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Estimation in the Cox Proportional Hazards Model with Left-Truncated and Interval-Censored Data

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We show that the nonparametric maximum likelihood estimate (NPMLE) of the regression coefficient from the joint likelihood (of the regression coefficient and the baseline survival) works well for the Cox proportional hazards model with left-truncated and interval-censored data, but the NPMLE may underestimate the baseline survival. Two alternatives are also considered: first, the marginal likelihood approach by extending Satten (1996, Biometrika83, 355–370) to truncated data, where the baseline distribution is eliminated as a nuisance parameter; and second, the monotone maximum likelihood estimate that maximizes the joint likelihood by assuming that the baseline distribution has a nondecreasing hazard function, which was originally proposed to overcome the underestimation of the survival from the NPMLE for left-truncated data without covariates (Tsai, 1988, Biometrika75, 319–324). The bootstrap is proposed to draw inference. Simulations were conducted to assess their performance. The methods are applied to the Massachusetts Health Care Panel Study data set to compare the probabilities of losing functional independence for male and female seniors.

Keywords: Bootstrap; Gibbs sampler; Gradient projection; Joint likelihood; Marginal likelihood; Monotone MLE; NPMLE

Document Type: Research Article


Affiliations: 1: Division of Biostatistics, School of Public Health, University of Minnesota, MMC 303, Minneapolis, Minnesota 55455, U.S.A., Email: 2: Departments of Biostatistics and Statistics, University of Wisconsin, 600 Highland Avenue-K6/446 CSC, Madison, Wisconsin 53792, U.S.A.

Publication date: 2002-03-01

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