Subgroup Analysis with Time‐to‐Event Data Under a Logistic‐Cox Mixture Model

Abstract

Subgroup detection has received increasing attention recently in different fields such as clinical trials, public management and market segmentation analysis. In these fields, people often face time‐to‐event data, which are commonly subject to right censoring. This paper proposes a semiparametric Logistic‐Cox mixture model for subgroup analysis when the interested outcome is event time with right censoring. The proposed method mainly consists of a likelihood ratio‐based testing procedure for testing the existence of subgroups. The expectation–maximization iteration is applied to improve the testing power, and a model‐based bootstrap approach is developed to implement the testing procedure. When there exist subgroups, one can also use the proposed model to estimate the subgroup effect and construct predictive scores for the subgroup membership. The large sample properties of the proposed method are studied. The finite sample performance of the proposed method is assessed by simulation studies. A real data example is also provided for illustration.

Subgroup detection and sample size calculation with proportional hazards regression for survival data

“…We have conducted simulations to compare with the method of Wu et al (denoted by EM Test). We consider simulation settings with the baseline models B1 and B2, η =0,0.2,and0.5, and sample size N =1000.…”

“…We consider simulation settings with the baseline models B1 and B2, η =0,0.2,and0.5, and sample size N =1000. Note that under the baseline model B1, the considered logistic‐Cox mixture model of Wu et al is correctly specified while it is misspecified under B2. The simulation results are summarized in Table .…”

“…To estimate the mean (12) and covariance function (13), we generate the grid points from −1 to 1 and the true change-plane parameter 0 is set to be −0.5, 0, or 0.5. In Table 5, we calculate the sample size that gives 90% power at the 0.05 level of significance.…”

“…These studies mainly focus on uncensored data. Wu et alextended the method of Shen and He to a logistic‐Cox regression for survival data. However, it requires strong parametric assumptions for covariate effects as in the work of Shen and He …”

Validating effectiveness of subgroup identification for longitudinal data

“…Shen and He 16 developed a procedure using a structured logistic-normal mixture model that not only classified the data but also tests for the existence of subgroups. This work was extended by Wu et al 17 for time-to-event data with the semiparametric logistic-cox mixture model. While these methods have advanced work in subgroup analysis, specifications for the data may not always be met.…”