Heteroscedastic transformation cure regression models

Cure models have been applied to analyze clinical trials with cures and age‐at‐onset studies with nonsusceptibility. Lu and Ying (On semiparametric transformation cure model. Biometrika 2004; 91:331?‐343. DOI: 10.1093/biomet/91.2.331) developed a general class of semiparametric transformation cure models, which assumes that the failure times of uncured subjects, after an unknown monotone transformation, follow a regression model with homoscedastic residuals. However, it cannot deal with frequently encountered heteroscedasticity, which may result from dispersed ranges of failure time span among uncured subjects' strata. To tackle the phenomenon, this article presents semiparametric heteroscedastic transformation cure models. The cure status and the failure time of an uncured subject are fitted by a logistic regression model and a heteroscedastic transformation model, respectively. Unlike the approach of Lu and Ying, we derive score equations from the full likelihood for estimating the regression parameters in the proposed model. The similar martingale difference function to their proposal is used to estimate the infinite‐dimensional transformation function. Our proposed estimating approach is intuitively applicable and can be conveniently extended to other complicated models when the maximization of the likelihood may be too tedious to be implemented. We conduct simulation studies to validate large‐sample properties of the proposed estimators and to compare with the approach of Lu and Ying via the relative efficiency. The estimating method and the two relevant goodness‐of‐fit graphical procedures are illustrated by using breast cancer data and melanoma data. Copyright © 2016 John Wiley & Sons, Ltd.