Joint modeling of survival and backwards recurrence outcomes: an analysis of factors associated with fertility treatment

The increase in methods focused on various types of survival outcomes has allowed practitioners to analyze data that are difficult or expensive to prospectively observe. Still, there are populations that are challenging to study. For example, obtaining a representative sample of couples attempting to become pregnant is difficult due to the dynamic nature of the population. This has led to an increase in the use of cross-sectional designs yielding backwards recurrent survival outcomes. In this paper, we consider the analysis of a survival outcome where subjects are observed if they are at-risk for a separate dependent survival outcome. The motivation for this problem is to determine which factors are associated with time-to-fertility-treatment (TTFT) among women currently attempting pregnancy in a cross-sectional sample. We propose appending a marginal accelerated failure time (AFT) model on TTFT with a conditional model on time-to-pregnancy (TTP) given TTFT to account for their dependence and avoid biases. We address challenges that arise due to the censoring of TTFT and the resulting increased computational complexity. The performance is validated via comprehensive simulation studies. We apply our approach to data from the National Survey of Family Growth to estimate the association insurance type has on TTFT, and estimate the impact of fertility treatment on TTP.