Debiased machine learning  for logistic  partially linear mediation models with high-dimensional confounders

In this paper, we propose debiased machine learning strategies for estimating direct effect, indirect effect and total effect in logistic partially linear mediation models with high-dimensional confounders. To obtain asymptotically efficient estimators for the effects of interest,two Neyman-orthogonal score functions are proposed to remove regularization biascaused by the estimation of the nuisance functions.To address nonlinearity and unextractability of the logit link, double data splitting is applied to estimate nuisance functions and mitigate potential overfitting. Theoretically, we establish rigorous asymptotic properties for the proposed estimators of all three effects and derive their asymptotic normal distributions. The satisfactoryperformance of our proposed estimators is demonstrated by simulation results and a real-world PM2.5 concentration data from Beijing.