Bayesian nonparametric generative models for causal inference with missing at random covariates.

We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process. The combination of the observed data model and causal assumptions allows us to identify any type of causal effect-differences, ratios, or quantile effects, either marginally or for subpopulations of interest. The proposed BNP model is well-suited for causal inference problems, as it does not require parametric assumptions about the distribution of confounders and naturally leads to a computationally efficient Gibbs sampling algorithm. By flexibly modeling the joint distribution, we are also able to impute (via data augmentation) values for missing covariates within the algorithm under an assumption of ignorable missingness, obviating the need to create separate imputed data sets. This approach for imputing the missing covariates has the additional advantage of guaranteeing congeniality between the imputation model and the analysis model, and because we use a BNP approach, parametric models are avoided for imputation. The performance of the method is assessed using simulation studies. The method is applied to data from a cohort study of human immunodeficiency virus/hepatitis C virus co-infected patients.

A Bayesian nonparametric approach to marginal structural models for point treatments and a continuous or survival outcome.

Marginal structural models (MSMs) are a general class of causal models for specifying the average effect of treatment on an outcome. These models can accommodate discrete or continuous treatments, as well as treatment effect heterogeneity (causal effect modification). The literature on estimation of MSM parameters has been dominated by semiparametric estimation methods, such as inverse probability of treatment weighted (IPTW). Likelihood-based methods have received little development, probably in part due to the need to integrate out confounders from the likelihood and due to reluctance to make parametric modeling assumptions. In this article we develop a fully Bayesian MSM for continuous and survival outcomes. In particular, we take a Bayesian nonparametric (BNP) approach, using a combination of a dependent Dirichlet process and Gaussian process to model the observed data. The BNP approach, like semiparametric methods such as IPTW, does not require specifying a parametric outcome distribution. Moreover, by using a likelihood-based method, there are potential gains in efficiency over semiparametric methods. An additional advantage of taking a fully Bayesian approach is the ability to account for uncertainty in our (uncheckable) identifying assumption. To this end, we propose informative prior distributions that can be used to capture uncertainty about the identifying "no unmeasured confounders" assumption. Thus, posterior inference about the causal effect parameters can reflect the degree of uncertainty about this assumption. The performance of the methodology is evaluated in several simulation studies. The results show substantial efficiency gains over semiparametric methods, and very little efficiency loss over correctly specified maximum likelihood estimates. The method is also applied to data from a study on neurocognitive performance in HIV-infected women and a study of the comparative effectiveness of antihypertensive drug classes.

Perfluoroalkyl Chemicals, Menstrual Cycle Length, and Fecundity: Findings from a Prospective Pregnancy Study.

BACKGROUND: Perfluoroalkyl substances have been associated with changes in menstrual cycle characteristics and fecundity, when modeled separately. However, these outcomes are biologically related, and we evaluate their joint association with exposure to perfluoroalkyl substances. METHODS: We recruited 501 couples from Michigan and Texas in 2005-2009 upon their discontinuing contraception and followed them until pregnancy or 12 months of trying. Female partners provided a serum sample on enrollment and completed daily journals on menstruation, intercourse, and pregnancy test results. We measured seven perfluoroalkyl substances in serum using liquid chromatography-tandem mass spectrometry. We assessed the association between perfluoroalkyl substances and menstrual cycle length using accelerated failure time models and between perfluoroalkyl substances and fecundity using a Bayesian joint modeling approach to incorporate cycle length. RESULTS: Menstrual cycles were 3% longer comparing women in the second versus first tertile of perfluorodecanoate (PFDeA; acceleration factor [AF] = 1.03, 95% credible interval [CrI] = [1.00, 1.05]), but 2% shorter for women in the highest versus lowest tertile of perfluorooctanoic acid (PFOA; AF = 0.98, 95% CrI = [0.96, 1.00]). When accounting for cycle length, relevant covariates, and remaining perfluoroalkyl substances, the probability of pregnancy was lower for women in second versus first tertile of perfluorononanoate (PFNA; odds ratio [OR] = 0.6, 95% CrI = [0.4, 1.0]) although not when comparing the highest versus lowest (OR = 0.7, 95% CrI = [0.3, 1.1]) tertile. CONCLUSIONS: In this prospective cohort study, we observed associations between two perfluoroalkyl substances and menstrual cycle length changes, and between select perfluoroalkyl substances and diminished fecundity at some (but not all) concentrations. See video abstract at, http://links.lww.com/EDE/B136.

Evaluation of methods to estimate missing days' supply within pharmacy data of the Clinical Practice Research Datalink (CPRD) and The Health Improvement Network (THIN).

PURPOSE: The extent to which days' supply data are missing in pharmacoepidemiologic databases and effective methods for estimation is unknown. We determined the percentage of missing days' supply on prescription and patient levels for oral anti-diabetic drugs (OADs) and evaluated three methods for estimating days' supply within the Clinical Practice Research Datalink (CPRD) and The Health Improvement Network (THIN). METHODS: We estimated the percentage of OAD prescriptions and patients with missing days' supply in each database from 2009 to 2013. Within a random sample of prescriptions with known days' supply, we measured the accuracy of three methods to estimate missing days' supply by imputing the following: (1) 28 days' supply, (2) mode number of tablets/day by drug strength and number of tablets/prescription, and (3) number of tablets/day via a machine learning algorithm. We determined incidence rates (IRs) of acute myocardial infarction (AMI) using each method to evaluate the impact on ascertainment of exposure time and outcomes. RESULTS: Days' supply was missing for 24 % of OAD prescriptions in CPRD and 33 % in THIN (affecting 48 and 57 % of patients, respectively). Methods 2 and 3 were very accurate in estimating days' supply for OADs prescribed at a consistent number of tablets/day. Method 3 was more accurate for OADs prescribed at varying number of tablets/day. IRs of AMI were similar across methods for most OADs. CONCLUSIONS: Missing days' supply is a substantial problem in both databases. Method 2 is easy and very accurate for most OADs and results in IRs comparable to those from method 3.

A Bayesian joint model of menstrual cycle length and fecundity.

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.

Accounting for length-bias and selection effects in estimating the distribution of menstrual cycle length.

Prospective pregnancy studies are a valuable source of longitudinal data on menstrual cycle length. However, care is needed when making inferences of such renewal processes. For example, accounting for the sampling plan is necessary for unbiased estimation of the menstrual cycle length distribution for the study population. If couples can enroll when they learn of the study as opposed to waiting for the start of a new menstrual cycle, then due to length-bias, the enrollment cycle will be stochastically larger than the general run of cycles, a typical property of prevalent cohort studies. Furthermore, the probability of enrollment can depend on the length of time since a woman's last menstrual period (a backward recurrence time), resulting in selection effects. We focus on accounting for length-bias and selection effects in the likelihood for enrollment menstrual cycle length, using a recursive two-stage approach wherein we first estimate the probability of enrollment as a function of the backward recurrence time and then use it in a likelihood with sampling weights that account for length-bias and selection effects. To broaden the applicability of our methods, we augment our model to incorporate a couple-specific random effect and time-independent covariate. A simulation study quantifies performance for two scenarios of enrollment probability when proper account is taken of sampling plan features. In addition, we estimate the probability of enrollment and the distribution of menstrual cycle length for the study population of the Longitudinal Investigation of Fertility and the Environment Study.

Are increased levels of self-reported psychosocial stress, anxiety, and depression associated with fecundity?

OBJECTIVE: To assess the association between self-reported measures of stress, anxiety, depression, and related constructs and fecundity. DESIGN: Prospective cohort study of women trying to conceive. SETTING: United Kingdom. PATIENT(S): Three hundred thirty-nine women aged 18-40 years who were attempting to conceive. INTERVENTION(S): Completed daily diaries for up to six cycles or until pregnancy was detected. For each cycle, stress biomarkers were measured and psychosocial questionnaires were completed. MAIN OUTCOME MEASURES(S): Fecundability odds ratios (FORs) and 95% confidence intervals were calculated using discrete time survival methods, and the day-specific probabilities of pregnancy were calculated using Bayesian statistical techniques. RESULT(S): Among the 339 women, 207 (61%) became pregnant during the study, 69 (20%) did not become pregnant, and 63 (19%) withdrew. After controlling for maternal age, parity, months trying to conceive before enrollment, smoking, caffeine use, and frequency of intercourse, we found no association between most psychosocial measures and FORs or the day-specific probabilities of pregnancy save for an increased FOR for women reporting higher versus lower levels of social support. CONCLUSION(S): Self-reported psychosocial stress, anxiety, and depression were not associated with fecundity. Any adverse effect of stress or psychological disturbance on fecundity does not appear to be detectable via the questionnaires administered.

A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy.

Menstrual cycle patterns are often used as indicators of female fecundity and are associated with hormonally dependent diseases such as breast cancer. A question of considerable interest is in identifying menstrual cycle patterns, and their association with fecundity. A source of data for addressing this question is prospective pregnancy studies that collect detailed information on reproductive aged women. However, methodological challenges exist in ascertaining the association between these two processes as the number of longitudinally measured menstrual cycles is relatively small and informatively censored by time to pregnancy (TTP), as well as the cycle length distribution being highly skewed. We propose a joint modeling approach with a mixed effects dispersion model for the menstrual cycle lengths and a discrete survival model for TTP to address this question. This allows us to assess the effect of important characteristics of menstrual cycle that are associated with fecundity. We are also able to assess the effect of fecundity predictors such as age at menarche, age, and parity on both these processes. An advantage of the proposed approach is the prediction of the TTP, thus allowing us to study the efficacy of menstrual cycle characteristics in predicting fecundity. We analyze two prospective pregnancy studies to illustrate our proposed method by building a model based on the Oxford Conception Study, and predicting for the New York State Angler Cohort Prospective Pregnancy Study. Our analysis has relevant findings for assessing fecundity.

Women's lifestyle behaviors while trying to become pregnant: evidence supporting preconception guidance.

OBJECTIVE: We sought to prospectively measure women's daily cigarette, alcohol, and caffeine use, while attempting pregnancy in relation to intentions to change. STUDY DESIGN: This was a cohort comprising 90 women enrolled upon discontinuing contraception and followed up prospectively until pregnant. Women reported number of daily cigarettes, and alcoholic and caffeinated beverages for 459 menstrual cycles while attempting pregnancy. RESULTS: A significant mean reduction in daily caffeinated drinks (estimate [EST] = -0.52; 95% confidence interval [CI], -0.70 to -0.33) was observed when compared to baseline usage. Intention to change was associated with a reduction in caffeinated drinks (EST = -0.32; 95% CI, -0.64 to 0.00), and with alcohol and cigarette usage from the first menstrual cycle (EST = -0.15; 95% CI, -0.28 to -0.02 and EST = -1.65; 95% CI, -3.12 to -0.19, respectively). CONCLUSION: A reduction in daily caffeine intake while attempting pregnancy was observed, but not in alcohol or cigarette use, underscoring the need for preconception guidance.

Stress reduces conception probabilities across the fertile window: evidence in support of relaxation.

OBJECTIVE: To assess salivary stress biomarkers (cortisol and α-amylase) and female fecundity. DESIGN: Prospective cohort design. SETTING: United Kingdom. PATIENT(S): 274 women aged 18 to 40 years who were attempting pregnancy. INTERVENTION(S): Observation for six cycles or until pregnancy: women collected basal saliva samples on day 6 of each cycle, and used fertility monitors to identify ovulation and pregnancy test kits for pregnancy detection. MAIN OUTCOME MEASURE(S): Salivary cortisol (µg/dL) and α-amylase (U/mL) concentration measurements; fecundity measured by time-to-pregnancy and the probability of pregnancy during the fertile window as estimated from discrete-time survival and Bayesian modeling techniques, respectively. RESULT(S): Alpha-amylase but not cortisol concentrations were negatively associated with fecundity in the first cycle (fecundity odds ratio=0.85; 95% confidence interval 0.67, 1.09) after adjusting for the couples' ages, intercourse frequency, and alcohol consumption. Statistically significant reductions in the probability of conception across the fertile window during the first cycle attempting pregnancy were observed for women whose salivary concentrations of α-amylase were in the upper quartiles in comparison with women in the lower quartiles (highest posterior density: -0.284; 95% interval -0.540, -0.029). CONCLUSION(S): Stress significantly reduced the probability of conception each day during the fertile window, possibly exerting its effect through the sympathetic medullar pathway.

Caffeine consumption and miscarriage: a prospective cohort study.

Caffeine consumption has been equivocally associated with miscarriage, despite an absence of prospective longitudinal measurement of caffeine intake during sensitive windows of human development. In response to this critical data gap, we analyzed daily caffeine consumption while attempting pregnancy through 12 menstrual cycles at risk for pregnancy and found that caffeine consumption did not increase the risk or hazard of miscarriage, even after adjusting for relevant covariates.