Non-Susceptibility and Heteroscedasticity in Event History Regression Models

Abstract

Attributable to genetic and environmental factors of the disease etiology, study subjects may not be susceptible to the disease of interest. An underlying assumption in the survival analysis is that all the study subjects are susceptible to the event. In general, this assumption does not adequately hold in event history analysis for studying time to an event other than death. In the analysis of non-susceptibility as a general phenomenon in biomedical, epidemiological and sociological research, recent studies proposed mixture models of regression analysis to formulate the probability of occurrence of an event and the time distribution of event occurrence. Lu and Ying (2004) proposed semiparametric transformation cure models with a unified estimating approach. We add a heteroscedastic component in their model to account for multiple crossings of survival curves, and provide an estimating procedure with a higher efficiency. Using the same ideas, we also consider the mean residual life regression models with the cured fraction. These works deal with only right censored data. To facilitate practical issues of both interval and right censored data, we present mixture parametric regression models and apply them to analyze age-at-onset studies and willingness-to-pay studies in a few epidemiological research projects in Taiwan.