A Bayesian mixture modeling approach for assessing the effects of correlated exposures in case-control studies

Bayesian Group Index Regression for Modeling Chemical Mixtures and Cancer Risk

There has been a growing interest in the literature on multiple environmental risk factors for diseases and an increasing emphasis on assessing multiple environmental exposures simultaneously in epidemiologic studies of cancer. One method used to analyze exposure to multiple chemical exposures is weighted quantile sum (WQS) regression. While WQS regression has been demonstrated to have good sensitivity and specificity when identifying important exposures, it has limitations including a two-step model fitting process that decreases power and model stability and a requirement that all exposures in the weighted index have associations in the same direction with the outcome, which is not realistic when chemicals in different classes have different directions and magnitude of association with a health outcome. Grouped WQS (GWQS) was proposed to allow for multiple groups of chemicals in the model where different magnitude and direction of associations are possible for each group. However, GWQS shares the limitation of WQS of a two-step estimation process and splitting of data into training and validation sets. In this paper, we propose a Bayesian group index model to avoid the estimation limitation of GWQS while having multiple exposure indices in the model. To evaluate the performance of the Bayesian group index model, we conducted a simulation study with several different exposure scenarios. We also applied the Bayesian group index method to analyze childhood leukemia risk in the California Childhood Leukemia Study (CCLS). The results showed that the Bayesian group index model had slightly better power for exposure effects and specificity and sensitivity in identifying important chemical exposure components compared with the existing frequentist method, particularly for small sample sizes. In the application to the CCLS, we found a significant negative association for insecticides, with the most important chemical being carbaryl. In addition, for children who were born and raised in the home where dust samples were taken, there was a significant positive association for herbicides with dacthal being the most important exposure. In conclusion, our approach of the Bayesian group index model appears able to make a substantial contribution to the field of environmental epidemiology.

Lagged kernel machine regression for identifying time windows of susceptibility to exposures of complex mixtures

The impact of neurotoxic chemical mixtures on children's health is a critical public health concern. It is well known that during early life, toxic exposures may impact cognitive function during critical time intervals of increased vulnerability, known as windows of susceptibility. Knowledge on time windows of susceptibility can help inform treatment and prevention strategies, as chemical mixtures may affect a developmental process that is operating at a specific life phase. There are several statistical challenges in estimating the health effects of time-varying exposures to multi-pollutant mixtures, such as: multi-collinearity among the exposures both within time points and across time points, and complex exposure-response relationships. To address these concerns, we develop a flexible statistical method, called lagged kernel machine regression (LKMR). LKMR identifies critical exposure windows of chemical mixtures, and accounts for complex non-linear and non-additive effects of the mixture at any given exposure window. Specifically, LKMR estimates how the effects of a mixture of exposures change with the exposure time window using a Bayesian formulation of a grouped, fused lasso penalty within a kernel machine regression (KMR) framework. A simulation study demonstrates the performance of LKMR under realistic exposure-response scenarios, and demonstrates large gains over approaches that consider each time window separately, particularly when serial correlation among the time-varying exposures is high. Furthermore, LKMR demonstrates gains over another approach that inputs all time-specific chemical concentrations together into a single KMR. We apply LKMR to estimate associations between neurodevelopment and metal mixtures in Early Life Exposures in Mexico and Neurotoxicology, a prospective cohort study of child health in Mexico City.

Assessing the Relation between Plasma PCB Concentrations and Elevated Autistic Behaviours using Bayesian Predictive Odds Ratios

Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by impaired social communication and repetitive or stereotypic behaviours. In utero exposure to environmental chemicals, such as polychlorinated biphenyls (PCBs), may play a role in the etiology of ASD. We examined the relation between plasma PCB concentrations measured during pregnancy and autistic behaviours in a subset of children aged 3⁻4 years old in the Maternal-Infant Research on Environmental Chemicals (MIREC) Study, a pregnancy and birth cohort of 546 mother-infant pairs from Canada (enrolled: 2008⁻2011). We quantified the concentrations of 6 PCB congeners that were detected in >40% of plasma samples collected during the 1st trimester. At age 3⁻4 years, caregivers completed the Social Responsiveness Scale-2 (SRS), a valid and reliable measure of children's reciprocal social and repetitive behaviours and restricted interests. We examined SRS scores as both a continuous and binary outcome, and we calculated Bayesian predictive odds ratios for more autistic behaviours based on a latent variable model for SRS scores >60. We found no evidence of an association between plasma PCB concentrations and autistic behaviour. However, we found small and imprecise increases in the mean SRS score and odds of more autistic behaviour for the highest category of plasma PCB concentrations compared with the lowest category; for instance, an average increase of 1.4 (95%PCI: -0.4, 3.2) in the mean SRS (exposure contrast highest versus lowest PCB category) for PCB138 translated to an odds ratio of 1.8 (95%PCI: 1.0, 2.9). Our findings illustrate the importance of measuring associations between PCBs and autistic behaviour on both continuous and binary scales.

A multivariate approach to investigate the combined biological effects of multiple exposures

Epidemiological studies provide evidence that environmental exposures may affect health through complex mixtures. Formal investigation of the effect of exposure mixtures is usually achieved by modelling interactions, which relies on strong assumptions relating to the identity and the number of the exposures involved in such interactions, and on the order and parametric form of these interactions. These hypotheses become difficult to formulate and justify in an exposome context, where influential exposures are numerous and heterogeneous. To capture both the complexity of the exposome and its possibly pleiotropic effects, models handling multivariate predictors and responses, such as partial least squares (PLS) algorithms, can prove useful. As an illustrative example, we applied PLS models to data from a study investigating the inflammatory response (blood concentration of 13 immune markers) to the exposure to four disinfection by-products (one brominated and three chlorinated compounds), while swimming in a pool. To accommodate the multiple observations per participant (n=60; before and after the swim), we adopted a multilevel extension of PLS algorithms, including sparse PLS models shrinking loadings coefficients of unimportant predictors (exposures) and/or responses (protein levels). Despite the strong correlation among co-occurring exposures, our approach identified a subset of exposures (n=3/4) affecting the exhaled levels of 8 (out of 13) immune markers. PLS algorithms can easily scale to high-dimensional exposures and responses, and prove useful for exposome research to identify sparse sets of exposures jointly affecting a set of (selected) biological markers. Our descriptive work may guide these extensions for higher dimensional data.

Assessment of Offspring DNA Methylation across the Lifecourse Associated with Prenatal Maternal Smoking Using Bayesian Mixture Modelling

A growing body of research has implicated DNA methylation as a potential mediator of the effects of maternal smoking in pregnancy on offspring ill-health. Data were available from a UK birth cohort of children with DNA methylation measured at birth, age 7 and 17. One issue when analysing genome-wide DNA methylation data is the correlation of methylation levels between CpG sites, though this can be crudely bypassed using a data reduction method. In this manuscript we investigate the effect of sustained maternal smoking in pregnancy on longitudinal DNA methylation in their offspring using a Bayesian hierarchical mixture model. This model avoids the data reduction used in previous analyses. Four of the 28 previously identified, smoking related CpG sites were shown to have offspring methylation related to maternal smoking using this method, replicating findings in well-known smoking related genes MYO1G and GFI1. Further weak associations were found at the AHRR and CYP1A1 loci. In conclusion, we have demonstrated the utility of the Bayesian mixture model method for investigation of longitudinal DNA methylation data and this method should be considered for use in whole genome applications.

Air toxics and birth defects: a Bayesian hierarchical approach to evaluate multiple pollutants and spina bifida

BACKGROUND

While there is evidence that maternal exposure to benzene is associated with spina bifida in offspring, to our knowledge there have been no assessments to evaluate the role of multiple hazardous air pollutants (HAPs) simultaneously on the risk of this relatively common birth defect. In the current study, we evaluated the association between maternal exposure to HAPs identified by the United States Environmental Protection Agency (U.S. EPA) and spina bifida in offspring using hierarchical Bayesian modeling that includes Stochastic Search Variable Selection (SSVS).

METHODS

The Texas Birth Defects Registry provided data on spina bifida cases delivered between 1999 and 2004. The control group was a random sample of unaffected live births, frequency matched to cases on year of birth. Census tract-level estimates of annual HAP levels were obtained from the U.S. EPA's 1999 Assessment System for Population Exposure Nationwide. Using the distribution among controls, exposure was categorized as high exposure (>95(th) percentile), medium exposure (5(th)-95(th) percentile), and low exposure (<5(th) percentile, reference). We used hierarchical Bayesian logistic regression models with SSVS to evaluate the association between HAPs and spina bifida by computing an odds ratio (OR) for each HAP using the posterior mean, and a 95% credible interval (CI) using the 2.5(th) and 97.5(th) quantiles of the posterior samples. Based on previous assessments, any pollutant with a Bayes factor greater than 1 was selected for inclusion in a final model.

RESULTS

Twenty-five HAPs were selected in the final analysis to represent "bins" of highly correlated HAPs (ρ > 0.80). We identified two out of 25 HAPs with a Bayes factor greater than 1: quinoline (ORhigh = 2.06, 95% CI: 1.11-3.87, Bayes factor = 1.01) and trichloroethylene (ORmedium = 2.00, 95% CI: 1.14-3.61, Bayes factor = 3.79).

CONCLUSIONS

Overall there is evidence that quinoline and trichloroethylene may be significant contributors to the risk of spina bifida. Additionally, the use of Bayesian hierarchical models with SSVS is an alternative approach in the evaluation of multiple environmental pollutants on disease risk. This approach can be easily extended to environmental exposures, where novel approaches are needed in the context of multi-pollutant modeling.

Effects of non-differential exposure misclassification on false conclusions in hypothesis-generating studies

Despite the theoretical success of obviating the need for hypothesis-generating studies, they live on in epidemiological practice. Cole asserted that “… there is boundless number of hypotheses that could be generated, nearly all of them wrong” and urged us to focus on evaluating “credibility of hypothesis”. Adopting a Bayesian approach, we put this elegant logic into quantitative terms at the study planning stage for studies where the prior belief in the null hypothesis is high (i.e., “hypothesis-generating” studies). We consider not only type I and II errors (as is customary) but also the probabilities of false positive and negative results, taking into account typical imperfections in the data. We concentrate on a common source of imperfection in the data: non-differential misclassification of binary exposure classifier. In context of an unmatched case-control study, we demonstrate—both theoretically and via simulations—that although non-differential exposure misclassification is expected to attenuate real effect estimates, leading to the loss of ability to detect true effects, there is also a concurrent increase in false positives. Unfortunately, most investigators interpret their findings from such work as being biased towards the null rather than considering that they are no less likely to be false signals. The likelihood of false positives dwarfed the false negative rate under a wide range of studied settings. We suggest that instead of investing energy into understanding credibility of dubious hypotheses, applied disciplines such as epidemiology, should instead focus attention on understanding consequences of pursuing specific hypotheses, while accounting for the probability that the observed “statistically significant” association may be qualitatively spurious.

Examining the association of lung cancer and highly correlated fibre size-specific asbestos exposures with a hierarchical Bayesian model

BACKGROUND

Asbestos is a known carcinogen. However, little is known about the differential effects of size-specific asbestos fibres. Previous research has examined the relationship with lung cancer of each fibre group in the absence of others. Attempts to model all fibre groups within a single regression model have failed due to high correlations across fibre size groups.

METHODS

We compare results from frequentist models for individual fibre size groups, and a hierarchical Bayesian model that included all fibre groups to estimate the relationship of size-specific asbestos fibre groups to lung cancer mortality. The hierarchical model assumes partial exchangeability of the effects of size-specific asbestos fibre groups to lung cancer, and is capable of handling the strong correlation of the exposure data.

RESULTS

When fibre groups are modelled independently with a frequentist model, there appears to be an increase in the dose-response with increasing fibre size. However, when subject to a hierarchical structure, this trend vanishes, and the effects of distinct fibre groups appear largely similar.

CONCLUSIONS

This is the first occasion where distinct asbestos fibre groups have been assessed in a single regression model; however, even the use of a hierarchical modelling structure does not appear to overcome all the statistical fluctuations arising from the high correlations across fibre groups. We believe these results should be compared with other occupational cohorts with similar fibre group information. Finally, results for the smallest fibre group may be suggestive of a carcinogenic potential for nanofibres.

Quantifying the potential impact of measurement error in an investigation of autism spectrum disorder (ASD)

The Early Autism Risk Longitudinal Investigation (EARLI), an ongoing study of a risk-enriched pregnancy cohort, examines genetic and environmental risk factors for autism spectrum disorders (ASDs). We simulated the potential effects of both measurement error (ME) in exposures and misclassification of ASD-related phenotype (assessed as Autism Observation Scale for Infants (AOSI) scores) on measures of association generated under this study design. We investigated the impact on the power to detect true associations with exposure and the false positive rate (FPR) for a non-causal correlate of exposure (X2, r=0.7) for continuous AOSI score (linear model) versus dichotomised AOSI (logistic regression) when the sample size (n), degree of ME in exposure, and strength of the expected (true) OR (eOR)) between exposure and AOSI varied. Exposure was a continuous variable in all linear models and dichotomised at one SD above the mean in logistic models. Simulations reveal complex patterns and suggest that: (1) There was attenuation of associations that increased with eOR and ME; (2) The FPR was considerable under many scenarios; and (3) The FPR has a complex dependence on the eOR, ME and model choice, but was greater for logistic models. The findings will stimulate work examining cost-effective strategies to reduce the impact of ME in realistic sample sizes and affirm the importance for EARLI of investment in biological samples that help precisely quantify a wide range of environmental exposures.

The association between different night shiftwork factors and breast cancer: a case-control study

BACKGROUND

Research on the possible association between shiftwork and breast cancer is complicated because there are many different shiftwork factors, which might be involved including: light at night, phase shift, sleep disruption and changes in lifestyle factors while on shiftwork (diet, physical activity, alcohol intake and low sun exposure).

METHODS

We conducted a population-based case-control study in Western Australia from 2009 to 2011 with 1205 incident breast cancer cases and 1789 frequency age-matched controls. A self-administered questionnaire was used to collect demographic, reproductive, and lifestyle factors and lifetime occupational history and a telephone interview was used to obtain further details about the shiftwork factors listed above.

RESULTS

A small increase in risk was suggested for those ever doing the graveyard shift (work between midnight and 0500 hours) and breast cancer (odds ratio (OR)=1.16, 95% confidence interval (CI)=0.97-1.39). For phase shift, we found a 22% increase in breast cancer risk (OR=1.22, 95% CI=1.01-1.47) with a statistically significant dose-response relationship (P=0.04). For the other shiftwork factors, risks were marginally elevated and not statistically significant.

CONCLUSION

We found some evidence that some of the factors involved in shiftwork may be associated with breast cancer but the ORs were low and there were inconsistencies in duration and dose-response relationships.