A regularized estimation approach for case‐cohort periodic follow‐up studies with an application to HIV vaccine trials

Abstract

This paper discusses regression analysis of the failure time data arising from case‐cohort periodic follow‐up studies, and one feature of such data, which makes their analysis much more difficult, is that they are usually interval‐censored rather than right‐censored. Although some methods have been developed for general failure time data, there does not seem to exist an established procedure for the situation considered here. To address the problem, we present a semiparametric regularized procedure and develop a simple algorithm for the implementation of the proposed method. In addition, unlike some existing procedures for similar situations, the proposed procedure is shown to have the oracle property, and an extensive simulation is conducted and it suggests that the presented approach seems to work well for practical situations. The method is applied to an HIV vaccine trial that motivated this study.

A unified approach to variable selection for Cox’s proportional hazards model with interval-censored failure time data

“…which implies that fðÁÞ is a contraction mapping from ½1=K 0 ; K 0 qþ1 to itself with probability tending to 1. Hence, according to the contraction mapping theorem, there exists one unique fixed-pointb (ii) From equation (19)…”

“…23 The value of m can be chosen by the cross-validation method, and in practice, one may perform grid search over some possible range of m or fix m to be the closest integer to n0.25. 19 Note that here Bernstein polynomials are chosen simply because of their natural monotone property and simplicity. Instead it is apparent that one could alternatively use other smooth functions such as B -spline functions and the proposed method could be similarly developed.…”

“…For the variable selection based on interval-censored failure time data, two parametric procedures were developed in Scolas et al 17 and Wu and Cook, 18 and in particular, the latter assumed that the baseline hazard function is a piecewise function. Also Zhao et al 19,20 considered a special case of interval-censored data, case II intervalcensored data, and proposed a semiparametric procedure. Note that in terms of estimation and variable selection on the proportional hazards model, one significant difference between right-censored data and interval-censored data is that for the former, a simple partial likelihood function is available and commonly used as the objective function in a penalized procedure, while there does not exist such function for the latter and one has to work with a much more complicated objective function.…”

Variable Selection for Interval‐censored Failure Time Data

“…(2020) and Zhao et al . (2020b), who provided some justifications both numerically and theoretically.…”

“…Also, as mentioned earlier, the algorithm is available at the R package CoxICPen with setting the weight argument to be the π i s. In addition, Zhao et al . (2020b) showed that the method with the use of the ALASSO penalty function has the oracle property. A limitation of the method is that it only applies to the situation with p < n .…”