Semiparametric current status regression model using kernel smoothing with application to HIV study

Abstract

In current status regression analysis, the responses are indirectly observed and the regression coefficients can not be estimated using the commonly used least squares estimate, instead semiparametric maximum likelihood estimate is used. As the nonparametric component estimate is a non-smooth step function, the regression coefficients are bundled inside it, so the asymptotic distribution of the estimated coefficients is an open problem. To overcome this issue, smoothed versions are proposed in the literature; however, in these versions the score equation for the regression coefficients is still not continuous, the estimate is not an exact solution of the score equation, and zero-crossing is used instead. Here we propose a modified smoothed version to make the score equation a continuous function of the regression coefficients, and thus the estimator is the exact solution of the score equation. Asymptotic distribution of the resulting estimators can be shown as in our related papers. Simulation studies are conducted to evaluate the performance of the method, and it demonstrates superior finite sample behavior. For illustration, we applied the method to the analysis of a real data set from a HIV study.