The use of the harmonic regression model is well accepted in the epidemiological and biostatistical communities as a standard procedure to examine seasonal patterns in disease occurrence. While these models may provide good fit to periodic patterns with relatively symmetric rises and falls, for some diseases the incidence fluctuates in a more complex manner. We propose a two-step harmonic regression approach to improve the model fit for data exhibiting sharp seasonal peaks. To capture such specific behavior, we first build a basic model and estimate the seasonal peak. At the second step, we apply an extended model using sine and cosine transform functions. These newly proposed functions mimic a quadratic term in the harmonic regression models and thus allow us to better fit the seasonal spikes. We illustrate the proposed method using actual and simulated data and recommend the new approach to assess seasonality in a broad spectrum of diseases manifesting sharp seasonal peaks.

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Background: Count data represents the number of occurrences of an event within a fixed period of time. In count data modelling, overdispersion is inevitable. Sometimes, this overdispersion may not be just due to the excess zeros but may be due to the presence of two or more mixtures. Hence the main objective is to examine for the presence of mixtures if any, with excess zeros and compare Generalized Poisson model, Mixture models with other count data models using real time and simulated data. Methods: Three real time over-dispersed datasets were used for the comparison of the models. The real time data models were compared using information criteria like AIC and BIC and regression coefficients. Data was also simulated using mixture Poisson with excess zeros. The simulation was repeated for different sample sizes were used to identify the better model. Results: Generalized Poisson showed consistently lower bias and MSE when compared to the other models for varying sample of sizes. AIC and BIC values were almost similar for Generalized Poisson, ZIP and Mixture Poisson model. Similar findings were also obtained from real time data. Conclusion: Generalized Poisson models provides a better fit for overdispersed data due to excess zeros, consistently in real time and simulated with varying sample sizes. Negative Binomial models can be redistricted or reevaluated against Generalized Poisson model.

a b s t r a c t Background/objectives: Diarrheal disease is one among the top five causes of death in low-and middle-income countries. It is the second leading cause of death in children under five years of age. Diarrheal disease contributes to the mortality of nearly 1.5 million children and globally there are about two billion cases of diarrheal diseases every year. In the present study, we studied the spatio-temporal pattern of acute diarrheal disease (ADD) ward-wise and to estimate and compare two widely used Bayesian models in the study of measuring relative risk of ADD in Chennai Corporation, Tamilnadu, India.Materials and methods: Data on ADD were obtained from Communicable disease hospital, Chennai, Tamilnadu, India from 2009-11. Geographical Information System (GIS) technique was used to map ADD data ward-wise and relative risk was estimated using empirical Bayes approach using Poisson gamma and Poisson log normal models.Results: Over a period of three years from 2009-11, nearly 7661 cases of ADD were reported in Chennai Corporation. The cumulative incidence rate of diarrhea was 142.6 cases per 100,000 population ranging from minimum of 0 to maximum of 1699.7 cases per year. Males had higher average incidence 147.4 cases than females with 137.7 cases per 100,000 population per year. Also, the cumulative incidence was higher in the age group of 0-4 years (306.8 cases) than that in any other category. Higher incidence was observed during the months of Apr-Jun (55.2 cases) than that in any other seasons. Choropleth map indicates that higher incidence of ADD was more prevailed in northern part of Chennai near coastal area which includes the wards from Tondiarpet, Basin bridge, and Pulianthope zones. The posterior relative risk estimate obtained using empirical Bayes approach identified 23, 30, and 19 wards having relative risk significantly greater than 1 for years 2009, 2010, and 2011, respectively. Fitting standardized morbidity ratio (SMR) and the other two models showed that, consistently Tondiarpet ward had the highest relative risk of ADD in all the three years (relative risk (95% credible interval) based on SMR, Poisson gamma and Poisson log normal

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