Failure-Time Mixture Models: Yet Another Way to Establish Efficacy
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0092-861512001 Copyright 0 2001 Drug Information Association Inc.
FAILURE-TIME MIXTURE MODELS: YET ANOTHER WAY TO ESTABLISH EFFICACY* KALLAPPAM. KOTI, PHD United States Food and Drug Adminisuation, Rockville, Maryland
We propose to use mixture survival models to establish the efJicacy of the trial treatment. In particular; we consider the lognormal distribution to model the right-censored event time and a logistic regression for the incidence part of the model. The model attempts to estimate simultaneously the effects of treatments on the acceleratioddeceleration of the timing of a given event and the surviving fraction-the proportion of the population for which the event may never occu): We use the SAS/lML subroutine NLPTR to obtain the maximum likelihood estimates of the model parameters. The estimates of the standard errors of the parameter estimates are computed from the inverse of the observed information matrix. We use the Cox-Snell residual plot based on the unconditional survivor functionfor evaluating goodness-of-fit of the model. The principal research hypothesis will be that under the trial treatment, the time-to-event will be more deceleratedaccelerated compared to the control, given that the event occurs. We suggest that this methodology could be considered as a means to establish efficacy. We emphasize that there can be a substantial advantage to using mixture models even when the log-rank test is valid and significant. Data on overall survival time from a typical colorectal cancer clinical trial are used to illustrate the procedure. Key Words: Clinical trial; Accelerated failure-time; Surviving fraction; Wald test
INTRODUCTION TYPICALLY, IN CLINICAL trials with a short treatment phase, the censoring is absent or minimal and in long-term studies, due to withdrawals, the survival data are likely to be heavily censored. In most cases, the KaplanMeier estimator is used to estimate the survival function and the log-rank (or the Wilcoxon) test is used to compare the test drug
Reprint address: Kallappa M. Koti, PhD, HFD-710. Room 15845, United States Food and Drug Administration, 5600 Fishers Lane, Rockville, MD 20857. Email: [email protected]. *The views expressed here are those of the author and not necessarily those of the United States Food and Drug Administration.
with placebo. The primary practical defect of the Kaplan-Meier estimator is that it underestimates the tail of the survival function for heavily right-censored survival data (1). A study of the bias of the Kaplan-Meier estimator for right-censored failure-time data is provided in Anderson et al. (2). The log-rank test tests the null hypothesis y~ = 1 under the proportional hazards model h,(t) = \v x b(t) where h,(t) and h(t) are hazard functions for the study drug and placebo, respectively. However, for alternatives outside this class, the logrank test may have poor properties (3). Miller (4) examined the asymptotic efficiency of the Kaplan-Meier product-limit estimator, relative to the maximum likelihood estimator of a parametric survi
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