Abstract
Effects of many medical procedures appear after a time lag, when a significant change occurs in subjects’ failure rate. This paper focuses on the detection and estimation of such changes which is important for the evaluation and comparison of treatments and prediction of their effects. Unlike the classical change-point model, measurements may still be identically distributed, and the change point is a parameter of their common survival function. Some of the classical change-point detection techniques can still be used but the results are different. Contrary to the classical model, the maximum likelihood estimator of a change point appears consistent, even in presence of nuisance parameters. However, a more efficient procedure can be derived from Kaplan-Meier estimation of the survival function followed by the least-squares estimation of the change point. Strong consistency of these estimation schemes is proved. The finite-sample properties are examined by a Monte Carlo study. Proposed methods are applied to a recent clinical trial of the treatment program for strong drug dependence.
Highlights
Change-point models studied in clinical research usually refer to changes in the failure rate
A new alternative estimation procedure is proposed based on Kaplan-Meier estimation of the survival function [16] followed by the least-squares estimation of the change point
Throughout the paper, τ0 denotes the true value of the change point; Λ (τ ) is the log-likelihood ratio given the occurrence of a change point at τ ; τ, λ0, and λ1 are the maximum likelihood estimators of τ, λ0, and λ1, respectively; and τ, λ 0, and λ 1 are the proposed least squares estimators of τ, λ0, and λ1, respectively
Summary
Change-point models studied in clinical research usually refer to changes in the failure rate. When a subject passes the change point, the failure rate typically reduces, and the probability of the overall survival increases This situation is conceptually and mathematically different from the classical change-point model, see e.g. A new alternative estimation procedure is proposed based on Kaplan-Meier estimation of the survival function [16] followed by the least-squares estimation of the change point For this scheme, strong consistency of all the estimators is established. Proposed methods show significant change points in the survival function for both control and treatment groups the change in the treatment group occurs earlier, about two weeks after receiving the treatment In simple words, it appears that if a regular user of methamphetamine stays away from the drug for two weeks after starting the treatment program, the probability of relapse on any day thereafter reduces significantly. Lemmas, and corollaries are in the Appendix section
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