Nonparametric Bayesian hierarchical model and multivariate meta-regression model for environmental epidemiology study

Abstract

In this research, we proposed statistical models for investigating three important topics in the field of environmental epidemiology. First, we proposed a Bayesian nonparametric sparse latent factor model for multivariate functional clustering to conduct a clustering analysis for Canadian air pollution data. Air pollution data, especially multiple air pollutants, can be considered multivariate functional data in a statistical view. While there exist a variety of methodologies for univariate functional clustering, the approach for multivariate functional clustering are less studied. Moreover, there is little research for the functional clustering methods incorporating additional covariate information. We propose a Bayesian nonparametric sparse latent factor model for covariate-dependent multivariate functional clustering. Multiple functional curves are represented by basis coefficients for splines and joint vectors of basis coefficients and covariates are are reduced to latent factors. Then, the factors are modeled using a Dirichlet process (DP) mixture of Gaussians to facilitate a model-based covariate dependent multivariate functional clustering. The method is further extended to a time-varying clustering while incorporating temporal dependency to handle sequential multivariate functional data. For this, dynamical hierarchical dirichlet process (dHDP) is applied instead of DP. The proposed methods are illustrated through a simulation study and applied to time-series data for daily mean concentrations of ozone ($O_3$), nitrogen dioxide ($NO_2$) and fine particulate matter ($PM_{2.5}$) collected for 25 cities in Canada from 1986-2015 to investigate the spatial and temporal patterns of Canadian air quality.

Secondly, we proposed a two-stage approach for meta-analysis using multivariate meta-regression model to investigate the suicide seasonality from suicide count data across multiple populations and evaluate the heterogeneity and underlying determinants. Previous studies have revealed the existence of the suicide seasonality in many countries, however its underlying factor and mechanism remain unclear. Comparison of seasonal suicide patterns across geographically, demographically and socioeconomically heterogeneous populations will help elucidate the underlying factors influencing these patterns and better explain the mechanisms of the phenomenon. However, almost all previous studies on seasonal suicides investigated a study population that was relatively homogeneous (e.g. a single city, a single country or a few communities within a country). We propose a two-stage approach using multivariate meta-regression model for analyzing suicide counts data from multiple populations through a unified statistical modelling framework. In the first stage, we examine the suicide seasonality for each community using a generalized linear model with a quasi-Poisson distribution. We modelled nonlinear and cyclic seasonal patterns of suicide through a cyclic B-spline basis function to the week variable. In the second stage, we pool the community-specific seasonality using multivariate meta-regression to obtain country-specific seasonality. For estimation, we used an iterative method to obtain a maximum likelihood estimation (MLE) within the framework of linear mixed models. We investigated the suicide seasonality across 354 communities from 12 countries and evaluate the heterogeneity of suicide seasonality and its underlying determinants.

Thirdly, we proposed a two-stage approach for meta-analysis using mixed effects meta-regression model to investigate how the minimum mortality temperature (MMT) has changed over time from the temperature-mortality data collected across multiple populations for the last several decades and evaluate the heterogeneity. MMT, which is the temperature where the mortality is minimized in the temperature-mortality association, is often considered an important indicator to assess the temperature-mortality association, indicating adaptation to climate. Recent studies have reported that the MMT has changed over the last decades in many countries indicating that people’s susceptibility to temperature has changed over time. However, most of previous studies on temperature-mortality association examined relatively homogeneous populations and the study design or the analytical methods are different over studies, which make it difficult to synthesize the results of those previous studies and to make an overall conclusion. We propose a two-stage approach using mixed effects meta-regression model for analyzing the temporal change of the MMT from multiple populations through a unified statistical modelling framework. In the first stage, we define 5-year subperiods and examine the MMT for each community and for each subperiod using a generalized linear model with a quasi-Poisson distribution. We modelled the nonlinear and delayed association between temperature and mortality through a distributed lag nonlinear model (DLNM) structure defining a cross basis for a bi-dimensional functional space describing at the same time the dependency along the temperature and in its lag dimension. In the second stage, we pool the time-varying community-specific MMT using mixed effects meta-regression. For estimation, we used an iterative method to obtain a maximum likelihood estimation (MLE) within the framework of linear mixed models. We investigated how the MMT has changed over time across 699 communities from 34 countries and evaluate the heterogeneity.