#### Title

Nonparametric Estimation for a Form of Doubly Censored Data, with Application to Two Problems in AIDS

#### 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. Two such problems are considered here, estimation of the distribution of time or number of sexual contacts between infection of an indidiual (an index case) and transmission of HIV to their sexual partner, and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody. Data regrding these two problems are available from certain partner studies, and the HIV Lookback Study. In both cases the statistical development is complicated by the fact that the times of both events are interval censored, so that the length of time between the events is never observed exactly. Nonparametric methods for estimation of the interval length distibution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution; particular attention is paid to identifiability issues.

#### Disciplines

Disease Modeling | Statistical Models | Survival Analysis

#### Suggested Citation

Jewell, Nicholas P.; Malani, Hina M.; and Vittinghoff, Eric, "Nonparametric Estimation for a Form of Doubly Censored Data, with Application to Two Problems in AIDS" (November 1992). *U.C. Berkeley Division of Biostatistics Working Paper Series.* Working Paper 38.

http://biostats.bepress.com/ucbbiostat/paper38

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## Comments

Published in Journal of the American Statistical Association (March 1994), 89(425), Applications and Case Studies, pp. 7-18.