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.
Zucker, D.M. and Lakatos, E. (1990) Weighted Log Rank Type Statistics for Comparing Survival Curves When There Is a Time Lag in the Effectiveness of Treatment. Biometrika, 77, 853-864. http://dx.doi.org/10.1093/biomet/77.4.853
He, P., Kong, G. and Su, Z. (2013) Estimating the Survival Functions for Right-Censored and Interval-Censored Data with Piecewise Constant Hazard Functions. Contemporary Clinical Trials, 36, 122-127.
Muller, H.G. and Wang, J.L. (1990) Nonparametric Analysis of Changes in Hazard Rates for Censored Survival Data: An Alternative to Change-Point Models. Biometrika, 77, 305-314. http://dx.doi.org/10.1093/biomet/77.2.305
Sertkaya, D. and Sözer, M.T. (2003) A Bayesian Approach to the Constant Hazard Model with a Change Point and an Application to Breast Cancer Data. Hacettepe Journal of Mathematics and Statistics, 32, 33-41.?
Urschel, H.C., Hanselka, L.L., Gromov, I., White, L. and Baron, M. (2007) Open-Label Study of a Proprietary Treatment Program Targeting Type a γ-Aminobutyric Acid Receptor Dysregulation in Methamphetamine Dependence. Mayo Clinic Proceedings, 82, 1170-1178. http://dx.doi.org/10.4065/82.10.1170
Yao, Y.-C. (1987) Approximating the Distribution of the Maximum Likelihood Estimate of the Change-Point in a Sequence of Independent Random Variables. Annals of Statistics, 15, 1321-1328.
Barndorff-Nielsen, O.E. and Cox, D.R. (1984) Bartlett Adjustments to the Likelihood Ratio Statistic and the Distribution of the Maximum Likelihood Estimator. Journal of the Royal Statistical Society: Series B, 46, 483-495.