Length-biased semi-competing risks models for cross-sectional data: an application to current duration of pregnancy attempt data.

Cross-sectional length-biased data arise from questions on the at-risk time for an event of interest from those who are at-risk but have yet to experience the event. For example, in the National Survey on Family Growth (NSFG), women who were currently attempting to become pregnant were asked how long they had been attempting pregnancy. Cross-sectional survival analysis methods use the observed at-risk times to make inference on the distribution of the unobserved time-to-failure. However, methodological gaps in these methods remain such as how to handle semi-competing risks. For example, if the women attempting pregnancy had undergone fertility treatment during their current pregnancy attempt. In this paper, we develop statistical methods that extend cross-sectional survival analysis methods to incorporate semi-competing risks. They can be used to estimate the distribution of the length of natural pregnancy attempts (i.e., without fertility treatment) while correctly accounting for women that sought fertility treatment prior to being sampled using cross-sectional data. We demonstrate our approach based on simulated data and an analysis of data from the NSFG. The proposed method results in separate survival curves for: time-to-natural-pregnancy, time-to-fertility treatment, and time-to-pregnancy after fertility treatment.