The nonparametric maximum likelihood estimator in a class of doubly censored current status data models with application to partner studies

Abstract

SUMMARY The California Partners' Study is an ongoing investigation of heterosexual HIV-transmission in partners of infected index cases (Padian et al., 1987; Shiboski & Jewell, 1990). We consider a nonparametric maximum likelihood estimator of the distribution of the time T the partner is exposed to an infected index partner until infection based on doubly censored current status data. We provide a modified iterative weighted pool adjacent violator algorithm for computation of the nonparametric maximum likelihood estimator and show that the estimator converges at rate n- 3. In addition, we propose confidence intervals for smooth functionals of the distribution of T. Simulations show good performance of the algorithm and confidence intervals. We apply our methodology to the California Partners' Study and discuss the implications of our results for doubly censored current status data models with other known distributions of the origin.