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A two-stage enrichment design is a type of adaptive design, which extends a stratified design with a futility analysis on the marker negative cohort at the first stage, and the second stage can be either a targeted design with only the marker positive stratum, or still the stratified design with both marker strata, depending on the result of the interim futility analysis. In this paper we consider the situation where the marker assay and the classification rule are possibly subject to error. We derive the sequential tests for the global hypothesis as well as the component tests for the overall cohort and the marker-positive cohort. We discuss the power analysis with the control of the type-I error rate and show the adverse impact of the misclassification on the powers. We also show the enhanced power of the two-stage enrichment over the one-stage design, and illustrate with examples of the recent successful development of immunotherapy in non-small-cell lung cancer.

In this paper, we derive the joint distribution of progression-free and overall survival as a function of transition probabilities in a multistate model. No assumptions on copulae or latent event times are needed and the model is allowed to be non-Markov. From the joint distribution, statistics of interest can then be computed. As an example, we provide closed formulas and statistical inference for Pearson's correlation coefficient between progression-free and overall survival in a parametric framework. The example is inspired by recent approaches to quantify the dependence between progression-free survival, a common primary outcome in Phase 3 trials in oncology and overall survival. We complement these approaches by providing methods of statistical inference while at the same time working within a much more parsimonious modeling framework. Our approach is completely general and can be applied to other measures of dependence. We also discuss extensions to nonparametric inference. Our analytical results are illustrated using a large randomized clinical trial in breast cancer.

This paper considers methods for estimating the association between progression‐free and overall survival in oncology trials. Copula‐based, nonparametric, and illness‐death model–based methods are reviewed. In addition, the approach based on an underlying illness‐death model is generalized to allow general parametric models. The performance of these methods, in terms of bias and efficiency, is investigated through simulation and also illustrated using data from a clinical trial of treatments for colon cancer. The simulations suggest that the illness‐death model–based method provides good estimates of Kendall's τ across several scenarios. In some situations, copula‐based methods perform well but their performance is sensitive to the choice of copula. The Clayton copula is most appropriate in scenarios, which might realistically reflect an oncology trial, but the use of copula models in practice is questionable.

Progression-free survival is an increasingly popular end point in oncology clinical trials. A complete blinded independent central review (BICR) is often required by regulators in an attempt to reduce the bias in progression-free survival (PFS) assessment. In this paper, we propose a new methodology that uses a sample-based BICR as an audit tool to decide whether a complete BICR is needed. More specifically, we propose a new index, the differential risk, to measure the reading discordance pattern, and develop a corresponding hypothesis testing procedure to decide whether the bias in local evaluation is acceptable. Simulation results demonstrate that our new index is sensitive to the change of discordance pattern; type I error is well controlled in the hypothesis testing procedure, and the calculated sample size provides the desired power. Copyright © 2016 John Wiley & Sons, Ltd.

In oncology clinical trials, progression-free survival (PFS), generally defined as the time from randomization until disease progression or death, has been a key endpoint to support licensing approval. In the U.S. Food and Drug Administration guidance for industry, May 2007, concerning the PFS as the primary or co-primary clinical trial endpoint, it is recommended to have tumor assessments verified by an independent review committee blinded to study treatments, especially in open-label studies. It is considered reassuring about the lack of reader-evaluation bias if treatment effect estimates from the investigators' and independent review committees' evaluations agree. The agreement between these evaluations may vary for subjects with short or long PFS, while there exist no such statistical quantities that can completely account for this temporal pattern of agreements. Therefore, in this paper, we propose a new method to assess temporal agreement between two time-to-event endpoints, while the two event times are assumed to have a positive probability of being identical. This method measures agreement in terms of the two event times being identical at a given time or both being greater than a given time. Overall scores of agreement over a period of time are also proposed. We propose a maximum likelihood estimation to infer the proposed agreement measures using empirical data, accounting for different censoring mechanisms, including reader's censoring (event from one reader dependently censored by event from the other reader). The proposed method is demonstrated to perform well in small samples via extensive simulation studies and is illustrated through a head and neck cancer trial.

Among the surrogate endpoints for overall survival (OS) in oncology trials, progression-free survival (PFS) is more and more taking the leading role. Although there have been some empirical investigations on the dependence structure between OS and PFS (in particular between the median OS and the median PFS), statistical models are almost non-existing. This paper aims at filling this gap by introducing an easy-to-handle model based on exponential time-to-event distributions that describe the dependence structure between OS and PFS. Based on this model, explicit formulae for individual correlations are derived together with a lower bound for the correlation of OS and PFS, which is given by the fraction of the two medians for OS and PFS. Two methods on how to estimate the parameter of the model from real data are discussed. One method is based on a maximum-likelihood estimator whereas the other method uses a plug-in approach. Three examples from non-small cell lung cancer are considered. In the first example, the parameters of the model are determined and the estimated survival curce is compared with the observed one. The second example explains how to obtain sample size estimates for OS based on assumptions on median PFS and OS. Finally, the third example provides a way of modelling and quantifying confounding effects that might explain a levelling of differences in OS although a difference in PFS is observed.

In oncology clinical trials, overall survival, time to progression, and progression-free survival are three commonly used endpoints. Empirical correlations among them have been published for different cancers, but statistical models describing the dependence structures are limited. Recently, Fleischer et al. proposed a statistical model that is mathematically tractable and shows some flexibility to describe the dependencies in a realistic way, based on the assumption of exponential distributions. This paper aims to extend their model to the more flexible Weibull distribution. We derived theoretical correlations among different survival outcomes, as well as the distribution of overall survival induced by the model. Model parameters were estimated by the maximum likelihood method and the goodness of fit was assessed by plotting estimated versus observed survival curves for overall survival. We applied the method to three cancer clinical trials. In the non-small-cell lung cancer trial, both the exponential and the Weibull models provided an adequate fit to the data, and the estimated correlations were very similar under both models. In the prostate cancer trial and the laryngeal cancer trial, the Weibull model exhibited advantages over the exponential model and yielded larger estimated correlations. Simulations suggested that the proposed Weibull model is robust for data generated from a range of distributions.