Hidden Markov Models to Estimate the Lagged Effects of Weather on Stroke and Ischemic Heart Disease

Abstract

The links between low temperature and the incidence of disease have been studied by many researchers. What remains still unclear is the exact nature of the relation, especially the mechanism by which the change of weather effects on the onset of diseases. The existence of lag period between exposure to temperature and its effect on mortality may reflect the nature of the onset of diseases. Therefore, to assess lagged effects becomes potentially important. The most of studies on lags used the method by Lag-distributed Poisson Regression, and neglected extreme case as random noise to get correlations. In order to assess the lagged effect, we proposed a new approach, i.e., Hidden Markov Model by Self Organized Map (HMM by SOM) apart from well-known regression models. HMM by SOM includes the randomness in its nature and encompasses the extreme cases which were neglected by auto-regression models. The daily data of the number of patients transported by ambulance in Nagoya, Japan, were used. SOM was carried out to classify the meteorological elements into six classes. These classes were used as “states” of HMM. HMM was used to describe a background process which might produce the time series of the incidence of diseases. The background process was considered to change randomly weather states, classified by SOM. We estimated the lagged effects of weather change on the onset of both cerebral infarction and ischemic heart disease. This fact is potentially important in that if one could trace a path in the chain of events leading from temperature change to death, one might be able to prevent it and avert the fatal outcome.