CONSISTENCY AND ASYMPTOTIC NORMALITY OF ESTIMATORS IN A PROPORTIONAL HAZARDS MODEL

WITH INTERVAL CENSORING AND LEFT TRUNCATION

SOMNATH DATTA^{1}*, GLEN A. SATTEN^{2} AND JOHN M. WILLIAMSON^{2}**

1Department of Statistics, University of Georgia, Athens, GA 30602, U.S.A. 2Division of HIV/AIDS Prevention: Surveillance and Epidemiology, MS E-48, National Center for HIV/AIDS, STD and TB Prevention, Centers for Disease Control and Prevention, Atlanta, GA 30333, U.S.A.

(Received August 18, 1997; revised November 12, 1998)

Abstract. Satten et al. (1998, J. Amer. Statist. Assoc., 93, 318–327) proposed an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations which are the score equations for the full data proportional hazards model, averaged over all rankings of imputed failure times consistent with the observed censoring intervals. In this paper, we extend this approach to incorporate data that are left-truncated and right censored (dynamic cohort data). Consistency and asymptotic normality of the estimators obtained in this way are established.

Key words and phrases: Cox model, current status data, interval censoring, left truncation, survival analysis.