Regression analysis of doubly truncated data based on pseudo-observations

• Published in: Journal of the Korean Statistical Society Vol. 50; no. 4; pp. 1197 - 1218
• Main Author: Shen, Pao-sheng
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.12.2021; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; Pseudo-observations; Generalized estimating equation; Double truncation; Jackknife
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-021-00113-9

Doubly truncated data arise when an individual is potentially observed only if its failure-time lies within a certain interval, unique to that individual. In this paper, we consider the pseudo-observations approach for estimating regression coefficients when data is subject to double truncation. The pseudo-observations generated from the nonparametric maximum likelihood estimates (NPMLE) of the survival function are used as response variables in a generalized estimating equation to estimate the parameters of the model. We look at two estimators for regression parameters of survival probabilities based on different ways of defining pseudo-observations, namely, the simple pseudo-observations (SPO) and stopped pseudo-observations (STPO). We establish asymptotic properties of the two estimators under some conditions. Simulations results show that the proportion of failed estimation based on STPO are smaller than that based on SPO. The estimator based on STPO performs adequately for finite samples while the estimator based on SPO can be very unstable when sample size is not large enough.