Premium
Estimation in the Cox Proportional Hazards Model with Left‐Truncated and Interval‐Censored Data
Author(s) -
Pan Wei,
Chappell Rick
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00064.x
Subject(s) - mathematics , statistics , covariate , proportional hazards model , confidence interval , inference , econometrics , survival function , hazard ratio , nuisance parameter , estimating equations , regression analysis , likelihood function , maximum likelihood , survival analysis , estimator , computer science , artificial intelligence
Summary. 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, Biometrika 83 , 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, Biometrika 75 , 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.