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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.

In biomedical studies, longitudinal processes are collected till time-to-event, sometimes on nested timescales (example, days within months). Most of the literature in joint modeling of longitudinal and time-to-event data has focused on modeling the mean or dispersion of the longitudinal process with the hazard for time-to-event. However, based on the motivating studies, it may be of interest to investigate how the cycle-level {\it geometric features} (such as the curvature, location and height of a peak), of a cyclical longitudinal process is associated with the time-to-event being studied. We propose a shared parameter joint model for a cyclical longitudinal process and a discrete survival time, measured on nested timescales, where the cycle-varying geometric feature is modeled through a linear mixed effects model and a proportional hazards model for the discrete survival time. The proposed approach allows for prediction of survival probabilities for future subjects based on their available longitudinal measurements. Our proposed model and approach is illustrated through simulation and analysis of Stress and Time-to-Pregnancy, a component of Oxford Conception Study. A joint modeling approach was used to assess whether the cycle-specific geometric features of the lutenizing hormone measurements, such as its peak or its curvature, are associated with time-to-pregnancy (TTP).

Retrospectively ascertained survival time may be subject to recall error. An example of discrete survival time with such recall error is time-to-pregnancy (TTP), the number of months non-contracepting couples require to get pregnant which is a measure of human fecundity. The epidemiological literature has demonstrated that retrospective TTP is subject to recall error and statistical models focusing on TTP have not accounted for the recall error. We propose a multistage model that utilizes women's retrospectively-reported TTP and associated certainty to estimate the TTP distribution. Our proposed model utilizes a discrete survival function that accounts for random heterogeneity arising from between women TTP data as well as a multinomial regression model to account for her certainty as accuracy may decline over time, i.e., depends on time since pregnancy in estimating the TTP distribution. Other novel features of the model include attention to whether the pregnancy was (un)planned as well as providing an approach to predict survival function for women without a reported TTP. Our model allows for the consideration of covariates for each of the underlying factors of (un)planned pregnancy, measure of certainty and TTP distribution. The proposed model is applicable for any discrete survival time when certainty in reporting may be a consideration. We use Monte Carlo simulations to assess the finite sample performance for the proposed estimators. We illustrate our proposed method using data from Upstate KIDS Study.

This report is designed to clarify a few points about the article "Semiparametric modeling of grouped current duration data with preferential reporting" by McLain, Sundaram, Thoma and Louis in Statistics in Medicine (McLain et al., 2014, hereafter MSTL) regarding using the methods under right censoring. In simulation studies, it has been found that bias can occur when right censoring is present. Current duration data normally does not have censored values, but censoring can be induced at a value, say tau, after which the data values are thought to be unreliable. As noted in MSTL, some right censored data require an assumption on the parametric form of the data beyond {\tau}. While this assumption was given in MSTL, the implications of the assumption were not sufficiently explored. Here we present simulations and evaluate the methods of MSTL under type I censoring, give some settings under which the method works well even in presence of censoring, state when the model is correctly specified and discuss the reasons of the bias., Comment: 7 pages