Non-parametric Bayesian prediction of landmark times for analysis of failure-time data
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Abstract
In clinical trials with failure-time primary outcomes, also known as "event-driven" designs, the statistical information is determined by total observed events. Examples of failure-time clinical trial endpoints include: time to death and time to disease progression. In trials with event-driven designs, the interim and final analyses are performed after a pre-specified number of events have been observed, based on a priori design considerations, rather than after observing patients for a pre-specified period of time.
The timing of these analyses represent important milestones in the conduct of the study. In particular, if a trial requires review of interim analyses by a Data Monitoring Committee (DMC), convening the DMC members requires much advance planning and effort. In addition, advanced knowledge of when these milestones will occur can allow trial sponsors to make informed decisions regarding resources and financial planning. It is therefore of interest to predict when a pre-specified number of events will be observed based on accumulating data.
Parametric and semi-parametric methods have been proposed for event prediction when data are right censored. In cases when the underlying failure time distribution is unknown or accumulated events are relatively sparse, these methods may not provide accurate or efficient prediction. We propose a method to predict the number of events that is a fully Bayesian non-parametric approach in modeling the survival probabilities that is more flexible and generalizes to interval censored data. We use a Gibbs sampler to sample from the posterior of the survival distribution to obtain point and interval estimates for the specified number of events.
We compare the accuracy and precision of this approach to proposed parametric and semi-parametric methods under a variety of data generating mechanisms, beginning with right-censored data. We then extend the study to interval-censored data, comparing the methods under data generated from varying assessment intervals. Finally we consider the scenario in which we are blinded to treatment assignment, incorporating a Bayesian approach to determine the probability of membership to a particular treatment group. We demonstrate the proposed method offers greater flexibility and has the ability to match or outperform existing methods under multiple clinical trial scenarios.