Optimal allocation strategies in platform trials with continuous endpoints.

Platform trials are randomized clinical trials that allow simultaneous comparison of multiple interventions, usually against a common control. Arms to test experimental interventions may enter and leave the platform over time. This implies that the number of experimental intervention arms in the trial may change as the trial progresses. Determining optimal allocation rates to allocate patients to the treatment and control arms in platform trials is challenging because the optimal allocation depends on the number of arms in the platform and the latter typically varies over time. In addition, the optimal allocation depends on the analysis strategy used and the optimality criteria considered. In this article, we derive optimal treatment allocation rates for platform trials with shared controls, assuming that a stratified estimation and a testing procedure based on a regression model are used to adjust for time trends. We consider both, analysis using concurrent controls only as well as analysis methods using concurrent and non-concurrent controls and assume that the total sample size is fixed. The objective function to be minimized is the maximum of the variances of the effect estimators. We show that the optimal solution depends on the entry time of the arms in the trial and, in general, does not correspond to the square root of k allocation rule used in classical multi-arm trials. We illustrate the optimal allocation and evaluate the power and type 1 error rate compared to trials using one-to-one and square root of k allocations by means of a case study.

A Bayesian analysis of mortality outcomes in multicentre clinical trials in critical care.

BACKGROUND: Multicentre RCTs are widely used by critical care researchers to answer important clinical questions. However, few trials evaluating mortality outcomes report statistically significant results. We hypothesised that the low proportion of trials reporting statistically significant differences for mortality outcomes is plausibly explained by lower-than-expected effect sizes combined with a low proportion of participants who could realistically benefit from studied interventions. METHODS: We reviewed multicentre trials in critical care published over a 10-yr period in the New England Journal of Medicine, the Journal of the American Medical Association, and the Lancet. To test our hypothesis, we analysed the results using a Bayesian model to investigate the relationship between the proportion of effective interventions and the proportion of statistically significant results for prior distributions of effect size and trial participant susceptibility. RESULTS: Five of 54 trials (9.3%) reported a significant difference in mortality between the control and the intervention groups. The median expected and observed differences in absolute mortality were 8.0% and 2.0%, respectively. Our modelling shows that, across trials, a lower-than-expected effect size combined with a low proportion of potentially susceptible participants is consistent with the observed proportion of trials reporting significant differences even when most interventions are effective. CONCLUSIONS: When designing clinical trials, researchers most likely overestimate true population effect sizes for critical care interventions. Bayesian modelling demonstrates that that it is not necessarily the case that most studied interventions lack efficacy. In fact, it is plausible that many studied interventions have clinically important effects that are missed.

The promise and pitfalls of composite endpoints in sepsis and COVID-19 clinical trials.

Composite endpoints reveal the tendency for statistical convention to arise locally within subfields. Composites are familiar in cardiovascular trials, yet almost unknown in sepsis. However, the VITAMINS trial in patients with septic shock adopted a composite of mortality and vasopressor-free days, and an ordinal scale describing patient status rapidly became standard in COVID studies. Aware that recent use could incite interest in such endpoints, we are motivated to flag their potential value and pitfalls for sepsis research and COVID studies.

A Bayesian basket trial design accounting for uncertainties of homogeneity and heterogeneity of treatment effect among subpopulations.

Basket trials are a recent and innovative approach in oncological clinical trial design. A basket trial is a type of clinical trial for which eligibility is based on the presence of a specific genomic alteration, irrespective of cancer type. Additionally, basket trials are often used to evaluate the response rate of an investigational therapy across several types of cancer. Recently developed statistical methods for evaluating the response rate in basket trials can be generally categorized into two groups: (a) those that account for the degrees of homogeneity/heterogeneity of response rates among subpopulations, and (b) those using borrowed response rate information across subpopulations to improve the statistical efficiency using Bayesian hierarchical models. In this study, we developed a new basket trial design that accounts for the uncertainties of homogeneity and heterogeneity of response rates among subpopulations using the Bayesian model averaging approach. We demonstrated the utility of the proposed method by comparing our approach against other methods for the two methodological groups using simulated and actual data. On an average, the proposed methods offered an intermediate performance between the BHM-weak and BHM-strong methods. The proposed method would be useful for "signal-finding" basket trials without prior information on the treatment effect of an investigational drug, in part because the proposed method does not require specifications regarding prior distributions of homogeneity response rates among subpopulations.

Optimal decision-making in oncology development programs based on probability of success for phase III utilizing phase II/III data on response and overall survival.

In clinical development, there is a trade-off between investment and level of confidence in the potential of the drug before going into phase III. Reduced investment requires the use of short-term endpoints. On new compounds, only limited information about the relationship between treatment effects of short- and long-term endpoints is usually available. Therefore, decision-making solely based on short-term endpoints does not seem desirable. Our goal is to plan an efficient development program, which uses short- and long-term endpoints data for decision-making. We found that with limited prior information and restrictions on maximum sample size, decision-making after phase II cannot be substantially improved. We follow the concept of a "phase 2+" design where after a go-to-phase-III-decision, further follow-up data from phase II are employed to make interim decisions on phase III. The program will be stopped early when additional phase II and/or available phase III data lead to a low probability of success (PoS). We utilize information from a multi-categorical short-term endpoint (response status) and a long-term endpoint (overall survival (OS)) to determine the PoS in phase III with OS as the primary endpoint. Optimal combinations of decision boundaries and time points are demonstrated in a simulation study. Our results show that the proposed second look using additional follow-up data from phase II/III improves PoS estimates compared to the first look, especially when prior data about the control arm is available. The proposed planning strategy allows a customized compromise between the quality of decision-making and program duration.

Strengthening the interpretability of clinical trial results by assessing the effect of informative censoring on the primary estimand in PRECISION.

BACKGROUND: The ICH E9(R1) addendum states that the strategy to account for intercurrent events should be included when defining an estimand, the treatment effect to be estimated based on the study objective. The estimator used to assess the treatment effect needs to be aligned with the estimand that accounted for intercurrent events. Regardless of the strategy, missing data resulting from patient premature withdrawal could undermine the robustness of the study results. Informative censoring due to dropouts in an events-based study is one such example. Sensitivity analyses using imputation methods are useful to examine the uncertainty due to informative censoring and address the robustness and strength of the study results. METHODS: We assessed the effect of premature patient withdrawal in the PRECISION study, a randomized non-inferiority clinical trial of patients with chronic arthritic pain that compared the cardiovascular safety of three nonsteroidal anti-inflammatory drugs-based treatment policies or paradigms. The protocol-defined use of concomitant or rescue medications was permitted since changes in pain medications due to insufficient analgesia were expected in patients in this long-term study. Anticipating that premature study discontinuations could potentially lead to informative censoring, a supplementary analysis was pre-specified in which censored outcomes due to the premature study discontinuation were imputed based on adverse events that were clinically associated with the primary endpoint (cardiovascular outcome based on the Antiplatelet Trialists Collaboration composite endpoint). Furthermore, tipping point analyses were conducted to test the robustness of the primary analysis results by assuming data censored not at random. The level of increase at which the primary study conclusion would change was estimated. RESULTS: For the analysis of time to first primary endpoint event through 30 months, 4065 out of the 24,081 enrolled patients were lost to follow-up, withdrew consent, or were no longer willing to participate in the study. These withdrawals occurred gradually and resulted in a cumulative total of 5893 censored patient-years of observation (10.2%). The rate of discontinuation and the baseline characteristics of the discontinued patients were similar across the three treatment groups. The non-inferiority conclusion from the primary analysis was confirmed in the supplementary analysis incorporating relevant adverse events. Furthermore, tipping point analyses demonstrated that in order to lose non-inferiority in the primary analysis, the risk of primary endpoint events during the censored observation time would have to increase by more than 2.7-fold in the celecoxib group while remaining constant in the other nonsteroidal anti-inflammatory drugs groups, demonstrating that the scenarios where the study results are invalid appear not plausible. CONCLUSIONS: Supplementary and sensitivity analyses presented to address informative censoring in PRECISION helped to further interpret and strengthen the study results.

Bayesian optimal phase II clinical trial design with time-to-event endpoint.

We propose a Bayesian optimal phase II (BOP2) design for clinical trials with a time-to-event endpoint (eg, progression-free survival [PFS]) or co-primary endpoints consisted of a time-to-event endpoint and a categorical endpoint (eg, PFS and toxicity). We use an exponential-inverse gamma model to model the time to event. At each interim, the go/no-go decision is made by comparing the posterior probabilities of the event of interest with an adaptive probability cutoff. The BOP2 design is flexible in the number of interim looks and applicable to both single-arm and two-arm trials. The design maximizes the power for detecting effective treatments, with a well-controlled type I error, thereby bridging the gap between Bayesian designs and frequentist designs. The BOP2 design is easy to implement. Its stopping boundary can be enumerated and included in study protocol before the onset of the trial for single-arm studies. Simulation studies show that the BOP2 design has favorable operating characteristics, with higher power and lower risk of incorrectly terminating the trial than some Bayesian phase II designs. The software to implement the BOP2 design will be freely available at www.trialdesign.org.

Statistical aspects in adjuvant and neoadjuvant trials for gastrointestinal cancer in 2020: focus on time-to-event endpoints.

PURPOSE OF REVIEW: Clinical-trial design, analysis, and interpretation entails the use of efficient and reliable endpoints. Statistical issues related to endpoints warrant continued attention, as they may have a substantial impact on the conduct of clinical trials and on interpretation of their results. RECENT FINDINGS: We review concepts and discuss recent developments related to the use of time-to-event endpoints in studies on adjuvant and neoadjuvant therapy for colon, pancreatic, and gastric adenocarcinomas. The definition of endpoints has varied to a considerable extent in these settings. Although these variations are relevant in interpreting results from individual trials, they probably have a small impact when considered in aggregate. In terms of surrogacy, most published reports so far have used aggregated data. A few studies based on the preferred method of a metaanalysis of individual-patient data have shown that disease-free survival (DFS) is a surrogate for overall survival in the adjuvant therapy of stage III colon cancer and in gastric cancer, whereas DFS with a landmark of six months is a surrogate for overall survival in the neoadjuvant therapy of adenocarcinoma of the esophagus, gastroesophageal junction, or stomach. SUMMARY: Testing novel agents in gastrointestinal cancer requires continued attention to statistical issues related to endpoints.

How to use frailtypack for validating failure-time surrogate endpoints using individual patient data from meta-analyses of randomized controlled trials.

BACKGROUND AND OBJECTIVE: The use of valid surrogate endpoints can accelerate the development of phase III trials. Numerous validation methods have been proposed with the most popular used in a context of meta-analyses, based on a two-step analysis strategy. For two failure time endpoints, two association measures are usually considered, Kendall's τ at individual level and adjusted R2 ([Formula: see text]) at trial level. However, [Formula: see text] is not always available mainly due to model estimation constraints. More recently, we proposed a one-step validation method based on a joint frailty model, with the aim of reducing estimation issues and estimation bias on the surrogacy evaluation criteria. The model was quite robust with satisfactory results obtained in simulation studies. This study seeks to popularize this new surrogate endpoints validation approach by making the method available in a user-friendly R package. METHODS: We provide numerous tools in the frailtypack R package, including more flexible functions, for the validation of candidate surrogate endpoints using data from multiple randomized clinical trials. RESULTS: We implemented the surrogate threshold effect which is used in combination with [Formula: see text] to make decisions concerning the validity of the surrogate endpoints. It is also possible thanks to frailtypack to predict the treatment effect on the true endpoint in a new trial using the treatment effect observed on the surrogate endpoint. The leave-one-out cross-validation is available for assessing the accuracy of the prediction using the joint surrogate model. Other tools include data generation, simulation study and graphic representations. We illustrate the use of the new functions with both real data and simulated data. CONCLUSION: This article proposes new attractive and well developed tools for validating failure time surrogate endpoints.

A flexible multi-domain test with adaptive weights and its application to clinical trials.

The design of a clinical trial is often complicated by the multi-systemic nature of the disease; a single endpoint often cannot capture the spectrum of potential therapeutic benefits. Multi-domain outcomes which take into account patient heterogeneity of disease presentation through measurements of multiple symptom/functional domains are an attractive alternative to a single endpoint. A multi-domain test with adaptive weights is proposed to synthesize the evidence of treatment efficacy over numerous disease domains. The test is a weighted sum of domain-specific test statistics with weights selected adaptively via a data-driven algorithm. The null distribution of the test statistic is constructed empirically through resampling and does not require estimation of the covariance structure of domain-specific test statistics. Simulations show that the proposed test controls the type I error rate, and has increased power over other methods such as the O'Brien and Wei-Lachin tests in scenarios reflective of clinical trial settings. Data from a clinical trial in a rare lysosomal storage disorder were used to illustrate the properties of the proposed test. As a strategy of combining marginal test statistics, the proposed test is flexible and readily applicable to a variety of clinical trial scenarios.

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes.

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context.

Methods and applications of percentile estimation.

Percentile is ubiquitous in statistics and plays a significant role in the day-to-day statistical application. FDA Guidance for Industry: Assay Development for Immunogenicity Testing of Therapeutic Protein Products (2016) recommends the use of a lower confidence limit of the percentile of the negative subject population as the cut point to guarantee a pre-specified false-positive rate with high confidence. Shen proposed and compared an exact t approach with some approximated approaches. However, the exact t approach might be compromised by computational time and complexity. In this article, we proposed to use a UMOVER method as a potential alternative for percentile estimation for one application to screening and confirmatory cut point determination due to its easy implementation and similar performance to the exact t approach. The applications and performance comparison with different approaches are investigated and discussed. Furthermore, we extended the proposed method for the comparison of the percentile of the test product and percentile of the reference product followed by numerical studies.

TITE-BOIN-ET: Time-to-event Bayesian optimal interval design to accelerate dose-finding based on both efficacy and toxicity outcomes.

One of the primary purposes of an oncology dose-finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de-escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late-onset outcomes. To solve these issues, we propose the time-to-event Bayesian optimal interval design to accelerate dose-finding based on cumulative and pending data of both efficacy and toxicity. The new design, named "TITE-BOIN-ET" design, is nonparametric and a model-assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose-finding trials compared with the model-based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE-BOIN-ET design has advantages compared with the model-based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE-BOIN-ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose-finding trials.

Sequential parallel comparison design with two coprimary endpoints.

A placebo-controlled randomized clinical trial is required to demonstrate that an experimental treatment is superior to its corresponding placebo on multiple coprimary endpoints. This is particularly true in the field of neurology. In fact, clinical trials for neurological disorders need to show the superiority of an experimental treatment over a placebo in two coprimary endpoints. Unfortunately, these trials often fail to detect a true treatment effect for the experimental treatment versus the placebo owing to an unexpectedly high placebo response rate. Sequential parallel comparison design (SPCD) can be used to address this problem. However, the SPCD has not yet been discussed in relation to clinical trials with coprimary endpoints. In this article, our aim was to develop a hypothesis-testing method and a method for calculating the corresponding sample size for the SPCD with two coprimary endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy. In addition, the usefulness of our methods is confirmed by returning to an SPCD trial with a single primary endpoint of Alzheimer disease-related agitation.

Comparisons of global tests on intersection hypotheses and their application in matched parallel gatekeeping procedures.

A clinical trial often has primary and secondary endpoints and comparisons of high and low doses of a study drug to a control. Multiplicity is not only caused by the multiple comparisons of study drugs versus the control, but also from the hierarchical structure of the hypotheses. Closed test procedures were proposed as general methods to address multiplicity. Two commonly used tests for intersection hypotheses in closed test procedures are the Simes test and the average method. When the treatment effect of a less efficacious dose is not much smaller than the treatment effect of a more efficacious dose for a specific endpoint, the average method has better power than the Simes test for the comparison of two doses versus control. Accordingly, for inferences for primary and secondary endpoints, the matched parallel gatekeeping procedure based on the Simes test for testing intersection hypotheses is extended here to allow the average method for such testing. This procedure is further extended to clinical trials with more than two endpoints as well as to clinical trials with more than two active doses and a control.

Bayesian design of biosimilars clinical programs involving multiple therapeutic indications.

In this paper, we propose a Bayesian design framework for a biosimilars clinical program that entails conducting concurrent trials in multiple therapeutic indications to establish equivalent efficacy for a proposed biologic compared to a reference biologic in each indication to support approval of the proposed biologic as a biosimilar. Our method facilitates information borrowing across indications through the use of a multivariate normal correlated parameter prior (CPP), which is constructed from easily interpretable hyperparameters that represent direct statements about the equivalence hypotheses to be tested. The CPP accommodates different endpoints and data types across indications (eg, binary and continuous) and can, therefore, be used in a wide context of models without having to modify the data (eg, rescaling) to provide reasonable information-borrowing properties. We illustrate how one can evaluate the design using Bayesian versions of the type I error rate and power with the objective of determining the sample size required for each indication such that the design has high power to demonstrate equivalent efficacy in each indication, reasonably high power to demonstrate equivalent efficacy simultaneously in all indications (ie, globally), and reasonable type I error control from a Bayesian perspective. We illustrate the method with several examples, including designing biosimilars trials for follicular lymphoma and rheumatoid arthritis using binary and continuous endpoints, respectively.

Two-stage phase II survival trial design.

Recently, molecularly targeted agents and immunotherapy have been advanced for the treatment of relapse or refractory cancer patients, where disease progression-free survival or event-free survival is often a primary endpoint for the trial design. However, methods to evaluate two-stage single-arm phase II trials with a time-to-event endpoint are currently processed under an exponential distribution, which limits application of real trial designs. In this paper, we developed an optimal two-stage design, which is applied to the four commonly used parametric survival distributions. The proposed method has advantages compared with existing methods in that the choice of underlying survival model is more flexible and the power of the study is more adequately addressed. Therefore, the proposed two-stage design can be routinely used for single-arm phase II trial designs with a time-to-event endpoint as a complement to the commonly used Simon's two-stage design for the binary outcome.

Covariate adjustment for randomized controlled trials revisited.

Covariate adjustment for the estimation of treatment effect for randomized controlled trials (RCT) is a simple approach with a long history, hence, its pros and cons have been well-investigated and published in the literature. It is worthwhile to revisit this topic since recently there has been significant investigation and development on model assumptions, robustness to model mis-specification, in particular, regarding the Neyman-Rubin model and the average treatment effect estimand. This paper discusses key results of the investigation and development and their practical implication on pharmaceutical statistics. Accordingly, we recommend that appropriate covariate adjustment should be more widely used for RCTs for both hypothesis testing and estimation.

The win ratio: Impact of censoring and follow-up time and use with nonproportional hazards.

The win ratio has been studied methodologically and applied in data analysis and in designing clinical trials. Researchers have pointed out that the results depend on follow-up time and censoring time, which are sometimes used interchangeably. In this article, we distinguish between follow-up time and censoring time, show theoretically the impact of censoring on the win ratio, and illustrate the impact of follow-up time. We then point out that, if the treatment has long-term benefit from a more important but less frequent endpoint (eg, death), the win ratio can show that benefit by following patients longer, avoiding masking by more frequent but less important outcomes, which occurs in conventional time-to-first-event analyses. For the situation of nonproportional hazards, we demonstrate that the win ratio can be a good alternative to methods such as landmark survival rate, restricted mean survival time, and weighted log-rank tests.

Cancer immunotherapy trial design with delayed treatment effect.

A challenge arising in cancer immunotherapy trial design is the presence of a delayed treatment effect wherein the proportional hazard assumption no longer holds true. As a result, a traditional survival trial design based on the standard log-rank test, which ignores the delayed treatment effect, will lead to substantial loss of statistical power. Recently, a piecewise weighted log-rank test is proposed to incorporate the delayed treatment effect into consideration of the trial design. However, because the sample size formula was derived under a sequence of local alternative hypotheses, it results in an underestimated sample size when the hazard ratio is relatively small for a balanced trial design and an inaccurate sample size estimation for an unbalanced design. In this article, we derived a new sample size formula under a fixed alternative hypothesis for the delayed treatment effect model. Simulation results show that the new formula provides accurate sample size estimation for both balanced and unbalanced designs.