Analyzing Highly Correlated Chemical Toxicants Associated with Time to Pregnancy Using Discrete Survival Frailty Modeling Via Elastic Net

Understanding the association between mixtures of environmental toxicants and time-to-pregnancy (TTP) is an important scientific question as sufficient evidence has emerged about the impact of individual toxicants on reproductive health and that individuals are exposed to a whole host of toxicants rather than an individual toxicant. Assessing mixtures of chemicals effects on TTP poses significant statistical challenges, namely (i) TTP being a discrete survival outcome, typically subject to left truncation and right censoring, (ii) chemical exposures being strongly correlated, (iii) accounting for some chemicals that bind to lipids, (iv) non-linear effects of some chemicals, and (v) high percentage concentration below the limit of detection (LOD) for some chemicals. We propose a discrete frailty modeling framework (named Discnet) that allows selection of correlated exposures while addressing the issues mentioned above. Discnet is shown to have better and stable FN and FP rates compared to alternative methods in various simulation settings. We did a detailed analysis of the LIFE Study, pertaining to polychlorinated biphenyls and time-to-pregnancy and found that older females, female exposure to cotinine (smoking), DDT conferred a delay in getting pregnant, which was consistent across prior sensitivity analyses to account for LOD as well as non-linear associations.