Bayesian hierarchical semiparametric regression with time-varying coefficients: application to a temperate-mortality association study

Abstract

Generalized linear models (GLM) are commonly used to examine an association between a response variable and several explanatory variables when the response variable does not follow a Gaussian (e.g. count variable). Often, the effects of the predictors are not linear and such nonlinear relationship can be incorporated into GLMs using semiparametric regression approaches. In addition, if the effects of the predictors change over other factors (e.g., time), a time-varying coefficient model can be combined with the GLMs. When a multi-site time series data is provided, interest is often on estimating time-varying nonlinear effects of predictors on a response variable both site-specifically and globally. In such case, a Bayesian hierarchical regression structure can be added to the GLM, which automatically allows for borrowing information across sites to provide a global estimate. Bayesian hierarchical model may also be beneficial in the statistical inference for city-specific estimates when missing data exist for certain time periods at some sites and similarity among cities can be assumed. In this paper, motivated by a temperature-mortality association study data for the population in 6 major cities in Japan, we propose a new statistical approach to investigate nonlinear time-varying effects of temperature on mortality both city-specifically and countrywide simultaneously. We call the proposed method a Bayesian hierarchical semiparametric time-varying coefficient regression model. Simulation studies show that the proposed model performs well and is particularly beneficial when missing data occur. We also apply the proposed model to the motivating example data.