title: Time series regression model for infectious disease and weather.
abstract: Time series regression has been developed and long used to evaluate the short-term associations of air pollution and weather with mortality or morbidity of non-infectious diseases. The application of the regression approaches from this tradition to infectious diseases, however, is less well explored and raises some new issues. We discuss and present potential solutions for five issues often arising in such analyses: changes in immune population, strong autocorrelations, a wide range of plausible lag structures and association patterns, seasonality adjustments, and large overdispersion. The potential approaches are illustrated with datasets of cholera cases and rainfall from Bangladesh and influenza and temperature in Tokyo. Though this article focuses on the application of the traditional time series regression to infectious diseases and weather factors, we also briefly introduce alternative approaches, including mathematical modeling, wavelet analysis, and autoregressive integrated moving average (ARIMA) models. Modifications proposed to standard time series regression practice include using sums of past cases as proxies for the immune population, and using the logarithm of lagged disease counts to control autocorrelation due to true contagion, both of which are motivated from "susceptible-infectious-recovered" (SIR) models. The complexity of lag structures and association patterns can often be informed by biological mechanisms and explored by using distributed lag non-linear models. For overdispersed models, alternative distribution models such as quasi-Poisson and negative binomial should be considered. Time series regression can be used to investigate dependence of infectious diseases on weather, but may need modifying to allow for features specific to this context.
authors.affiliation: Department of Pediatric Infectious Diseases, Institute of Tropical Medicine, Nagasaki University, 1-12-4 Sakamoto, Nagasaki 852-8523, Japan. Electronic address: chisato.imai@gmail.com.
authors.forename: Chisato
authors.initials: C
authors.lastname: Imai
authors.affiliation: Department of Social and Environmental Health, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH UK. Electronic address: ben.armstrong@lshtm.ac.uk.
authors.forename: Ben
authors.initials: B
authors.lastname: Armstrong
authors.affiliation: Department of Social and Environmental Health, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH UK. Electronic address: Zaid.Chalabi@lshtm.ac.uk.
authors.forename: Zaid
authors.initials: Z
authors.lastname: Chalabi
authors.affiliation: Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. Electronic address: punam.mangtani@lshtm.ac.uk.
authors.forename: Punam
authors.initials: P
authors.lastname: Mangtani
authors.affiliation: Department of Pediatric Infectious Diseases, Institute of Tropical Medicine, Nagasaki University, 1-12-4 Sakamoto, Nagasaki 852-8523, Japan. Electronic address: hashizum@nagasaki-u.ac.jp.
authors.forename: Masahiro
authors.initials: M
authors.lastname: Hashizume
mesh_terms: D003141:Communicable Diseases / Q000635:transmission; D004198:Disease Susceptibility; D006801:Humans; D008962:Models, Theoretical; D012044:Regression Analysis; D012621:Seasons; D014887:Weather
keywords: Climate; Infectious disease; Method; Time series; Weather