Semiparametric probit models with univariate and bivariate current-status data

Multivariate current-status data are frequently encountered in biomedical and public health studies. Semiparametric regression models have been extensively studied for univariate current-status data, but most existing estimation procedures are computationally intensive, involving either penalization or smoothing techniques. It becomes more challenging for the analysis of multivariate current-status data. In this article, we study the maximum likelihood estimations for univariate and bivariate current-status data under the semiparametric probit regression models. We present a simple computational procedure combining the expectation-maximization algorithm with the pool-adjacent-violators algorithm for solving the monotone constraint on the baseline function. Asymptotic properties of the maximum likelihood estimators are investigated, including the calculation of the explicit information bound for univariate current-status data, as well as the asymptotic consistency and convergence rate for bivariate current-status data. Extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes. We demonstrate the estimation procedure with two real data examples in the areas of diabetic and HIV research.