Abstract
ABSTRACT The generalized additive model (GAM) has been used in many epidemiological studies where frequently the response variable is a nonnegative integer-valued time series. However, GAM assume that the observations are independent, which is generally not the case in time series. In this paper, an autoregressive moving average (ARMA) component is incorporated to the GAM. The resulting GAM-ARMA model is based on the generalized linear autoregressive moving average (GLARMA) model where some linear components are replaced by natural splines. Numerical simulations are presented and show that the ARMA component influences the estimation. In a real data analysis of the effects of air pollution on respiratory disease in the metropolitan area of Belo Horizonte, Brazil, it is shown that the proposed model presents a better fit when compared to the classical GAM approach, that does not take into account the autocorrelation of the data.
Highlights
Epidemiological data are frequently treated as time series of counts because they record the relative frequency of certain events that occur in successive time intervals and the observations are correlated.Many epidemiological studies have been carried out to investigate the impact of ambient air pollution concentrations and meteorological conditions on human health
A new methodology called generalized additive model (GAM)-autoregressive moving average (ARMA) was proposed, based on the generalized linear autoregressive moving average (GLARMA) model introduced by Davis et al (2003)
The GAM-ARMA model allows the fitting of semiparametric models, accommodating covariates with linear and non-linear relation with the response variable in count data with time correlation
Summary
Many epidemiological studies have been carried out to investigate the impact of ambient air pollution concentrations and meteorological conditions on human health. Roberts (2004), Stafoggia et al (2008) and other authors found the evidence of interactive effects between temperature and air pollution (e.g., particulate matter and ozone) on mortality and adverse health outcomes Such studies are an alert about the importance of controlling and reducing air pollutant emissions, and provide support for health departments in resource allocation. In this work a more general model for count data is proposed, which is able to handle both the autocorrelation structure of the time series and the nonlinearity existing in the covariates. This model is composed of a GAM with an ARMA component and is called a GAM-ARMA model.
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