatment effects: A systematic review.

BACKGROUND: After an initial recommendation from the World Health Organisation, trials of patients hospitalised with COVID-19 often include an ordinal clinical status outcome, which comprises a series of ordered categorical variables, typically ranging from 'Alive and discharged from hospital' to 'Dead'. These ordinal outcomes are often analysed using a proportional odds model, which provides a common odds ratio as an overall measure of effect, which is generally interpreted as the odds ratio for being in a higher category. The common odds ratio relies on the assumption of proportional odds, which implies an identical odds ratio across all ordinal categories; however, there is generally no statistical or biological basis for which this assumption should hold; and when violated, the common odds ratio may be a biased representation of the odds ratios for particular categories within the ordinal outcome. In this study, we aimed to evaluate to what extent the common odds ratio in published COVID-19 trials differed to simple binary odds ratios for clinically important outcomes. METHODS: We conducted a systematic review of randomised trials evaluating interventions for patients hospitalised with COVID-19, which used a proportional odds model to analyse an ordinal clinical status outcome, published between January 2020 and May 2021. We assessed agreement between the common odds ratio and the odds ratio from a standard logistic regression model for three clinically important binary outcomes: 'Alive', 'Alive without mechanical ventilation', and 'Alive and discharged from hospital'. RESULTS: Sixteen randomised clinical trials, comprising 38 individual comparisons, were included in this study; of these, only 6 trials (38%) formally assessed the proportional odds assumption. The common odds ratio differed by more than 25% compared to the binary odds ratios in 55% of comparisons for the outcome 'Alive', 37% for 'Alive without mechanical ventilation', and 24% for 'Alive and discharged from hospital'. In addition, the common odds ratio systematically underestimated the odds ratio for the outcome 'Alive' by -16.8% (95% confidence interval: -28.7% to -2.9%, p = 0.02), though differences for the other outcomes were smaller and not statistically significant (-8.4% for 'Alive without mechanical ventilation' and 3.6% for 'Alive and discharged from hospital'). The common odds ratio was statistically significant for 18% of comparisons, while the binary odds ratio was significant in 5%, 16%, and 3% of comparisons for the outcomes 'Alive', 'Alive without mechanical ventilation', and 'Alive and discharged from hospital', respectively. CONCLUSION: The common odds ratio from proportional odds models often differs substantially to odds ratios from clinically important binary outcomes, and similar to composite outcomes, a beneficial common OR from a proportional odds model does not necessarily indicate a beneficial effect on the most important categories within the ordinal outcome.

Starting a conversation about estimands with public partners involved in clinical trials: a co-developed tool.

BACKGROUND: Clinical trials aim to draw conclusions about the effects of treatments, but a trial can address many different potential questions. For example, does the treatment work well for patients who take it as prescribed? Or does it work regardless of whether patients take it exactly as prescribed? Since different questions can lead to different conclusions on treatment benefit, it is important to clearly understand what treatment effect a trial aims to investigate-this is called the 'estimand'. Using estimands helps to ensure trials are designed and analysed to answer the questions of interest to different stakeholders, including patients and public. However, there is uncertainty about whether patients and public would like to be involved in defining estimands and how to do so. Public partners are patients and/or members of the public who are part of, or advise, the research team. We aimed to (i) co-develop a tool with public partners that helps explain what an estimand is and (ii) explore public partner's perspectives on the importance of discussing estimands during trial design. METHODS: An online consultation meeting was held with 5 public partners of mixed age, gender and ethnicities, from various regions of the UK. Public partner opinions were collected and a practical tool describing estimands, drafted before the meeting by the research team, was developed. Afterwards, the tool was refined, and additional feedback sought via email. RESULTS: Public partners want to be involved in estimand discussions. They found an introductory tool, to be presented and described to them by a researcher, helpful for starting a discussion about estimands in a trial design context. They recommended storytelling, analogies and visual aids within the tool. Four topics related to public partners' involvement in defining estimands were identified: (i) the importance of addressing questions that are relevant to patients and public in trials, (ii) involving public partners early on, (iii) a need for education and communication for all stakeholders and (iv) public partners and researchers working together. CONCLUSIONS: We co-developed a tool for researchers and public partners to use to facilitate the involvement of public partners in estimand discussions.

Informative cluster size in cluster-randomised trials: A case study from the TRIGGER trial.

BACKGROUND: Recent work has shown that cluster-randomised trials can estimate two distinct estimands: the participant-average and cluster-average treatment effects. These can differ when participant outcomes or the treatment effect depends on the cluster size (termed informative cluster size). In this case, estimators that target one estimand (such as the analysis of unweighted cluster-level summaries, which targets the cluster-average effect) may be biased for the other. Furthermore, commonly used estimators such as mixed-effects models or generalised estimating equations with an exchangeable correlation structure can be biased for both estimands. However, there has been little empirical research into whether informative cluster size is likely to occur in practice. METHOD: We re-analysed a cluster-randomised trial comparing two different thresholds for red blood cell transfusion in patients with acute upper gastrointestinal bleeding to explore whether estimates for the participant- and cluster-average effects differed, to provide empirical evidence for whether informative cluster size may be present. For each outcome, we first estimated a participant-average effect using independence estimating equations, which are unbiased under informative cluster size. We then compared this to two further methods: (1) a cluster-average effect estimated using either weighted independence estimating equations or unweighted cluster-level summaries, and (2) estimates from a mixed-effects model or generalised estimating equations with an exchangeable correlation structure. We then performed a small simulation study to evaluate whether observed differences between cluster- and participant-average estimates were likely to occur even if no informative cluster size was present. RESULTS: For most outcomes, treatment effect estimates from different methods were similar. However, differences of >10% occurred between participant- and cluster-average estimates for 5 of 17 outcomes (29%). We also observed several notable differences between estimates from mixed-effects models or generalised estimating equations with an exchangeable correlation structure and those based on independence estimating equations. For example, for the EQ-5D VAS score, the independence estimating equation estimate of the participant-average difference was 4.15 (95% confidence interval: -3.37 to 11.66), compared with 2.84 (95% confidence interval: -7.37 to 13.04) for the cluster-average independence estimating equation estimate, and 3.23 (95% confidence interval: -6.70 to 13.16) from a mixed-effects model. Similarly, for thromboembolic/ischaemic events, the independence estimating equation estimate for the participant-average odds ratio was 0.43 (95% confidence interval: 0.07 to 2.48), compared with 0.33 (95% confidence interval: 0.06 to 1.77) from the cluster-average estimator. CONCLUSION: In this re-analysis, we found that estimates from the various approaches could differ, which may be due to the presence of informative cluster size. Careful consideration of the estimand and the plausibility of assumptions underpinning each estimator can help ensure an appropriate analysis methods are used. Independence estimating equations and the analysis of cluster-level summaries (with appropriate weighting for each to correspond to either the participant-average or cluster-average treatment effect) are a desirable choice when informative cluster size is deemed possible, due to their unbiasedness in this setting.

Handling misclassified stratification variables in the analysis of randomised trials with continuous outcomes.

Many trials use stratified randomisation, where participants are randomised within strata defined by one or more baseline covariates. While it is important to adjust for stratification variables in the analysis, the appropriate method of adjustment is unclear when stratification variables are affected by misclassification and hence some participants are randomised in the incorrect stratum. We conducted a simulation study to compare methods of adjusting for stratification variables affected by misclassification in the analysis of continuous outcomes when all or only some stratification errors are discovered, and when the treatment effect or treatment-by-covariate interaction effect is of interest. The data were analysed using linear regression with no adjustment, adjustment for the strata used to perform the randomisation (randomisation strata), adjustment for the strata if all errors are corrected (true strata), and adjustment for the strata after some errors are discovered and corrected (updated strata). The unadjusted model performed poorly in all settings. Adjusting for the true strata was optimal, while the relative performance of adjusting for the randomisation strata or the updated strata varied depending on the setting. As the true strata are unlikely to be known with certainty in practice, we recommend using the updated strata for adjustment and performing subgroup analyses, provided the discovery of errors is unlikely to depend on treatment group, as expected in blinded trials. Greater transparency is needed in the reporting of stratification errors and how they were addressed in the analysis.

Fluid Optimisation in Emergency Laparotomy (FLO-ELA) Trial: study protocol for a multi-centre randomised trial of cardiac output-guided fluid therapy compared to usual care in patients undergoing major emergency gastrointestinal surgery.

INTRODUCTION: Postoperative morbidity and mortality in patients undergoing major emergency gastrointestinal surgery are a major burden on healthcare systems. Optimal management of perioperative intravenous fluids may reduce mortality rates and improve outcomes from surgery. Previous small trials of cardiac-output guided haemodynamic therapy algorithms in patients undergoing gastrointestinal surgery have suggested this intervention results in reduced complications and a modest reduction in mortality. However, this existing evidence is based mainly on elective (planned) surgery, with little evaluation in the emergency setting. There are fundamental clinical and pathophysiological differences between the planned and emergency surgical setting which may influence the effects of this intervention. A large definitive trial in emergency surgery is needed to confirm or refute the potential benefits observed in elective surgery and to inform widespread clinical practice. METHODS: The FLO-ELA trial is a multi-centre, parallel-group, open, randomised controlled trial. 3138 patients aged 50 and over undergoing major emergency gastrointestinal surgery will be randomly allocated in a 1:1 ratio using minimisation to minimally invasive cardiac output monitoring to guide protocolised administration of intra-venous fluid, or usual care without cardiac output monitoring. The trial intervention will be carried out during surgery and for up to 6 h postoperatively. The trial is funded through an efficient design call by the National Institute for Health and Care Research Health Technology Assessment (NIHR HTA) programme and uses existing routinely collected datasets for the majority of data collection. The primary outcome is the number of days alive and out of hospital within 90 days of randomisation. Participants and those delivering the intervention will not be blinded to treatment allocation. Participant recruitment started in September 2017 with a 1-year internal pilot phase and is ongoing at the time of publication. DISCUSSION: This will be the largest contemporary randomised trial examining the effectiveness of perioperative cardiac output-guided haemodynamic therapy in patients undergoing major emergency gastrointestinal surgery. The multi-centre design and broad inclusion criteria support the external validity of the trial. Although the clinical teams delivering the trial interventions will not be blinded, significant trial outcome measures are objective and not subject to detection bias. TRIAL REGISTRATION: ISRCTN 14729158. Registered on 02 May 2017.

Using re-randomisation designs to increase the efficiency and applicability of retention studies within trials: a case study.

BACKGROUND: Poor retention in randomised trials can lead to serious consequences to their validity. Studies within trials (SWATs) are used to identify the most effective interventions to increase retention. Many interventions could be applied at any follow-up time point, but SWATs commonly assess interventions at a single time point, which can reduce efficiency. METHODS: The re-randomisation design allows participants to be re-enrolled and re-randomised whenever a new retention opportunity occurs (i.e. a new follow-up time point where the intervention could be applied). The main advantages are as follows: (a) it allows the estimation of an average effect across time points, thus increasing generalisability; (b) it can be more efficient than a parallel arm trial due to increased sample size; and (c) it allows subgroup analyses to estimate effectiveness at different time points. We present a case study where the re-randomisation design is used in a SWAT. RESULTS: In our case study, the host trial is a dental trial with two available follow-up points. The Sticker SWAT tests whether adding the trial logo's sticker to the questionnaire's envelope will result in a higher response rate compared with not adding the sticker. The primary outcome is the response rate to postal questionnaires. The re-randomisation design could double the available sample size compared to a parallel arm trial, resulting in the ability to detect an effect size around 28% smaller. CONCLUSION: The re-randomisation design can increase the efficiency and generalisability of SWATs for trials with multiple follow-up time points.

Using modified intention-to-treat as a principal stratum estimator for failure to initiate treatment.

BACKGROUND: A common intercurrent event affecting many trials is when some participants do not begin their assigned treatment. For example, in a double-blind drug trial, some participants may not receive any dose of study medication. Many trials use a 'modified intention-to-treat' approach, whereby participants who do not initiate treatment are excluded from the analysis. However, it is not clear (a) the estimand being targeted by such an approach and (b) the assumptions necessary for such an approach to be unbiased. METHODS: Using potential outcome notation, we demonstrate that a modified intention-to-treat analysis which excludes participants who do not begin treatment is estimating a principal stratum estimand (i.e. the treatment effect in the subpopulation of participants who would begin treatment, regardless of which arm they were assigned to). The modified intention-to-treat estimator is unbiased for the principal stratum estimand under the assumption that the intercurrent event is not affected by the assigned treatment arm, that is, participants who initiate treatment in one arm would also do so in the other arm (i.e. if someone began the intervention, they would also have begun the control, and vice versa). RESULTS: We identify two key criteria in determining whether the modified intention-to-treat estimator is likely to be unbiased: first, we must be able to measure the participants in each treatment arm who experience the intercurrent event, and second, the assumption that treatment allocation will not affect whether the participant begins treatment must be reasonable. Most double-blind trials will satisfy these criteria, as the decision to start treatment cannot be influenced by the allocation, and we provide an example of an open-label trial where these criteria are likely to be satisfied as well, implying that a modified intention-to-treat analysis which excludes participants who do not begin treatment is an unbiased estimator for the principal stratum effect in these settings. We also give two examples where these criteria will not be satisfied (one comparing an active intervention vs usual care, where we cannot identify which usual care participants would have initiated the active intervention, and another comparing two active interventions in an unblinded manner, where knowledge of the assigned treatment arm may affect the participant's choice to begin or not), implying that a modified intention-to-treat estimator will be biased in these settings. CONCLUSION: A modified intention-to-treat analysis which excludes participants who do not begin treatment can be an unbiased estimator for the principal stratum estimand. Our framework can help identify when the assumptions for unbiasedness are likely to hold, and thus whether modified intention-to-treat is appropriate or not.

Eliminating Ambiguous Treatment Effects Using Estimands.

Most reported treatment effects in medical research studies are ambiguously defined, which can lead to misinterpretation of study results. This is because most authors do not attempt to describe what the treatment effect represents, and instead require readers to deduce this based on the reported statistical methods. However, this approach is challenging, because many methods provide counterintuitive results. For example, some methods include data from all patients, yet the resulting treatment effect applies only to a subset of patients, whereas other methods will exclude certain patients while results will apply to everyone. Additionally, some analyses provide estimates pertaining to hypothetical settings in which patients never die or discontinue treatment. Herein we introduce estimands as a solution to the aforementioned problem. An estimand is a clear description of what the treatment effect represents, thus saving readers the necessity of trying to infer this from study methods and potentially getting it wrong. We provide examples of how estimands can remove ambiguity from reported treatment effects and describe their current use in practice. The crux of our argument is that readers should not have to infer what investigators are estimating; they should be told explicitly.

Estimands in cluster-randomized trials: choosing analyses that answer the right question.

BACKGROUND: Cluster-randomized trials (CRTs) involve randomizing groups of individuals (e.g. hospitals, schools or villages) to different interventions. Various approaches exist for analysing CRTs but there has been little discussion around the treatment effects (estimands) targeted by each. METHODS: We describe the different estimands that can be addressed through CRTs and demonstrate how choices between different analytic approaches can impact the interpretation of results by fundamentally changing the question being asked, or, equivalently, the target estimand. RESULTS: CRTs can address either the participant-average treatment effect (the average treatment effect across participants) or the cluster-average treatment effect (the average treatment effect across clusters). These two estimands can differ when participant outcomes or the treatment effect depends on the cluster size (referred to as 'informative cluster size'), which can occur for reasons such as differences in staffing levels or types of participants between small and large clusters. Furthermore, common estimators, such as mixed-effects models or generalized estimating equations with an exchangeable working correlation structure, can produce biased estimates for both the participant-average and cluster-average treatment effects when cluster size is informative. We describe alternative estimators (independence estimating equations and cluster-level analyses) that are unbiased for CRTs even when informative cluster size is present. CONCLUSION: We conclude that careful specification of the estimand at the outset can ensure that the study question being addressed is clear and relevant, and, in turn, that the selected estimator provides an unbiased estimate of the desired quantity.

Access to unpublished protocols and statistical analysis plans of randomised trials.

BACKGROUND: Access to protocols and statistical analysis plans (SAPs) increases the transparency of randomised trial by allowing readers to identify and interpret unplanned changes to study methods, however they are often not made publicly available. We sought to determine how often study investigators would share unavailable documents upon request. METHODS: We used trials from two previously identified cohorts (cohort 1: 101 trials published in high impact factor journals between January and April of 2018; cohort 2: 100 trials published in June 2018 in journals indexed in PubMed) to determine whether study investigators would share unavailable protocols/SAPs upon request. We emailed corresponding authors of trials with no publicly available protocol or SAP up to four times. RESULTS: Overall, 96 of 201 trials (48%) across the two cohorts had no publicly available protocol or SAP (11/101 high-impact cohort, 85/100 PubMed cohort). In total, 8/96 authors (8%) shared some trial documentation (protocol only [n = 5]; protocol and SAP [n = 1]; excerpt from protocol [n = 1]; research ethics application form [n = 1]). We received protocols for 6/96 trials (6%), and a SAP for 1/96 trial (1%). Seventy-three authors (76%) did not respond, 7 authors responded (7%) but declined to share a protocol or SAP, and eight email addresses were invalid (8%). A total of 329 emails were sent (an average of 41 emails for every trial which sent documentation). After emailing authors, the total number of trials with an available protocol increased by only 3%, from 52% in to 55%. CONCLUSIONS: Most study investigators did not share their unpublished protocols or SAPs upon direct request. Alternative strategies are needed to increase transparency of randomised trials and ensure access to protocols and SAPs.

Evaluating how clear the questions being investigated in randomised trials are: systematic review of estimands.

OBJECTIVES: To evaluate how often the precise research question being addressed about an intervention (the estimand) is stated or can be determined from reported methods, and to identify what types of questions are being investigated in phase 2-4 randomised trials. DESIGN: Systematic review of the clarity of research questions being investigated in randomised trials in 2020 in six leading general medical journals. DATA SOURCE: PubMed search in February 2021. ELIGIBILITY CRITERIA FOR SELECTING STUDIES: Phase 2-4 randomised trials, with no restrictions on medical conditions or interventions. Cluster randomised, crossover, non-inferiority, and equivalence trials were excluded. MAIN OUTCOME MEASURES: Number of trials that stated the precise primary question being addressed about an intervention (ie, the primary estimand), or for which the primary estimand could be determined unambiguously from the reported methods using statistical knowledge. Strategies used to handle post-randomisation events that affect the interpretation or existence of patient outcomes, such as intervention discontinuations or uses of additional drug treatments (known as intercurrent events), and the corresponding types of questions being investigated. RESULTS: 255 eligible randomised trials were identified. No trials clearly stated all the attributes of the estimand. In 117 (46%) of 255 trials, the primary estimand could be determined from the reported methods. Intercurrent events were reported in 242 (95%) of 255 trials; but the handling of these could only be determined in 125 (49%) of 255 trials. Most trials that provided this information considered the occurrence of intercurrent events as irrelevant in the calculation of the treatment effect and assessed the effect of the intervention regardless (96/125, 77%)-that is, they used a treatment policy strategy. Four (4%) of 99 trials with treatment non-adherence owing to adverse events estimated the treatment effect in a hypothetical setting (ie, the effect as if participants continued treatment despite adverse events), and 19 (79%) of 24 trials where some patients died estimated the treatment effect in a hypothetical setting (ie, the effect as if participants did not die). CONCLUSIONS: The precise research question being investigated in most trials is unclear, mainly because of a lack of clarity on the approach to handling intercurrent events. Clear reporting of estimands is necessary in trial reports so that all stakeholders, including clinicians, patients and policy makers, can make fully informed decisions about medical interventions. SYSTEMATIC REVIEW REGISTRATION: PROSPERO CRD42021238053.

Rethinking intercurrent events in defining estimands for tuberculosis trials.

BACKGROUND/AIMS: Tuberculosis remains one of the leading causes of death from an infectious disease globally. Both choices of outcome definitions and approaches to handling events happening post-randomisation can change the treatment effect being estimated, but these are often inconsistently described, thus inhibiting clear interpretation and comparison across trials. METHODS: Starting from the ICH E9(R1) addendum's definition of an estimand, we use our experience of conducting large Phase III tuberculosis treatment trials and our understanding of the estimand framework to identify the key decisions regarding how different event types are handled in the primary outcome definition, and the important points that should be considered in making such decisions. A key issue is the handling of intercurrent (i.e. post-randomisation) events (ICEs) which affect interpretation of or preclude measurement of the intended final outcome. We consider common ICEs including treatment changes and treatment extension, poor adherence to randomised treatment, re-infection with a new strain of tuberculosis which is different from the original infection, and death. We use two completed tuberculosis trials (REMoxTB and STREAM Stage 1) as illustrative examples. These trials tested non-inferiority of new tuberculosis treatment regimens versus a control regimen. The primary outcome was a binary composite endpoint, 'favourable' or 'unfavourable', which was constructed from several components. RESULTS: We propose the following improvements in handling the above-mentioned ICEs and loss to follow-up (a post-randomisation event that is not in itself an ICE). First, changes to allocated regimens should not necessarily be viewed as an unfavourable outcome; from the patient perspective, the potential harms associated with a change in the regimen should instead be directly quantified. Second, handling poor adherence to randomised treatment using a per-protocol analysis does not necessarily target a clear estimand; instead, it would be desirable to develop ways to estimate the treatment effects more relevant to programmatic settings. Third, re-infection with a new strain of tuberculosis could be handled with different strategies, depending on whether the outcome of interest is the ability to attain culture negativity from infection with any strain of tuberculosis, or specifically the presenting strain of tuberculosis. Fourth, where possible, death could be separated into tuberculosis-related and non-tuberculosis-related and handled using appropriate strategies. Finally, although some losses to follow-up would result in early treatment discontinuation, patients lost to follow-up before the end of the trial should not always be classified as having an unfavourable outcome. Instead, loss to follow-up should be separated from not completing the treatment, which is an ICE and may be considered as an unfavourable outcome. CONCLUSION: The estimand framework clarifies many issues in tuberculosis trials but also challenges trialists to justify and improve their outcome definitions. Future trialists should consider all the above points in defining their outcomes.

Estimands for factorial trials.

Factorial trials offer an efficient method to evaluate multiple interventions in a single trial, however the use of additional treatments can obscure research objectives, leading to inappropriate analytical methods and interpretation of results. We define a set of estimands for factorial trials, and describe a framework for applying these estimands, with the aim of clarifying trial objectives and ensuring appropriate primary and sensitivity analyses are chosen. This framework is intended for use in factorial trials where the intent is to conduct "two-trials-in-one" (ie, to separately evaluate the effects of treatments A and B), and is comprised of four steps: (i) specifying how additional treatment(s) (eg, treatment B) will be handled in the estimand, and how intercurrent events affecting the additional treatment(s) will be handled; (ii) designating the appropriate factorial estimator as the primary analysis strategy; (iii) evaluating the interaction to assess the plausibility of the assumptions underpinning the factorial estimator; and (iv) performing a sensitivity analysis using an appropriate multiarm estimator to evaluate to what extent departures from the underlying assumption of no interaction may affect results. We show that adjustment for other factors is necessary for noncollapsible effect measures (such as odds ratio), and through a trial re-analysis we find that failure to consider the estimand could lead to inappropriate interpretation of results. We conclude that careful use of the estimands framework clarifies research objectives and reduces the risk of misinterpretation of trial results, and should become a standard part of both the protocol and reporting of factorial trials.

Combining factorial and multi-arm multi-stage platform designs to evaluate multiple interventions efficiently.

BACKGROUND: Factorial designs and multi-arm multi-stage (MAMS) platform designs have many advantages, but the practical advantages and disadvantages of combining the two designs have not been explored. METHODS: We propose practical methods for a combined design within the platform trial paradigm where some interventions are not expected to interact and could be given together. RESULTS: We describe the combined design and suggest diagrams that can be used to represent it. Many properties are common both to standard factorial designs, including the need to consider interactions between interventions and the impact of intervention efficacy on power of other comparisons, and to standard multi-arm multi-stage designs, including the need to pre-specify procedures for starting and stopping intervention comparisons. We also identify some specific features of the factorial-MAMS design: timing of interim and final analyses should be determined by calendar time or total observed events; some non-factorial modifications may be useful; eligibility criteria should be broad enough to include any patient eligible for any part of the randomisation; stratified randomisation may conveniently be performed sequentially; and analysis requires special care to use only concurrent controls. CONCLUSION: A combined factorial-MAMS design can combine the efficiencies of factorial trials and multi-arm multi-stage platform trials. It allows us to address multiple research questions under one protocol and to test multiple new treatment options, which is particularly important when facing a new emergent infection such as COVID-19.

Re-randomisation trials in multi-episode settings: Estimands and independence estimators.

Often patients may require treatment on multiple occasions. The re-randomisation design can be used in such multi-episode settings, as it allows patients to be re-enrolled and re-randomised for each new treatment episode they experience. We propose a set of estimands that can be used in multi-episode settings, focusing on issues unique to multi-episode settings, namely how each episode should be weighted, how the patient's treatment history in previous episodes should be handled, and whether episode-specific effects or average effects across all episodes should be used. We then propose independence estimators for each estimand, and show the manner in which many re-randomisation trials have been analysed in the past (a simple comparison between all intervention episodes vs. all control episodes) corresponds to a per-episode added-benefit estimand, that is, the average effect of the intervention across all episodes, over and above any benefit conferred from the intervention in previous episodes. We show this estimator is generally unbiased, and describe when other estimators will be unbiased. We conclude that (i) consideration of these estimands can help guide the choice of which analysis method is most appropriate; and (ii) the re-randomisation design with an independence estimator can be a useful approach in multi-episode settings.