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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).

Equivocal findings have been reported on the association between maternal depression and children's growth, possibly because of the limited attention to its disproportionate impact by child sex. The relationship between the timing of maternal depression and children's growth was assessed in a population-based prospective birth cohort, with particular attention to sex differences.The Upstate KIDS Study comprised 4,394 children followed through 3 years of age from 2008 to 2010. Maternal depression was measured antenatally by linkage with hospital discharge records before delivery and postnatally by depressive symptoms reported from questionnaires. Children's growth was measured by sex- and age-specific weight, height, weight for height, and BMI. Adjusted linear mixed effects models were used to estimate growth outcomes for the full sample and separately by plurality and sex.Antenatal depression was associated with lower weight for age (-0.24 z score units; 95% confidence interval [CI]: -0.43, -0.05) and height for age (-0.26 z score units; 95% CI: -0.51, -0.02) among singleton boys. Postnatal depressive symptoms were associated with higher weight for height (0.21 z score units; 95% CI: 0.01, 0.42) among singleton girls.The findings of this study suggest that antenatal depression was associated with lower weight and smaller height only for boys, whereas postnatal depressive symptoms were associated with higher weight for height only for girls. The timing of depression and the mechanisms of sex-specific responses require further examination.

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

Menstrual cycle length (MCL) has been shown to play an important role in couple fecundity, which is the biologic capacity for reproduction irrespective of pregnancy intentions. However, a comprehensive assessment of its role requires a fecundity model that accounts for male and female attributes and the couple's intercourse pattern relative to the ovulation day. To this end, we employ a Bayesian joint model for MCL and pregnancy. MCLs follow a scale multiplied (accelerated) mixture model with Gaussian and Gumbel components; the pregnancy model includes MCL as a covariate and computes the cycle-specific probability of pregnancy in a menstrual cycle conditional on the pattern of intercourse and no previous fertilization. Day-specific fertilization probability is modeled using natural, cubic splines. We analyze data from the Longitudinal Investigation of Fertility and the Environment Study (the LIFE Study), a couple based prospective pregnancy study, and find a statistically significant quadratic relation between fecundity and menstrual cycle length, after adjustment for intercourse pattern and other attributes, including male semen quality, both partner's age, and active smoking status (determined by baseline cotinine level 100 ng/mL). We compare results to those produced by a more basic model and show the advantages of a more comprehensive approach.

Effect estimates of paternal urinary BPA, phthalate quartiles and mean change in birth outcomes, with no observed statistical significance, LIFE Study, 2005-2009. (DOCX 26 kb)

Effect estimates of maternal urinary BPA, phthalate quartiles and mean change in birth outcomes, with no observed statistical significance, LIFE Study, 2005-2009. (DOCX 21 kb)

Distribution of birth outcomes by infant sex, LIFE Study, 2005-2009. (PDF 19 kb)

Critical data gaps remain regarding infertility treatment and child development. We assessed the utility of a birth certificate registry for developing a population cohort aimed at answering such questions.We utilised the Upstate New York livebirth registry (n = 201,063) to select births conceived with (n = 4024) infertility treatment or exposed infants, who were then frequency-matched by residence to a random sample of infants conceived without (n = 14,455) treatment or unexposed infants, 2008-10. Mothers were recruited at 2-4 months postpartum and queried about their reproductive histories, including infertility treatment for comparison with birth certificate data. Overall, 1297 (32%) mothers of exposed and 3692 of unexposed (26%) infants enrolled.Twins represented 22% of each infant group. The percentage of infants conceived with/without infertility treatment was similar whether derived from the birth registry or maternal report: 71% none, 16% drugs or intrauterine insemination, and 14% assisted reproductive technologies (ART). Concordant reporting between the two data sources was 93% for no treatment, 88% for ART, and 83% for fertility drugs, but differed by plurality. Exposed infants had slightly (P 0.01) earlier gestations than unexposed infants (38.3 ± 2.8 and 38.7 ± 2.7 weeks, respectively) based upon birth certificates but not maternal report (38.7 ± 2.7 and 38.7 ± 2.9, respectively). Conversely, mean birthweight was comparable using birth certificates (3157 ± 704 and 3194 ± 679 g, respectively), but differed using maternal report (3167 ± 692 and 3224 ± 661, respectively P 0.05).The birth certificate registry is a suitable sampling framework as measured by concordance with maternally reported infertility treatment. Future efforts should address the impact of factors associated with discordant reporting on research findings.

BACKGROUND:: Environmental chemicals may be associated with endometriosis. No published research has focused on the possible role of perfluorochemicals (PFCs) despite their widespread presence in human tissues. METHODS:: We formulated two samples. The first was an operative sample comprising 495 women aged 18-44 years scheduled for laparoscopy/laparotomy at one of 14 participating clinical sites in the Salt Lake City or San Francisco area, 2007-2009. The second was a population-based sample comprising 131 women matched to the operative sample on age and residence within a 50-mile radius of participating clinics. Interviews and anthropometric assessments were conducted at enrollment, along with blood collection for the analysis of nine PFCs, which were quantified using liquid chromatography-tandem mass spectrometry. Endometriosis was defined based on surgical visualization (in the operative sample) or magnetic resonance imaging (in the population sample). Using logistic regression, we estimated odds ratios (ORs) and 95% confidence intervals (CIs) for each PFC (log-transformed), adjusting for age and body mass index, and then parity. RESULTS:: Serum perfluorooctanoic acid (PFOA; OR = 1.89 [95% CI = 1.17-3.06]) and perfluorononanoic acid (2.20 [1.02-4.75]) were associated with endometriosis in the operative sample; findings were moderately attenuated with parity adjustment (1.62 [0.99-2.66] and 1.99 [0.91-4.33], respectively). Perfluorooctane sulfonic acid (1.86 [1.05-3.30]) and PFOA (2.58 [1.18-5.64]) increased the odds for moderate/severe endometriosis, although the odds were similarly attenuated with parity adjustment (OR = 1.50 and 1.86, respectively). CONCLUSIONS:: Select PFCs were associated with an endometriosis diagnosis. These associations await corroboration. Copyright © 2012 by Lippincott Williams & Wilkins.

Buck Louis GM, Schisterman EF, Sweeney AM, Wilcosky TC, Gore-Langton RE, Lynch CD, Boyd Barr D, Schrader SM, Kim S, Chen Z, Sundaram R, on behalf of the LIFE Study. Designing prospective cohort studies for assessing reproductive and developmental toxicity during sensitive windows of human reproduction and development – the LIFE Study. Paediatric and Perinatal Epidemiology 2011; 25: 413–424.

Summary of pre-pregnancy serum polybrominated and polychlorinated biphenyl levels. Table S2. Correlation between polychlorinated biphenyl (PCB) congeners. (DOCX 45 kb)

Summary of pre-pregnancy serum polybrominated and polychlorinated biphenyl levels. Table S2. Correlation between polychlorinated biphenyl (PCB) congeners. (DOCX 45 kb)