A gradient boosting decision tree based estimation method for the mixture cure model

Cure models are useful tools for analyzing censored survival data with a cured fraction. However, existing semiparametric estimation methods still rely on restrictive parametric assumptions, and existing nonparametric estimation methods only work with single covariates. In this work, we propose a gradient boosting decision tree based method to estimate the mixture cure model. The new method inherits the features of the original gradient boosting decision tree method and provides more accurate estimates of the cure probability and the relative risk for uncured subjects than existing methods when there are no a priori parametric assumptions on the forms of complex covariate effects in the model. This is demonstrated with small mean square errors in the estimates of the cure probability, relative risk score, and survival function in a simulation study with large samples. The method also has the potential to deal with high-dimensional covariates. The proposed method is illustrated with a large sample study of colon cancer.