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Randomized trials seek efficient treatment effect estimation within target populations, yet scientific interest often also centers on subpopulations. Although there are typically too few subjects within each subpopulation to efficiently estimate these subpopulation treatment effects, one can gain precision by borrowing strength across subpopulations, as is the case in a basket trial. While dynamic borrowing has been proposed as an efficient approach to estimating subpopulation treatment effects on primary endpoints, additional efficiency could be gained by leveraging the information found in secondary endpoints. We propose a multisource exchangeability model (MEM) that incorporates secondary endpoints to more efficiently assess subpopulation exchangeability. Across simulation studies, our proposed model almost uniformly reduces the mean squared error when compared to the standard MEM that only considers data from the primary endpoint by gaining efficiency when subpopulations respond similarly to the treatment and reducing the magnitude of bias when the subpopulations are heterogeneous. We illustrate our model's feasibility using data from a recently completed trial of very low nicotine content cigarettes to estimate the effect on abstinence from smoking within three priority subpopulations. Our proposed model led to increases in the effective sample size two to four times greater than under the standard MEM., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)

Background: Considering multiple endpoints in clinical trials provide a more comprehensive understanding of treatment effects and may lead to increased power or reduced sample size, which may be beneficial in rare diseases. Besides the small sample sizes, allocation bias is an issue that affects the validity of these trials. We investigate the impact of allocation bias on testing decisions in clinical trials with multiple endpoints and offer a tool for selecting an appropriate randomization procedure (RP)., Methods: We derive a model for quantifying the effect of allocation bias depending on the RP in the case of two-arm parallel group trials with continuous multiple endpoints. We focus on two approaches to analyze multiple endpoints, either the Šidák procedure to show efficacy in at least one endpoint and the all-or-none procedure to show efficacy in all endpoints., Results: To evaluate the impact of allocation bias on the test decision we propose a biasing policy for multiple endpoints. The impact of allocation on the test decision is measured by the family-wise error rate of the Šidák procedure and the type I error rate of the all-or-none procedure. Using the biasing policy we derive formulas to calculate these error rates. In simulations we show that, for the Šidák procedure as well as for the all-or-none procedure, allocation bias leads to inflation of the mean family-wise error and mean type I error, respectively. The strength of this inflation is affected by the choice of the RP., Conclusion: Allocation bias should be considered during the design phase of a trial to increase validity. The developed methodology is useful for selecting an appropriate RP for a clinical trial with multiple endpoints to minimize allocation bias effects., (© 2024. The Author(s).)

In a randomized controlled trial with time-to-event endpoint, some commonly used statistical tests to test for various aspects of survival differences, such as survival probability at a fixed time point, survival function up to a specific time point, and restricted mean survival time, may not be directly applicable when external data are leveraged to augment an arm (or both arms) of an RCT. In this paper, we propose a propensity score-integrated approach to extend such tests when external data are leveraged. Simulation studies are conducted to evaluate the operating characteristics of three propensity score-integrated statistical tests, and an illustrative example is given to demonstrate how these proposed procedures can be implemented., (© 2024 Pharmaceutical Statistics. This article has been contributed to by U.S. Government employees and their work is in the public domain in the USA.)

The sample size of a clinical trial has to be large enough to ensure sufficient power for achieving the aim the study. On the other side, for ethical and economical reasons it should not be larger than necessary. The sample size allocation is one of the parameters that influences the required total sample size. For two-arm superiority and non-inferiority trials with binary endpoints, we performed extensive computations over a wide range of scenarios to determine the optimal allocation ratio that minimizes the total sample size if all other parameters are fixed. The results demonstrate, that for both superiority and non-inferiority trials the optimal allocation may deviate considerably from the case of equal sample size in both groups. However, the saving in sample size when allocating the total sample size optimally as compared to balanced allocation is typically small., (© 2024 The Authors. Pharmaceutical Statistics published by John Wiley & Sons Ltd.)

It is not uncommon for a substantial proportion of patients to be cured (or survive long-term) in clinical trials with time-to-event endpoints, such as the endometrial cancer trial. When designing a clinical trial, a mixture cure model should be used to fully consider the cure fraction. Previously, mixture cure model sample size calculations were based on the proportional hazards assumption of latency distribution between groups, and the log-rank test was used for deriving sample size formulas. In real studies, the latency distributions of the two groups often do not satisfy the proportional hazards assumptions. This article has derived a sample size calculation formula for a mixture cure model with restricted mean survival time as the primary endpoint, and did simulation and example studies. The restricted mean survival time test is not subject to proportional hazards assumptions, and the difference in treatment effect obtained can be quantified as the number of years (or months) increased or decreased in survival time, making it very convenient for clinical patient-physician communication. The simulation results showed that the sample sizes estimated by the restricted mean survival time test for the mixture cure model were accurate regardless of whether the proportional hazards assumptions were satisfied and were smaller than the sample sizes estimated by the log-rank test in most cases for the scenarios in which the proportional hazards assumptions were violated., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Multi-arm trials are increasingly of interest because for many diseases; there are multiple experimental treatments available for testing efficacy. Several novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining stopping boundaries. For example, the method of Jaki and Magirr for time-to-event endpoint, implemented in R package MAMS , requires complicated computational efforts to obtain stopping boundaries. In this study, we develop a group sequential MAMS survival trial design based on the sequential conditional probability ratio test. The proposed method is an improvement of the Jaki and Magirr's method in the following three directions. First, the proposed method provides explicit solutions for both futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational efforts for the trial design. Second, the proposed method provides an accurate number of events for the fixed sample and group sequential designs. Third, the proposed method uses a new procedure for interim analysis which preserves the study power.

Sequential, multiple assignment, randomized trial (SMART) designs are appropriate for comparing adaptive treatment interventions, in which intermediate outcomes (called tailoring variables) guide subsequent treatment decisions for individual patients. Within a SMART design, patients may be re-randomized to subsequent treatments following the outcomes of their intermediate assessments. In this paper, we provide an overview of statistical considerations necessary to design and implement a two-stage SMART design with a binary tailoring variable and a survival final endpoint. A chronic lymphocytic leukemia trial with a final endpoint of progression-free survival is used as an example for the simulations to assess how design parameters, including, choice of randomization ratios for each stage of randomization, and response rates of the tailoring variable affect the statistical power. We assess the choice of weights from restricted re-randomization on data analyses and appropriate hazard rate assumptions. Specifically, for a given first-stage therapy and prior to the tailoring variable assessment, we assume equal hazard rates for all patients randomized to a treatment arm. After the tailoring variable assessment, individual hazard rates are assumed for each intervention path. Simulation studies demonstrate that the response rate of the binary tailoring variable impacts power as it directly impacts the distribution of patients. We also confirm that when the first stage randomization is 1:1, it is not necessary to consider the first stage randomization ratio when applying the weights. We provide an R-shiny application for obtaining power for a given sample size for SMART designs.

As part of the drug development process, interim analysis is frequently used to design efficient phase II clinical trials. A stochastic curtailment framework is often deployed wherein a decision to continue or curtail the trial is taken at each interim look based on the likelihood of observing a positive or negative treatment effect if the trial were to continue to its anticipated end. Thus, curtailment can take place due to evidence of early efficacy or futility. Traditionally, in the case of time-to-event endpoints, interim monitoring is conducted in a two-arm clinical trial using the log-rank test, often with the assumption of proportional hazards. However, when this is violated, the log-rank test may not be appropriate, resulting in loss of power and subsequently inaccurate sample sizes. In this paper, we propose stochastic curtailment methods for two-arm phase II trial with the flexibility to allow non-proportional hazards. The proposed methods are built utilizing the concept of relative time assuming that the survival times in the two treatment arms follow two different Weibull distributions. Three methods - conditional power, predictive power and Bayesian predictive probability - are discussed along with corresponding sample size calculations. The monitoring strategy is discussed with a real-life example.

This manuscript consists of two topics. Firstly, we explore the utility of internal pilot study (IPS) approach for reestimating sample size at an interim stage when a reliable estimate of the nuisance shape parameter of the Weibull distribution for modeling survival data is unavailable during the planning phase of a study. Although IPS approach can help rescue the study power, it is noted that the adjusted sample size can be as much as twice the initially planned sample size, which may put substantial practical constraints to continue the study. Secondly, we discuss Bayesian predictive probability for conducting interim analyses to obtain preliminary evidence of efficacy or futility of an experimental treatment warranting early termination of a clinical trial. In the context of single-arm clinical trials with time-to-event endpoints following Weibull distribution, we present the calculation of the Bayesian predictive probability when the shape parameter of the Weibull distribution is unknown. Based on the data accumulated at the interim, we propose two approaches which rely on the posterior mode or the entire posterior distribution of the shape parameter. To account for uncertainty in the shape parameter, it is recommended to incorporate its entire posterior distribution in our calculation.

When the primary endpoints in randomized clinical trials require long term follow-up or are costly to measure, it is often desirable to assess treatment effects on surrogate instead of clinical endpoints. Prior to adopting a surrogate endpoint for such purposes, the extent of its surrogacy on the primary endpoint must be assessed. There is a rich statistical literature on assessing surrogacy in the overall population, much of which is based on quantifying the proportion of treatment effect on the primary endpoint that is explained by the treatment effect on the surrogate endpoint. However, the surrogacy of an endpoint may vary across different patient subgroups according to baseline demographic characteristics, and limited methods are currently available to assess overall surrogacy in the presence of potential surrogacy heterogeneity. In this paper, we propose methods that incorporate covariates for baseline information, such as age, to improve overall surrogacy assessment. We use flexible semi-non-parametric modeling strategies to adjust for covariate effects and derive a robust estimate for the proportion of treatment effect of the covariate-adjusted surrogate endpoint. Simulation results suggest that the adjusted surrogate endpoint has greater proportion of treatment effect compared to the unadjusted surrogate endpoint. We apply the proposed method to data from a clinical trial of infliximab and assess the adequacy of the surrogate endpoint in the presence of age heterogeneity., Competing Interests: Declaration of conflicting interestsThe authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.