Generalized linear mixed models for spatio-temporal data with an application to leptospirosis in thailand

Abstract

The objectives of this research are to estimate the morbidity rates of Leptospirosis in each month of all provinces in Thailand, to determine the trend of leptospirosis over time, to investigate factors influencing on the morbidity rates, and to construct the disease maps of the leptospirosis. The generalized linear mixed model (GLMM) in which the spatial effects follow the conditional autoregressive model (CAR) and the temporal effects follow a linear trend. The estimated morbidity rates are used to construct the disease maps. The dependent variables are the numbers of leptospirosis patients in each month of each province and are assumed to have a Poisson distribution. The data are secondary data at a provincial level. The factors considered are rainfall, averaged temperatures, and regions. The results show that the factors influencing on the morbidity rates are rainfall (Relative Risk (RR) = 1.0013), averaged temperature (RR = 0.9922), north region (RR = 10.6440), northeast region, (RR = 14.3249), southern region (RR = 15.5491), western region (RR = 3.6219), and eastern region (RR = 1.0103), where the central region is a reference region, and a linear trend (RR = 1.0183). The top ten province and months with high morbidity rates (per 1,000,000 population), ranking from largest to smallest values, are Phangnga in September (59.00), Phangnga in August (33.49), Sisaket in October (23.14), Sisaket in August ศรีสะเกษ (22.60), Sisaket in September (22.57), Phngnga in October (22.55), Loei in September (21.11), Phangnga in July (20.81), Phangnga in May (20.72), and Phangnga in June (20.47), respectively. The leptospirosis maps are easy for readers to identify which areas are at high risk. They are a useful tool for planning and controlling the leptospirosis.