The Nonparametric Maximum Likelihood Estimator in a Class of Doubly Censored Current Status Data Models with Application to Partner Studies

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van der Laan, Mark J.; Andrews, Chris
AIDS partner study; current status data; iterative weighted pool adjacent violator algorithm; Statistical Methodology; Statistical Theory
article description
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). In addition to the HIV-status of the partner at the recruiting time one also observes the initial time of the partnership and a lower bound for the infection time of the index case. Following Jewell, Malani & Vittinghoff (1994) we assume that the infection time of the index case is uniformly distributed over the interval determined by the lower bound and the recruiting time, but no further assumptions are made. We consider an NPMLE of the distribution of the time T the partner is exposed to an infected index partner until infection. We show that the model is a doubly censored current status data model as introduced in Jewell, Malani & Vittinghoff (1994) with a special known distribution of the origin. We provide a modified iterative Weighted Pool Adjacent Violator Algorithm for computation of the NPMLE. It is shown that the NPMLE converges. In addition, we propose confidence intervals for smooth functionals of the distribution of T. Simulations show good performance of the algorithm, confidence intervals and provide a practical comparison of this NPMLE with the NPMLE if all partnerships are already in existence at the infection time of the index case as used in Shiboski & Jewell (1990). We apply our methodology to the California Partners' Study. We discuss the implications of our results for doubly censored current status data models with other known distributions of the origin.