The Cox proportional hazards (PH) model is a common statistical technique employed for analyzing time-to-event data. The assumption of proportional hazards, however, is not always appropriate in real applications. In cases where the assumption is not tenable, threshold regression (TR) and other survival methods, which do not require the PH assumption, are available and widely used. These alternative methods generally assume that the study data constitute simple random samples. In particular, threshold regression has not been studied in the setting of complex surveys that involve 1) differential selection probabilities of study subjects and 2) intra-cluster correlations induced by multistage cluster sampling. In this paper, we extend TR procedures to account for complex sampling designs. The pseudo-maximum likelihood estimation technique is applied to estimate the TR model parameters. Computationally efficient Taylor linearization variance estimators that consider both the intra-cluster correlation and the differential selection probabilities are developed. The proposed methods are evaluated using simulation experiments with various complex designs and illustrated empirically using mortality-linked NHANES III Phase II genetic data.
This is a joint work with Yan Li, Tao Xiao, and Dandan Liao. The manuscript has recently been accepted for publication in the journal of Statistics in Medicine.