Infinite hidden Markov models for multiple multivariate time series with missing data.

Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper, we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sampling and dynamic programming, to sample the hidden states, and a Bayesian multiple imputation algorithm to impute missing data. In simulation studies, our model excels in estimating hidden states and state-specific means and imputing observations that are missing at random or below the limit of detection. We validate our imputation approach on data from the Fort Collins Commuter Study. We show that the estimated hidden states improve imputations for data that are missing at random compared to existing approaches. In a case study of the Fort Collins Commuter Study, we describe the inferential gains obtained from our model including improved imputation of missing data and the ability to identify shared patterns in activity and exposure among repeated sampling days for individuals and among distinct individuals.

Using non-parametric Bayes shrinkage to assess relationships between multiple environmental and social stressors and neonatal size and body composition in the Healthy Start cohort.

BACKGROUND: Both environmental and social factors have been linked to birth weight and adiposity at birth, but few studies consider the effects of exposure mixtures. Our objective was to identify which components of a mixture of neighborhood-level environmental and social exposures were driving associations with birth weight and adiposity at birth in the Healthy Start cohort. METHODS: Exposures were assessed at the census tract level and included air pollution, built environment characteristics, and socioeconomic status. Prenatal exposures were assigned based on address at enrollment. Birth weight was measured at delivery and adiposity was measured using air displacement plethysmography within three days. We used non-parametric Bayes shrinkage (NPB) to identify exposures that were associated with our outcomes of interest. NPB models were compared to single-predictor linear regression. We also included generalized additive models (GAM) to assess nonlinear relationships. All regression models were adjusted for individual-level covariates, including maternal age, pre-pregnancy BMI, and smoking. RESULTS: Results from NPB models showed most exposures were negatively associated with birth weight, though credible intervals were wide and generally contained zero. However, the NPB model identified an interaction between ozone and temperature on birth weight, and the GAM suggested potential non-linear relationships. For associations between ozone or temperature with birth weight, we observed effect modification by maternal race/ethnicity, where effects were stronger for mothers who identified as a race or ethnicity other than non-Hispanic White. No associations with adiposity at birth were observed. CONCLUSIONS: NPB identified prenatal exposures to ozone and temperature as predictors of birth weight, and mothers who identify as a race or ethnicity other than non-Hispanic White might be disproportionately impacted. However, NPB models may have limited applicability when non-linear effects are present. Future work should consider a two-stage approach where NPB is used to reduce dimensionality and alternative approaches examine non-linear effects.