  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.
