#### Title

Double Censoring and All That: Problems in Biostatistical Inference

#### Abstract

In many epidemiologic studies of Human Immunodeficiency Virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. In many such cases, statistical estimation of properties of this distribution is complicated by the fact that observation of the times of both events is subject to interval censoring so that the length of time between the events is never observed exactly. Following De Gruttola and Lagakos (1989), we call such data doubled censored. We describe several kinds of studies of the natural history of HIV disease that give rise to doubly censored data and consider estimation of the distribution function of the time interval between events in some special cases. The analysis of covariate effects in these situations is also briefly addressed. The estimation techniques that we discuss provide illustrations of several general statistical problems of current interest including semiparametric model estimation, mixture models, partially or semi-linear versions of the generalized linear models and asymptotics.

#### Disciplines

Disease Modeling | Statistical Methodology | Statistical Theory | Survival Analysis

#### Suggested Citation

Jewell, Nicholas P., "Double Censoring and All That: Problems in Biostatistical Inference" (January 1994). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 43.

http://biostats.bepress.com/ucbbiostat/paper43

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## Comments

Complete text appears in Proceedings of CIMAT Conference on Biostatistics & Statistical Inference, V. Perez-Abreu and D. Sprott (eds.), 1994.