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Cure rate quantile regression accommodating both finite and infinite survival times
Author(s) -
Wu Yuanshan,
Yin Guosheng
Publication year - 2017
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11306
Subject(s) - quantile regression , statistics , covariate , quantile , mathematics , outlier , estimator , proportional hazards model , econometrics , population , asymptotic distribution , regression analysis , survival analysis , regression , medicine , environmental health
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