Identification of subgroups via partial linear regression modeling approach.

In clinical trials, treatment effects often vary from subject to subject. Some subjects may benefit more than others from a specific treatment. One of the aims of subgroup analysis is to identify if there are subgroups of subjects with differential treatment effects. As in standard analysis, we first test if subgroups with differential treatment effects exist; if they do, we classify the subjects into different subgroups based on their covariate profiles; otherwise, we conclude no subgroups have differential treatment effects in this population. Existing methods utilize regression models, particularly linear models, for such analysis. However, in practice, not all effects of covariates on responses are linear. To address this issue, the article proposes a more flexible model, the partial linear model with a nonlinear monotone function to describe some specific effects of covariates and with a linear component to describe the effects of other covariates, develops model-fitting algorithm and derives model asymptotics. We then utilize the Wald statistic to test the existence of subgroups and the Neyman-Pearson rule to classify subjects into the subgroups. Simulation studies are conducted to evaluate the finite sample performance of the proposed method by comparing it with the commonly used linear models. Finally, we apply the methods to analyzing a real clinical trial.