Competing risks quantile regression at work: in-depth exploration of the role of public child support for the duration of maternity leave

Abstract

Despite its emergence as a frequently used method for the empirical analysis of multivariate data, quantile regression is yet to become a mainstream tool for the analysis of duration data. We present a pioneering empirical study on the grounds of a competing risks quantile regression model. We use large-scale maternity duration data with multiple competing risks derived from German linked social security records to analyse how public policies are related to the length of economic inactivity of young mothers after giving birth. Our results show that the model delivers detailed insights into the distribution of transitions out of maternity leave. It is found that cumulative incidences implied by the quantile regression model differ from those implied by a proportional hazards model. To foster the use of the model, we make an R-package (cmprskQR) available. ARTICLE HISTORY

Quantile Regression Models and Their Applications: A Review

“…Other R packages are also available for specific QR topics. For example, R package "cmprskQR" [69] is developed for analysis of competing risks using QR; package "lqmm" [107], and "qrLMM" [108], deal mainly with longitudinal data via QR-based linear or non-linear mixed-effects models. SAS currently also includes a "quantreg" procedure, which is similar as the R "quantreg" package.…”

“…Peng and Huang [60] developed an estimator which is very close to Nelson-Aalen estimator. Most recently, great work is still expanding this area to recurrent events [61][62][63], various censoring types [64][65][66], competing risks [65,[67][68][69].…”