Reflection on modern methods: good practices for applied statistical learning in epidemiology.

Statistical learning includes methods that extract knowledge from complex data. Statistical learning methods beyond generalized linear models, such as shrinkage methods or kernel smoothing methods, are being increasingly implemented in public health research and epidemiology because they can perform better in instances with complex or high-dimensional data-settings in which traditional statistical methods fail. These novel methods, however, often include random sampling which may induce variability in results. Best practices in data science can help to ensure robustness. As a case study, we included four statistical learning models that have been applied previously to analyze the relationship between environmental mixtures and health outcomes. We ran each model across 100 initializing values for random number generation, or 'seeds', and assessed variability in resulting estimation and inference. All methods exhibited some seed-dependent variability in results. The degree of variability differed across methods and exposure of interest. Any statistical learning method reliant on a random seed will exhibit some degree of seed sensitivity. We recommend that researchers repeat their analysis with various seeds as a sensitivity analysis when implementing these methods to enhance interpretability and robustness of results.

Early prenatal exposure to suspected endocrine disruptor mixtures is associated with lower IQ at age seven.

BACKGROUND: Endocrine disrupting chemicals (EDCs) are xenobiotics with the ability to interfere with hormone action, even at low levels. Prior environmental epidemiology studies link numerous suspected EDCs, including phthalates and bisphenol A (BPA), to adverse neurodevelopmental outcomes. However, results for some chemicals were inconsistent and most assessed one chemical at a time. OBJECTIVES: To evaluate the overall impact of prenatal exposure to an EDC mixture on neurodevelopment in school-aged children, and identify chemicals of concern while accounting for co-exposures. METHODS: Among 718 mother-child pairs from the Swedish Environmental Longitudinal, Mother and child, Asthma and allergy study (SELMA) study, we used Weighted Quantile Sum (WQS) regression to assess the association between 26 EDCs measured in 1st trimester urine or blood, with Wechsler Intelligence Scale for Children (IV) Intelligence Quotient (IQ) scores at age 7 years. Models were adjusted for child sex, gestational age, mother's education, mother's IQ (RAVEN), weight, and smoking status. To evaluate generalizability, we conducted repeated holdout validation, a machine learning technique. RESULTS: Using repeated holdout validation, IQ scores were 1.9-points (CI = -3.6, -0.2) lower among boys for an inter-quartile-range (IQR) change in the WQS index. BPF made the largest contribution to the index with a weight of 14%. Other chemicals of concern and their weights included PBA (9%), TCP (9%), MEP (6%), MBzP (4%), PFOA (6%), PFOS (5%), PFHxS (4%), Triclosan (5%), and BPA (4%). While we did observe an inverse association between EDCs and IQ among all children when training and testing the WQS index estimate on the full dataset, these results were not robust to repeated holdout validation. CONCLUSION: Among boys, early prenatal exposure to EDCs was associated with lower intellectual functioning at age 7. We identified bisphenol F as the primary chemical of concern, suggesting that the BPA replacement compound may not be any safer for children. Future studies are needed to confirm the potential neurotoxicity of replacement analogues.

Dynamic growth metrics for examining prenatal exposure impacts on child growth trajectories: Application to perfluorooctanoic acid (PFOA) and postnatal weight gain.

BACKGROUND: Epidemiologic studies investigating prenatal exposures in relation to growth typically rely on cumulative growth measures such as weight or BMI. However, less is known about how prenatal exposure may impact other aspects of growth dynamics, including timing and velocity. OBJECTIVES: To describe and apply a nonlinear growth model previously used in other health science fields to characterize postnatal growth trajectories for use in environmental epidemiology studies. METHODS: We used a double logistic function to model child weight trajectories from birth to 5.5 years using data from the Swedish Environmental Longitudinal Mother and Child, Asthma and Allergy (SELMA) study. From this, we approximated several infant growth metrics: 1) duration of time needed to complete 90% of the infant growth spurt (Δt1), 2) the maximum growth rate in infancy or infant peak growth velocity (PGV), 3) the age at infant PGV (δ1), a measure of growth tempo, and 4) the weight plateau at the end of the infant growth spurt (α1). We assessed these metrics in relation to prenatal perfluorooctanoic acid (PFOA) exposure among 1334 mother-child pairs, and differences between boys and girls. RESULTS: Average estimated infant PGV and its timing (δ1) were 0.68 kg/month and 3.4 months, respectively. Mean infant growth spurt duration (Δt1) was 13 months, ending at an average weight plateau (α1) of 8.2 kg. Higher prenatal PFOA concentrations were related to a longer duration of infant growth (Δt1: 0.06; 95% CI = 0.01, 0.11). PGV was not impacted, but higher prenatal PFOA concentrations were significantly related to delayed infant PGV (δ1: 0.58; 95% CI = 0.17, 0.99) and a higher post-spurt weight plateau (α1: 0.81; 95% CI = 0.21, 1.41). After adjusting for false discovery, results were only significant for δ1 and α1. We observed a significant interaction by sex for the association with δ1, and stratified analyses revealed the association was only significant among girls. CONCLUSION: Model-derived growth metrics were consistent with published growth standards. This novel application of nonlinear growth modeling enabled detection of altered infant growth dynamics in relation to prenatal PFOA exposure. Our results may help describe how PFOA yields lower birthweights, but higher weight later in childhood. Future applications may characterize adolescent growth or additional metrics of biological interest.

A longitudinal study of polychlorinated biphenyls and neuropsychological function among older adults from New York State.

BACKGROUND: Cross-sectional studies have linked greater polychlorinated biphenyl (PCB) exposure to adverse neuropsychological effects in older adults, including learning, memory, and depressive symptoms. However, no studies among older adults have evaluated the association over time. OBJECTIVES: To assess the effect of serum PCB levels on neuropsychological function over a 14-year period in a cohort of older men and women from a PCB-contaminated area of New York State. METHODS: In 2000-2002, we assessed serum PCB levels and neuropsychological function (including the California Verbal Learning Test Trial 1 (CVLTT1) for verbal memory and learning, and the Beck Depression Index (BDI) for depressive symptoms) in 253 men and women, ages 55-74 years. A total of 116 (46%) persons repeated the PCB and neuropsychological assessment 14 years later. To assess the association over time, we used generalized estimating equations with clustering variables time, total PCB (∑PCB), and ∑PCB × time, and adjusted for baseline age, sex, smoking, and total serum-lipids. For statistically significant ∑PCB × time interactions, we evaluated the association between PCBs and either verbal memory and learning or depressive symptoms while holding ∑PCB constant at the 10th and 90th percentiles to clarify the direction of the interaction. RESULTS: Over the study period, serum ∑PCB levels (wet-weight) declined by 22%, and were associated with different patterns of change over time for memory (∑PCB × Time ß = 0.08 p = 0.009) and depressive symptoms (∑PCB × Time ß = -0.16 p = 0.013). Specifically, verbal memory and learning decreased (ß = -0.08 p = 0.008) and depressive symptoms increased (ß = 0.17 p = 0.008) among persons with low exposure (∑PCB levels at the 10th percentile), while persons with high exposure (90th percentile) showed non-significant improvements. DISCUSSION: In this cohort, declining ∑PCB levels were likely due at least in part to low rates of local fish consumption in recent decades, given the ban since 1976. The decreased verbal memory and learning and increased depressive symptoms over time among persons with low serum ∑PCB levels is consistent with studies of normative aging. However, the small improvements in those outcomes among those with high serum ∑PCB levels was unexpected. Healthy survivor selection bias or uncontrolled confounding may explain this result. It may also indicate that the neurotoxic impacts of PCBs in older adults are not permanent, but future studies are needed to confirm this possibility.

Repeated holdout validation for weighted quantile sum regression.

Weighted Quantile Sum (WQS) regression is a method commonly used in environmental epidemiology to assess the impact of chemical mixtures in relation to a health outcome of interest. Data are partitioned into a single training and test set to reduce sample-specific chemical weights. However, in typical epidemiology sample sizes, this may produce unstable chemical weights and WQS index estimates, and investigators may resort to training and testing on the same data. To solve this problem, we propose repeated holdout validation whereby data are randomly partitioned 100 times, producing a distribution of validated results. Taking the mean as the final estimate, confidence estimates may also be calculated for inference. Further, this method helps characterize the variability in chemical weights, aiding in the identification of chemicals of concern. This is important since it may direct future research into specific chemicals. Using data from 718 mother-child pairs in the Swedish Environmental Longitudinal, Mother and Child, Asthma and Allergy (SELMA) study, we assessed the association between prenatal exposure to 26 endocrine disrupting chemicals and child Intelligence Quotient (IQ). Results using a single partition were unstable, varying by random seed. The WQS index estimate was significant when all data was used (e.g. no partition) (ß = -2.2 CI = -3.43, -0.98), but attenuated and nonsignificant using repeated holdout validation (ß = -0.82 CI = -2.11, 0.45). When implementing WQS in epidemiologic studies with limited sample sizes, repeated holdout validation is a viable alternative to using a single, or no partitioning. Repeated holdout can both stabilize results and help characterize the uncertainty in identifying chemicals of concern, while maintaining some of the the rigor of holdout validation. •Repeated holdout validation improves the stability of WQS estimates in finite study samples•Uncertainty in identifying toxic chemicals of concern is acknowledged and characterized.

Occupational exposure to perfluoroalkyl substances and serum levels of perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) in an aging population from upstate New York: a retrospective cohort study.

PURPOSE: Perfluoroalkyl substances (PFASs) are environmentally persistent amphiphilic compounds. Exposure to two PFASs, perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) is linked to specific occupations and industries. This study examines the contribution of past occupational PFAS exposure to serum PFOS and PFOA levels among 154 older adults in New York State. METHODS: Serum PFOS and PFOA levels were compared to data from the National Health and Nutrition Examination Survey (NHANES). Potential occupational exposure to any PFAS was determined from work histories, reviewed by an industrial hygienist, and assessed in relation to current serum PFOS and PFOA levels using exposure probability, duration and cumulative exposure. RESULTS: We observed 25% higher serum PFOS and 80% higher PFOA levels in study participants compared to NHANES. No participants reported PFAS chemical manufacturing work, but n = 68 reported work in occupations and industries known to use PFASs. We found that participants with high cumulative workplace exposure had 34% higher serum PFOS levels compared to participants without occupational exposure, adjusted for age, sex and income. Serum PFOS levels were 26% higher for participants with longer occupational exposure durations. The probability of occupational PFAS exposure metric was not associated with serum PFOS. Serum PFOA was not associated with any measure of occupational exposure. CONCLUSION: Occupational exposure may contribute to total PFOS body burden in this study population, even among workers not directly involved in manufacturing PFASs. PFAS exposure assessments should evaluate the workplace as a potential source, even when workplace exposures are assumed to be low or moderate.