Marginal cure rate models for long-term survivors - Chen, Jianfeng (Kansas State University, 2019)
Two-component mixture models for long-term survivors, known as cure rate models, have been widely used and intensively discussed in the literature. In most applications, much of attention has been put on interpreting the covariate effects on the two components of the model: the cure fraction and the conditional hazard rate. However, for this mixture model, it is very challenging to give a straightforward interpretation of covariate effects on the overall survival responses, especially when the covariates are shared by these two components of the model. By overall survival responses, we mean the population survival outcomes such as the overall survival rate or the overall instantaneous death rate. In our study, we propose two marginal cure rate models that can offer a general framework to investigate the covariate effects on the overall survival outcomes from the marginal perspective and, most importantly, provide nice interpretations. These two models are named as Marginal Mean Survival Rate Model and Marginal Mean Hazard Rate Model. Technically, novel reparameterizations are used to relate the covariates directly to the marginal mean survival rate or hazard rate. These parameterizations then can be purposely imposed into the likelihood function of a standard cure rate model and all parameters can be estimated via the regular likelihood approach. We evaluate the proposed marginal models extensively with simulation studies and further use the liver cancer data from the SEER registry as an illustration of the proposed model. Moreover, we propose a semi-parametric approach based on the Bernstein polynomials to relax the assumption of parametric baseline hazard for the noncured subpopulation. The performance of the proposed semi-parametric method is also evaluated through an extensive simulation study and illustrated with SEER liver cancer data. Finally, as motivated by the microarray data of breast cancer patients from The Cancer Genome Atlas (TCGA) program, we extend the proposed marginal mean hazard rate model to high-dimensional settings. We handle the high-dimensional covariates with the use of variable selection method based on LASSO-type penalized likelihood function. The model estimation can be easily done with a minimum programming effort by using the techniques of quadratic approximation and cyclic coordinate descent algorithm. The simulation results show that our approach for high-dimensional settings performs reasonably well in terms of low False Positive and False Negative Rates. We then apply our approach to a subset of TCGA microarray data for illustration.
Keywords: Marginal survival outcome; Mixture model; High-dimensional data; Variable selection; Berstein polynomial; Semi-parametric approach