The Cox proportional hazards (PH) model is a common statistical technique used for analyzing time-to-event data. The assumption of PH, 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, TR has not been studied in the setting of complex surveys that involve (1) differential selection probabilities of study subjects and (2) intracluster 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 intracluster correlation and the differential selection probabilities are developed. The proposed methods are evaluated by using simulation experiments with various complex designs and illustrated empirically by using mortality-linked Third National Health and Nutrition Examination Survey Phase II genetic data.
Keywords: cox proportional hazard; cure rate; intracluster correlation; pseudo-maximum likelihood estimation; stratified multistage sampling.
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