title: Using a generalized additive model with autoregressive terms to study the effects of daily temperature on mortality.
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.
authors.affiliation: Department of Biostatistics, School of Public Health, Fudan University, Shanghai, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Yang
authors.forename: Guoyou
authors.initials: G
authors.lastname: Qin
authors.forename: Naiqing
authors.initials: N
authors.lastname: Zhao
authors.forename: Chunfang
authors.initials: C
authors.lastname: Wang
authors.forename: Guixiang
authors.initials: G
authors.lastname: Song
mesh_terms: D000397:Air Pollution; D003627:Data Interpretation, Statistical; D004781:Environmental Exposure; D004784:Environmental Monitoring; D016021:Epidemiologic Studies; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D009026:Mortality; D012044:Regression Analysis; D013696:Temperature