Current duration data arise in cross-sectional studies from questions on the length of time from an initiating event to the time of interview. For example, in the National Survey on Family Growth, women who were considered at risk for pregnancy were asked (i) 'Are you currently attempting pregnancy?' and (ii) 'If yes, how many months have you been attempting to get pregnant?' The responses to (ii), referred to as the current durations, are length-biased because women with longer durations are more likely to answer yes to question (i) and therefore be included in the sample. Previous methods to analyze such data include continuous time nonparametric and parametric approaches. In this article, we propose a semiparametric Cox model and a piecewise constant baseline model (used to account for digit preference) to analyze grouped current duration data. We discuss and investigate through simulation studies, the robustness properties of the proposed methods when digit preference is present. Lastly, we present an analysis of the current duration data resulting from the 2002 National Survey on Family Growth. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.