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Open Access Research article

Using a generalized additive model with autoregressive terms to study the effects of daily temperature on mortality

Lei Yang1, Guoyou Qin1, Naiqing Zhao1*, Chunfang Wang2 and Guixiang Song2

Author affiliations

1 Department of Biostatistics, School of Public Health, Fudan University, Shanghai, China

2 Vital Statistics Division, Shanghai Municipal Center for Disease Control & Prevention, Shanghai, China

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Citation and License

BMC Medical Research Methodology 2012, 12:165  doi:10.1186/1471-2288-12-165

Published: 30 October 2012

Abstract

Background

Generalized Additive Model (GAM) provides a flexible and effective technique for modelling nonlinear time-series in studies of the health effects of environmental factors. However, GAM assumes that errors are mutually independent, while time series can be correlated in adjacent time points. Here, a GAM with Autoregressive terms (GAMAR) is introduced to fill this gap.

Methods

Parameters in GAMAR are estimated by maximum partial likelihood using modified Newton’s method, and the difference between GAM and GAMAR is demonstrated using two simulation studies and a real data example. GAMM is also compared to GAMAR in simulation study 1.

Results

In the simulation studies, the bias of the mean estimates from GAM and GAMAR are similar but GAMAR has better coverage and smaller relative error. While the results from GAMM are similar to GAMAR, the estimation procedure of GAMM is much slower than GAMAR. In the case study, the Pearson residuals from the GAM are correlated, while those from GAMAR are quite close to white noise. In addition, the estimates of the temperature effects are different between GAM and GAMAR.

Conclusions

GAMAR incorporates both explanatory variables and AR terms so it can quantify the nonlinear impact of environmental factors on health outcome as well as the serial correlation between the observations. It can be a useful tool in environmental epidemiological studies.