Goodness of Fit Tests for Randomly Truncated Data

Abstract

For randomly truncated data, the product-limit estimate of the survival curve is the maximum likelihood estimate (MLE). However, it is no longer true when the truncation mechanism is parameterized. The semiparametric model provides an alternative estimate for the survival curve. Let G be the distribution function of the truncation variable. In this article, we propose a chi-sqaure test to test the goodness of fit under random truncation. Both the simple and composite null hypotheses are considered. The size and power of the chi-square test are evaluated for small and moderate sample sizes using Monte Carlo simulations. A real life data is also presented.