Inference with Bivariate Truncated Data

Authors: Quale C.M.; Laan M.J.v.d.

Source: Lifetime Data Analysis, Volume 6, Number 4, December 2000 , pp. 391-408(18)

Publisher: Springer

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Abstract:

In this paper we build on previous work for estimation of the bivariate distribution of the time variables T_{1} and T_{2}when they are observable only on the condition that one of the time variables, say T_{1}, is greater than (left-truncation) or less than (right truncation) some observed time variable C_{1}. In this paper, we introduce several results based on the Influence Curve (which we derive in this paper) of the NPMLE of the distributionF of (T_1,T_2) developed by van der Laan (van der Laan, 1996). Specifically we will: prove that the NPMLE is asymptotically equivalent to an estimator developed by Gürler (Gürler, 1997), derive the asymptotic distribution of the NPMLE based on its Influence Curve, present tests to determine the amount of dependence between T_1 and T_2, present the results of simulation studies that compare the NPMLE and Gürler's estimator and evaluate the performance of both the above mentioned tests and confidence intervals of Fbased on the asymptotic distribution of the NPMLE, and finally we will apply the methods in a data analysis in which we also point out practical issues that arise in the implementation of the estimator.

Keywords: bivariate truncation; non-parametric maximum likelihood; influence curves

Language: English

Document Type: Regular paper

Affiliations: 1: Dept. of Biostatistics, University of California at Berkeley

Publication date: 2000-12-01