Weather Variability and the Incidence of Cryptosporidiosis: Comparison of Time Series Poisson Regression and SARIMA Models
Introduction
Cryptosporidiosis is an intestinal illness caused by a microscopic parasite called Cryptosporidium. This organism has been recognized as a parasite of a wide variety of vertebrates, but it was not known to cause disease in humans until 1976. Since then, it has been identified as a cause of sporadic human gastrointestinal disease as well as of large outbreaks, particularly water-borne outbreaks 1, 2. It has been estimated that between 250 million and 500 million humans are infected annually with Cryptosporidium in Asia, Africa and Latin America (3). Over the last 9 years (1996–2004), a total of 5744 laboratory-confirmed cryptosporidiosis cases have been identified in Queensland, Australia (4). The major symptoms are abdominal cramps and watery diarrhea. In immunocompromised hosts, Cryptosporidium can cause severe and life-threatening diarrhea (5). The incubation period for cryptosporidiosis ranges from 2 to 12 days and averages about 7 days (3). There is no effective treatment for the disease, and thus prevention remains the sole public health strategy.
The incidence of cryptosporidiosis has been shown to peak between summer and autumn. However, the patterns reported have been variable, with higher prevalence in hot months, cool months, or rainy seasons (6). The reasons for such seasonal heterogeneity are poorly understood (7). Furthermore, few studies have examined the relationship between weather variables and cryptosporidiosis in literature, although there appears to be seasonal patterns of cryptosporidiosis.
Time series analyses have been increasingly used in epidemiological research.8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 Both generalized linear models (GLMs), in particular Poisson regression, and seasonal auto-regression integrated moving average (SARIMA) models have been widely used in the analyses of time series data 22, 23, 24, 25. Recently, more flexible semiparametric extensions in the form of generalized additive models (GAMs) have also been used for epidemiological time series (15). SARIMA models have been traditionally used for forecasting in economics and have become well established in the commercial and industrial fields 11, 12. We are compelled to use Poisson regression or more traditional SARIMA models because there is a paucity of models for time-series count data and the lack of available software applications that allow the implementation of previously developed theory. These models allow more explicit description of seasonal and other temporal changes in complex data sets. However, both Poisson regression and SARIMA models have not been systematically compared by analyzing the same set of infectious disease data.
The aims of this paper are three-fold. First, it examines the potential impact of weather variability on the transmission of cryptosporidiosis. Second, it explores the difference in the predictive ability between Poisson regression and SARIMA models. Finally, the possibility of developing an empirical forecast system was investigated using time-series models for cryptosporidiosis in Brisbane, Australia.
Section snippets
Study Area
Brisbane, the capital of Queensland State, is a subtropical city situated on the eastern coast of Australia and covers approximately 1326 km2 (Fig. 1). Within the administrative boundaries of Brisbane City Council, which also determined the study area of this investigation, the population size was 883,449 on June 30, 2001 (26). In this study, Brisbane was chosen as the main research site because it has the highest population density with most cases (23.4%) of cryptosporidiosis during the period
Descriptive Analysis
Table 1 shows the summary statistics for each variable. The monthly mean incidence rate of cryptosporidiosis, maximum temperature, rainfall, and relative humidity was 1.45/100,000, 26.40°C, 76.82 mm, and 51.87%, respectively, between 1996 and 2004 in Brisbane. Fig. 2, A shows that there was a striking variation in the monthly incidence rate of cryptosporidiosis in Brisbane. The number of cases was the highest in February 2002 (178 cases; incidence rate: 20.12/100,000). The large peaks of
Discussion
The results of this study suggest that weather variability (particularly maximum temperature) may have played a significant role in the transmission of cryptosporidiosis in Brisbane either directly or through other unmeasured variables. The key determinants of the cryptosporidiosis transmission observed in this analysis included maximum temperature at lags of 1 to 3 months and relative humidity at a lag of 1 month. We obtained similar results from two different time series models: SARIMA and
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