Covariate-adjusted quantile inference with competing risks

A mark-specific quantile regression model

Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

Competing risks survival data under middle censoring-An application to COVID-19 pandemic

Survival data is being analysed here under the middle censoring scheme, using specifically quantile function modelling under competing risks. The use of middle censoring scheme has been shown to be very appropriate under the COVID-19 pandemic scenario. Cause-specific quantile inference under middle censoring is employed. Such quantile inferences are obtained through cumulative incidence function based on cause-specific proportional hazards model. The baseline lifetime is assumed to follow a very general parametric model namely the Weibull distribution, and is independent of the censoring mechanism. We obtain estimates of the unknown parameters and cause specific quantile functions under classical as well as a Bayesian set-up. A Monte Carlo simulation study assesses the relative performance of the different estimators. Finally, a real life data analysis is given for illustration of the proposed methods.