Cure rate quantile regression accommodating both finite and infinite survival times

Abstract

In survival analysis a proportion of patients may be cured by the treatment, and thus they become risk‐free of the event of interest and their survival times change to infinity. The existence of such a survival fraction often makes the underlying population more heterogeneous and heavily right‐skewed. Compared with the traditional mean‐ or hazard‐based regression methods, quantile regression is more suitable for such survival data as it is more robust against outliers or infinite survival times. Moreover, it offers a comprehensive assessment of the covariate effects on the survival times at different quantile levels. We propose a new cure rate quantile regression model for the entire population including both finite and infinite survival times. By invoking non‐parametric functional estimation an iterative algorithm is developed to estimate the cure rate parameters. The scheme of redistribution‐of‐mass to the right for censored data is adopted to estimate the quantile regression parameters. The consistency and asymptotic normality of the proposed estimators are established. Extensive simulation studies are conducted to evaluate the finite‐sample performance of the proposed method, which is further illustrated with a phase III melanoma clinical trial study. The Canadian Journal of Statistics 45: 29–43; 2017 © 2016 Statistical Society of Canada

Quantile Regression for Survival Data

“…Due to space limitations, we omit many important relevant method developments. These include, but are not limited to, cure rate quantile regression methods (Wu & Yin 2013, 2017a and censored quantile regression methods attending to regression quantile monotonicity across quantile levels, such as semiparametric copula quantile regression (De Backer et al 2017). Some important problems not covered in this article but worth attention are quantile regression for survival data with high-dimensional covariates, survival data with time-dependent covariates, and survival data with missing covariates.…”