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.     

Four case studies to highlight some opportunities and challenges in developing anti‐bacterial and anti‐fungal agents

Since the first properly randomized control trial of streptomycin for pulmonary tuberculosis in the late 1940s, society has made great advances in combating bacterial infections and in developing vaccines to prevent such infections. One constant challenge that anti‐bacterial clinical development must grapple with is to determine the potential benefit of newer agents over existing agents, in an era when anti‐bacterial resistance is a constantly shifting target. By contrast, the development of anti‐fungal agents went into high gear only in the late 1980s and early 1990s in an effort to manage fungal infections in cancer patients receiving chemotherapy, especially in patients with haematologic malignancies, bone marrow transplantation, or lymphoma. The pursuit of anti‐fungal agents intensified with the AIDS epidemic. The evaluation of anti‐fungal agents often faces complications brought on by competing risks in situations where the underlying infections are associated with a high chance of mortality or severe morbidity. In this paper, we use four case studies to illustrate some of the challenges and opportunities in developing anti‐bacterial and anti‐fungal agents. The illustrations touch on not only statistical issues, but also issues related to the availability of new anti‐bacterials in the future. Some suggestions on how statisticians could take advantage of the opportunities and answer to the challenges are also included. Copyright © 2005 John Wiley & Sons, Ltd.     

The impact of period effects on dose level contrasts in alternating cross‐over designs for first‐time‐in‐human studies

For first‐time‐in‐human studies with small molecules alternating cross‐over designs are often employed and at study end are analyzed using linear models. We discuss the impact of including a period effect in the model on the precision with which dose level contrasts can be estimated and quantify the bias of least squares estimators if a period effect is inherent in the data that is not accounted for in the model. We also propose two alternative designs that allow a more precise estimation of dose level contrasts compared with the standard design when period effects are included in the model. Copyright © 2010 John Wiley & Sons, Ltd.     

Group sequential monitoring based on the weighted log‐rank test statistic with the Fleming–Harrington class of weights in cancer vaccine studies

In recent years, immunological science has evolved, and cancer vaccines are now approved and available for treating existing cancers. Because cancer vaccines require time to elicit an immune response, a delayed treatment effect is expected and is actually observed in drug approval studies. Accordingly, we propose the evaluation of survival endpoints by weighted log‐rank tests with the Fleming–Harrington class of weights. We consider group sequential monitoring, which allows early efficacy stopping, and determine a semiparametric information fraction for the Fleming–Harrington family of weights, which is necessary for the error spending function. Moreover, we give a flexible survival model in cancer vaccine studies that considers not only the delayed treatment effect but also the long‐term survivors. In a Monte Carlo simulation study, we illustrate that when the primary analysis is a weighted log‐rank test emphasizing the late differences, the proposed information fraction can be a useful alternative to the surrogate information fraction, which is proportional to the number of events. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Log‐rank permutation tests for trend: saddlepoint p‐values and survival rate confidence intervals

Suppose p + 1 experimental groups correspond to increasing dose levels of a treatment and all groups are subject to right censoring. In such instances, permutation tests for trend can be performed based on statistics derived from the weighted log‐rank class. This article uses saddlepoint methods to determine the mid‐P‐values for such permutation tests for any test statistic in the weighted log‐rank class. Permutation simulations are replaced by analytical saddlepoint computations which provide extremely accurate mid‐P‐values that are exact for most practical purposes and almost always more accurate than normal approximations. The speed of mid‐P‐value computation allows for the inversion of such tests to determine confidence intervals for the percentage increase in mean (or median) survival time per unit increase in dosage. The Canadian Journal of Statistics 37: 5‐16; 2009 © 2009 Statistical Society of Canada     

Adaptative Designs for Multi-Arm Clinical Trials: The Play-the-Winner Rule Revisited

Adaptative designs for clinical trials that are based on a generalization of the “play-the-winner” rule are considered as an alternative to previously developed models. Theoretical and numerical results show that these designs perform better for the usual criteria. Bayesian methods are proposed for the statistical analysis of these designs.     

Phase II trial design with growth modulation index as the primary endpoint

Molecularly targeted, genomic‐driven, and immunotherapy‐based clinical trials continue to be advanced for the treatment of relapse or refractory cancer patients, where the growth modulation index (GMI) is often considered a primary endpoint of treatment efficacy. However, there little literature is available that considers the trial design with GMI as the primary endpoint. In this article, we derived a sample size formula for the score test under a log‐linear model of the GMI. Study designs using the derived sample size formula are illustrated under a bivariate exponential model, the Weibull frailty model, and the generalized treatment effect size. The proposed designs provide sound statistical methods for a single‐arm phase II trial with GMI as the primary endpoint.     

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.     

A COMPARISON OF ANALYSIS METHODS FOR LATE‐STAGE VARIETY EVALUATION TRIALS

The statistical analysis of late‐stage variety evaluation trials using a mixed model is described, with one‐ or two‐stage approaches to the analysis. Two sets of trials, from Australia and the UK, were used to provide realistic scenarios for a simulation study to evaluate the different methods of analysis. This study showed that a one‐stage approach gave the most accurate predictions of variety performance overall or within each environment, across a range of models, as measured by mean squared error of prediction or realized genetic gain. A weighted two‐stage approach performed adequately for variety predictions both overall and within environments, but a two‐stage unweighted approach performed poorly in both cases. A generalized heritability measure was developed to compare methods.     

Properties of the weighted log‐rank test in the design of confirmatory studies with delayed effects

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log‐rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type‐I error rate of the of the weighted log‐rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.     

Comparison of the restricted mean survival time with the hazard ratio in superiority trials with a time‐to‐event end point

With the emergence of novel therapies exhibiting distinct mechanisms of action compared to traditional treatments, departure from the proportional hazard (PH) assumption in clinical trials with a time‐to‐event end point is increasingly common. In these situations, the hazard ratio may not be a valid statistical measurement of treatment effect, and the log‐rank test may no longer be the most powerful statistical test. The restricted mean survival time (RMST) is an alternative robust and clinically interpretable summary measure that does not rely on the PH assumption. We conduct extensive simulations to evaluate the performance and operating characteristics of the RMST‐based inference and against the hazard ratio–based inference, under various scenarios and design parameter setups. The log‐rank test is generally a powerful test when there is evident separation favoring 1 treatment arm at most of the time points across the Kaplan‐Meier survival curves, but the performance of the RMST test is similar. Under non‐PH scenarios where late separation of survival curves is observed, the RMST‐based test has better performance than the log‐rank test when the truncation time is reasonably close to the tail of the observed curves. Furthermore, when flat survival tail (or low event rate) in the experimental arm is expected, selecting the minimum of the maximum observed event time as the truncation timepoint for the RMST is not recommended. In addition, we recommend the inclusion of analysis based on the RMST curve over the truncation time in clinical settings where there is suspicion of substantial departure from the PH assumption.     

Restricted mean survival time as a summary measure of time‐to‐event outcome

Many clinical research studies evaluate a time‐to‐event outcome, illustrate survival functions, and conventionally report estimated hazard ratios to express the magnitude of the treatment effect when comparing between groups. However, it may not be straightforward to interpret the hazard ratio clinically and statistically when the proportional hazards assumption is invalid. In some recent papers published in clinical journals, the use of restricted mean survival time (RMST) or τ ‐year mean survival time is discussed as one of the alternative summary measures for the time‐to‐event outcome. The RMST is defined as the expected value of time to event limited to a specific time point corresponding to the area under the survival curve up to the specific time point. This article summarizes the necessary information to conduct statistical analysis using the RMST, including the definition and statistical properties of the RMST, adjusted analysis methods, sample size calculation, information fraction for the RMST difference, and clinical and statistical meaning and interpretation. Additionally, we discuss how to set the specific time point to define the RMST from two main points of view. We also provide developed SAS codes to determine the sample size required to detect an expected RMST difference with appropriate power and reconstruct individual survival data to estimate an RMST reference value from a reported survival curve.     

Hazard ratio inference in stratified clinical trials with time‐to‐event endpoints and limited sample size

The stratified Cox model is commonly used for stratified clinical trials with time‐to‐event endpoints. The estimated log hazard ratio is approximately a weighted average of corresponding stratum‐specific Cox model estimates using inverse‐variance weights; the latter are optimal only under the (often implausible) assumption of a constant hazard ratio across strata. Focusing on trials with limited sample sizes (50‐200 subjects per treatment), we propose an alternative approach in which stratum‐specific estimates are obtained using a refined generalized logrank (RGLR) approach and then combined using either sample size or minimum risk weights for overall inference. Our proposal extends the work of Mehrotra et al, to incorporate the RGLR statistic, which outperforms the Cox model in the setting of proportional hazards and small samples. This work also entails development of a remarkably accurate plug‐in formula for the variance of RGLR‐based estimated log hazard ratios. We demonstrate using simulations that our proposed two‐step RGLR analysis delivers notably better results through smaller estimation bias and mean squared error and larger power than the stratified Cox model analysis when there is a treatment‐by‐stratum interaction, with similar performance when there is no interaction. Additionally, our method controls the type I error rate while the stratified Cox model does not in small samples. We illustrate our method using data from a clinical trial comparing two treatments for colon cancer.     

Planning for an adaptive design: a case study in COPD

We discuss the practical and clinical considerations encountered when planning a Phase IIa trial in chronic obstructive pulmonary disease (COPD). Various adaptive strategies for reducing the cost of the trial and the statistical implications of these are explored. Use of the EAST software to evaluate the properties of the study designs with one or more interim analyses for futility, efficacy or either is described. We emphasize the rationale for choosing between alternative designs and the relationship between the clinical and statistical considerations.     

Weighted re‐randomization tests for minimization with unbalanced allocation

Re‐randomization test has been considered as a robust alternative to the traditional population model‐based methods for analyzing randomized clinical trials. This is especially so when the clinical trials are randomized according to minimization, which is a popular covariate‐adaptive randomization method for ensuring balance among prognostic factors. Among various re‐randomization tests, fixed‐entry‐order re‐randomization is advocated as an effective strategy when a temporal trend is suspected. Yet when the minimization is applied to trials with unequal allocation, fixed‐entry‐order re‐randomization test is biased and thus compromised in power. We find that the bias is due to non‐uniform re‐allocation probabilities incurred by the re‐randomization in this case. We therefore propose a weighted fixed‐entry‐order re‐randomization test to overcome the bias. The performance of the new test was investigated in simulation studies that mimic the settings of a real clinical trial. The weighted re‐randomization test was found to work well in the scenarios investigated including the presence of a strong temporal trend. Copyright © 2013 John Wiley & Sons, Ltd.     

Practical approaches for design and analysis of clinical trials of infertility treatments: crossover designs and the Mantel–Haenszel method are recommended

Crossover designs have some advantages over standard clinical trial designs and they are often used in trials evaluating the efficacy of treatments for infertility. However, clinical trials of infertility treatments violate a fundamental condition of crossover designs, because women who become pregnant in the first treatment period are not treated in the second period. In previous research, to deal with this problem, some new designs, such as re‐randomization designs, and analysis methods including the logistic mixture model and the beta‐binomial mixture model were proposed. Although the performance of these designs and methods has previously been evaluated in large‐scale clinical trials with sample sizes of more than 1000 per group, the actual sample sizes of infertility treatment trials are usually around 100 per group. The most appropriate design and analysis for these moderate‐scale clinical trials are currently unclear. In this study, we conducted simulation studies to determine the appropriate design and analysis method of moderate‐scale clinical trials for irreversible endpoints by evaluating the statistical power and bias in the treatment effect estimates. The Mantel–Haenszel method had similar power and bias to the logistic mixture model. The crossover designs had the highest power and the smallest bias. We recommend using a combination of the crossover design and the Mantel–Haenszel method for two‐period, two‐treatment clinical trials with irreversible endpoints. Copyright © 2015 John Wiley & Sons, Ltd.     

A Bayesian dose‐finding design for drug combination clinical trials based on the logistic model

In early phase dose‐finding cancer studies, the objective is to determine the maximum tolerated dose, defined as the highest dose with an acceptable dose‐limiting toxicity rate. Finding this dose for drug‐combination trials is complicated because of drug–drug interactions, and many trial designs have been proposed to address this issue. These designs rely on complicated statistical models that typically are not familiar to clinicians, and are rarely used in practice. The aim of this paper is to propose a Bayesian dose‐finding design for drug combination trials based on standard logistic regression. Under the proposed design, we continuously update the posterior estimates of the model parameters to make the decisions of dose assignment and early stopping. Simulation studies show that the proposed design is competitive and outperforms some existing designs. We also extend our design to handle delayed toxicities. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian nonparametric statistics: A new toolkit for discovery in cancer research

Many commonly used statistical methods for data analysis or clinical trial design rely on incorrect assumptions or assume an over‐simplified framework that ignores important information. Such statistical practices may lead to incorrect conclusions about treatment effects or clinical trial designs that are impractical or that do not accurately reflect the investigator's goals. Bayesian nonparametric (BNP) models and methods are a very flexible new class of statistical tools that can overcome such limitations. This is because BNP models can accurately approximate any distribution or function and can accommodate a broad range of statistical problems, including density estimation, regression, survival analysis, graphical modeling, neural networks, classification, clustering, population models, forecasting and prediction, spatiotemporal models, and causal inference. This paper describes 3 illustrative applications of BNP methods, including a randomized clinical trial to compare treatments for intraoperative air leaks after pulmonary resection, estimating survival time with different multi‐stage chemotherapy regimes for acute leukemia, and evaluating joint effects of targeted treatment and an intermediate biological outcome on progression‐free survival time in prostate cancer.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.