Stephanie Werren: Pseudo-Likelihood Methods for the Analysis of Interval Censored Data

Adviser: Prof. Dr. Marloes Maathuis

March 2011

Abstract:

We study the work of Sen and Banerjee (2007), focusing on their method based on a
pseudo-likelihood-ratio statistic to obtain point-wise confidence intervals for null hypotheses on the distribution function of the survival time in a mixed-case interval censoring model. Mixed-case interval censored data arises naturally in clinical trials and a variety of other applied fields. The setting of such a model is one where n independent individuals are under study and each individual is observed a random number of times at possibly different observation time-points. At each observation time it is recorded whether an event happened or not and one is interested in estimating the distribution function of the time to such an event, also called failure. However, the time to failure cannot be observed directly, but is subject to interval censoring. That is, one only obtains the information whether failure occurred between two successive observation time-points or not.

We extend the results from Sen and Banerjee (2007) to mixed-case interval censored data with competing risks. This is data, where the failure is caused from one of R risks, where R ∈ N is fixed. We define a naive pseudo-likelihood estimator for the distribution function of the event that the system failed from risk r for each r = 1, 2, . . . ,R, analogous to Jewell, Van der Laan, and Henneman (2003). We prove consistency and the asymptotic limit distribution of the naive estimators and present a method to draw point-wise confidence intervals for these sub-distribution functions based on the pseudo-likelihood-ratio statistic introduced by Sen and Banerjee (2007).

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