Statistical analyses of data from studies of human immunodeficiency virus (HIV) transmission in partners of infected individuals often focus on estimation of the per contact probability of virus transmission, or infectivity. Of particular interest is evaluating whether the infectivity changes during the course of a partnership and identifying factors that influence the infectiousness of the initially infected partner (called the index case) and the susceptibility of the uninfected partner. Estimation and inference are complicated by limitations in partner study data, which may include unknown time of infection for either or both partners and inaccurate or incomplete information on the number and frequency of contacts. Using techniques from survival analysis, we extend earlier work of Jewell and Shiboski by developing semiparametric models for partner study data that allow variation in the infectivity according to time since infection of the index case. These models provide a unifying framework for investigations of infectivity based on data from various types of partner studies. The necessary statistical methodology requires analysis of binary regression models with complementary log-log links, where components of the regression function are subject to smoothness or isotonicity constraints. The methods are illustrated on data sets from studies of heterosexual transmission.