A Sexual Partnership Duration: Characterizing Sampling Conditions That Permit unbiased Estimation of Survivorship and Effect on It of Covariates

Partnership duration data are commonly obtained through surveys that collect information on relationships that are ongoing during a fixed time window. This sampling mechanism leads to duration data that are left truncated and right censored; such data have been analysed using the standard truncation product limit estimator (TPLE). In this paper, we describe a common sampling scheme for collecting sexual partnership data, discuss a key assumption required for the TPLE to be unbiased, and provide the conditions under which the nonparametric maximum likelihood estimator of the relationship duration distribution is unique and consistent. We also investigate the conditions required for the consistency of the regression coefcient from a Cox proportional hazards model that apply even when the distribution of duration is not completely identifiable due to restrictions on the support of the truncation distribution. Lastly, we will provide some illustrative examples on estimating distribution of most recent partnerships and present spline regression results based on partnership data collected from sexual behavior survey in Mochudi, Botswana.