Statistica Sinica 16(2006), 135-151

ASYMPTOTIC RESULTS FOR FITTING SEMIPARAMETRIC

TRANSFORMATION MODELS TO FAILURE TIME DATA

FROM CASE-COHORT STUDIES

Lan Kong$^1$, Jianwen Cai$^2$ and Pranab K. Sen$^2$

$^1$University of Pittsburgh and $^2$University of North Carolina at Chapel Hill

Abstract: Semiparametric transformation models are considered for failure time data from case-cohort studies, where the covariates are assembled only for a randomly selected subcohort from the entire cohort and additional cases outside the subcohort. We present the estimating procedures for the regression parameters and survival probability. The asymptotic properties of the resulting estimators are developed based on asymptotic results for U-statistics, martingales, stochastic processes and finite population sampling.

Key words and phrases: Asymptotic distribution, case-cohort design, consistency, finite population sampling, semiparametric transformation models, U-statistic.