Statistical inference for logistic partially linear model under two-phase sampling design

Proper inferences are of great interest to study investigators dealing with data from biased sampling designs. Within the framework of the logistic partially linear model, we address an inference problem for data collected using an innovative two-phase sampling design proposed by Wang et al., where certain covariates are only available in the second-phase. B-splines are used to approximate the nonparametric component, and a pseudo-likelihood method is employed to estimate the regression parameters. We derive the large sample properties of the proposed estimators, further illustrated through simulation studies. We apply the proposed procedure to analyze a real dataset from biomedical research to assess its practical application.