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With the rapid development of new anti‐cancer agents which are cytostatic, new endpoints are needed to better measure treatment efficacy in phase II trials. For this purpose, Von Hoff (1998) proposed the growth modulation index (GMI), that is, the ratio between times to progression or progression‐free survival times in two successive treatment lines. An essential task in studies using GMI as an endpoint is to estimate the distribution of GMI. Traditional methods for survival data have been used for estimating the GMI distribution because censoring is common for GMI data. However, we point out that the independent censoring assumption required by traditional survival methods is always violated for GMI, which may lead to severely biased results. In this paper, we construct both nonparametric and parametric estimators for the distribution of GMI, accounting for the dependent censoring of GMI. Extensive simulation studies show that our nonparametric estimators perform well in practical situations and outperform existing estimators, and our parametric estimators perform better than our nonparametric estimators and existing estimators when the parametric model is correctly specified. A phase II clinical trial using GMI as the primary endpoint is provided for illustration. [ABSTRACT FROM AUTHOR]

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., (© 2019 John Wiley & Sons, Ltd.)

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., (© 2018 The Authors. Statistics in Medicine Published by 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. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within‐patient correlation between the outcomes and within‐hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster‐specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease‐free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study. [ABSTRACT FROM AUTHOR]

Summary: Multiple randomized controlled trials, each comparing a subset of competing interventions, can be synthesized by means of a network meta‐analysis to estimate relative treatment effects between all interventions in the evidence base. Here we focus on estimating relative treatment effects for time‐to‐event outcomes. Cancer treatment effectiveness is frequently quantified by analyzing overall survival (OS) and progression‐free survival (PFS). We introduce a method for the joint network meta‐analysis of PFS and OS that is based on a time‐inhomogeneous tri‐state (stable, progression, and death) Markov model where time‐varying transition rates and relative treatment effects are modeled with parametric survival functions or fractional polynomials. The data needed to run these analyses can be extracted directly from published survival curves. We demonstrate use by applying the methodology to a network of trials for the treatment of non‐small‐cell lung cancer. The proposed approach allows the joint synthesis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost‐effectiveness analyses. [ABSTRACT FROM AUTHOR]

The past decade has witnessed an increasing trend in utilizing external control data in clinical trials, especially in the form of synthetic control arms (SCA) derived from real‐world or historical trial data. Including such data in clinical trial analysis can improve trial feasibility and efficiency, provided the issues caused by non‐randomization and systematic differences are appropriately addressed. Current methodology development in this area focuses on establishing the comparability of patient baseline characteristics between arms, and more research is needed to ensure comparability of other elements such as endpoints. Motivated by the comparative analysis of SCA progression‐free survival (PFS) and trial arm PFS, we aim to address another important but little discussed issue for external time‐to‐event (TTE) data that depend on disease assessment schedules (DAS). Since DAS are generally inconsistent across different data sources, we propose a proper statistical inference framework that harmonizes the DAS through data augmentation by multiple imputation. We demonstrate through extensive simulations that the proposed framework is unbiased in estimating median TTE and hazard ratio, well controls the type I error and achieves desirable power for log‐rank test, while the unadjusted analysis can be biased and suffer from severe type I error inflation or power loss depending on the direction of the bias. Given the desirable performance, we recommend the proposed framework for comparative analysis using external DAS‐based TTE data in clinical trials. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A Bayesian biomarker‐based phase I/II design (BIPSE) is presented for immunotherapy trials with a progression‐free survival (PFS) endpoint. The objective is to identify the subgroup‐specific optimal dose, defined as the dose with the best risk‐benefit tradeoff in each biomarker subgroup. We jointly model the immune response, toxicity outcome, and PFS with information borrowing across subgroups. A plateau model is used to describe the marginal distribution of the immune response. Conditional on the immune response, we model toxicity using probit regression and model PFS using the mixture cure rate model. During the trial, based on the accumulating data, we continuously update model estimates and adaptively randomize patients to doses with high desirability within each subgroup. Simulation studies show that the BIPSE design has desirable operating characteristics in selecting the subgroup‐specific optimal doses and allocating patients to those optimal doses, and outperforms conventional designs. [ABSTRACT FROM AUTHOR]

A surrogate endpoint can be used instead of the most relevant clinical endpoint to assess the efficiency of a new treatment. Before being used, a surrogate endpoint must be validated based on appropriate methods. Numerous validation approaches have been proposed with the most popular used in a context of meta-analysis, based on a two-step analysis strategy. For two failure-time endpoints, two association measurements are usually used, Kendall's τ at the individual level and the adjusted coefficient of determination ( Rtrial,adj2 ) at the trial level. However, Rtrial,adj2 is not always available due to model estimation constraints. We propose a one-step validation approach based on a joint frailty model, including both individual-level and trial-level random effects. Parameters have been estimated using a semiparametric penalized marginal log-likelihood method, and various numerical integration approaches were considered. Both individual- and trial-level surrogacy were evaluated using a new definition of Kendall's τ and the coefficient of determination. Estimators' performances were evaluated using simulation studies and satisfactory results were found. The model was applied to individual patient data meta-analyses in gastric cancer to assess disease-free survival as a surrogate for overall survival, as part of the evaluation of adjuvant therapy. [ABSTRACT FROM AUTHOR]

Therapeutic advances in cancer mean that it is now impractical to performed phase III randomized trials evaluating experimental treatments on the basis of overall survival. As a result, the composite endpoint of progression-free survival has been routinely adopted in recent years as it is viewed as enabling a more timely and cost-effective approach to assessing the clinical benefit of novel interventions. This article considers design of cancer trials directed at the evaluation of treatment effects on progression-free survival. In particular, we derive sample size criteria based on an illness-death model that considers cancer progression and death jointly while accounting for the fact that progression is assessed only intermittently. An alternative approach to design is also considered in which the sample size is derived based on a misspecified Cox model, which uses the documented time of progression as the progression time rather than dealing with the interval censoring. Simulation studies show the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

Cancer clinical trials are routinely designed to assess the effect of treatment on disease progression and death, often in terms of a composite endpoint called progression-free survival. When progression status is known only at periodic assessment times, the progression time is interval censored, and complications arise in the analysis of progression-free survival. Despite the advances in methods for dealing with interval-censored data, naive methods such as right-endpoint imputation are widely adopted in this setting. We examine the asymptotic and empirical properties of estimators of the marginal progression-free survival functions and associated treatment effects under this scheme. Specifically, we explore the determinants of the asymptotic bias and point out that there is typically a loss in power of tests for treatment effects. [ABSTRACT FROM AUTHOR]