A Study to detect the seasonal effect of chickenpox in Bangladesh

Transcription

1 STATISTICA ÎN ALTE ŢĂRI: A Study to detect the seasonal effect of chickenpox in M. O. Ullah, M.Sc. in Biostatistics, Assistant professor M. J. Uddin, M.Sc. in Statistics, Assistant professor Dr. M. Rahman, MBBS, Skin Specialist Sylhet Sonkramok Badi Hospital, Sylhet, M. Nazrul Islam, M.Sc. in Statistics, Assistant professor M.T. Uddin, M.Sc. in Statistics, Associate professor Prezentăm în limba engleză informaţii şi date statistice dintr-un Studiu realizat în domeniul sănătăţii publice privind detectarea efectelor unei boli infecţioase într-o ţară din Asia Abstract The infectious diseases create severe health problem every countries in the world in every years. Chickenpox is one of them. In this paper, we have tried to detect the seasonal effect of chickenpox in using secondary data. The Poisson regression model was used to find out the results in this study. The analyses show that the chickenpox is the highest in the month of May (spring season) and there is significant (p=0.0001) seasonal effect of chickenpox in. Keywords: Infectious disease, Chickenpox, Seasonal, Poisson regression. *** An infectious disease is a clinically evident disease resulting from the presence of pathogenic microbial agents, including pathogenic viruses, pathogenic bacteria, fungi, protozoa, and aberrant proteins known as prions. Infectious pathologies are usually qualified as contagious diseases (also called communicable diseases) due to their potentiality of transmission from Revista Română de Statistică nr. 12 /

2 one person or species to another. Transmission of an infectious disease may occur through one or more of diverse pathways including physical contact with infected individuals. These infecting agents may also be transmitted through liquids, food, body fluids, contaminated objects, airborne inhalation, or through vector-borne spread [7]. Chickenpox is a highly contagious illness caused by initial infection with varicella zoster virus (VZV) that results in a blister-like irritation, itching, tiredness, and fever. Chickenpox has a day incubation period and is spread easily through aerosolized droplets from the nasopharynx of ill individuals or through direct contact with secretions from the irritation. The irritation appears first on the trunk and face, but can extend over the whole body causing between 250 to 500 itchy blisters in unvaccinated persons. Former to use of the varicella vaccine, most cases of chickenpox occurred in persons younger than 15 years of age and the disease had annual cycles, peaking in the spring of each year [6]. Following initial infection there is usually lifelong protective immunity from further episodes of chickenpox. Pregnant women and those with a suppressed immune system are at highest risk of serious complications. The most common late complication of chicken pox is shingles, caused by reactivation of the varicella zoster virus decades after the initial episode of chickenpox [5]. At first the varicella vaccine was developed by Michiaki Takahashi in 1974 derived from the Oka strain. It has been available in the U.S. since 1995 to inoculate against the disease. Some countries require the varicella vaccination before entering elementary school. Protection is not life long and further vaccination is necessary five years after the primary immunization [3]. Chickenpox infection is milder in young children, and symptomatic treatment with sodium bicarbonate baths or antihistamine medication may reduce itching [8]. The disease can be more severe for adults persons, though the incidence is much less common. Infection in adults is associated with greater morbidity and mortality because of pneumonia, hepatitis and encephalitis. Particularly, up to 10% of pregnant women with chickenpox develop pneumonia, the severity that increases with onset later in gestation. In England and Wales, 75% of deaths because of chickenpox are in adults [4]. This paper focuses to find out the seasonal effect on the number of infected people by chickenpox using Poisson regression. Materials and Methods The data were collected from Infectious Diseases Hospital at Sylhet (locally known as Sylhet Sonkramok Badi Haspatal ) in. The 62 Romanian Statistical Review nr. 12 / 2009

3 dataset contains number of infected individuals who are older than 12 years by chickenpox at every month in In the present century, more attention is paying on infectious disease analysis using both Mathematical and Statistical approaches. In this paper, we used Poisson regression (7-8) model to find out the seasonal effect of chickenpox in. The model becomes Log(E(Y)) = b + 0 b 1 Where, Y is the number of infected people by chickenpox, X is the months. Poisson regression is a form of regression analysis used to model for count data. It assumes the response variable Y follows a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. To find out the results of this model, we used the procedure GENMOD choosing distribution is Poisson and link =log at the model statement in statistical software SAS 9. X Results and Discussion Statistică medicală In this section at first we have tried to explore the data, then to fit the data using the Poisson regression. The number of infected people is plotted in the following figure. Figure 1 shows that from January to May the number of infected people increases after then it decreases rapidly. From August to November the disease is almost zero but from December, it s going to high again. That is it shows cyclical pattern. The highest number of chickenpox in the month of May (spring season) is 9. The figure also indicates that the more people are infected from January - May compare to June - December. Figure 2 shows that the data do not follow normal distribution, therefore it s not suitable to use simple linear regression in this data. Since Poisson regression (2) fitted this kind of non normal and count data very well, it is better to use Poisson regression model. In a linear regression model, the intercept is the estimated average value of the response variable when the independent variable is equal to zero. In a Poisson regression model, the antilog of the intercept represents the estimated average count when the independent variable is zero. Since exp(2.4025) = 11.05, we would say that the estimated average count at time zero is We might be tempted to make the intercept equal to 11. While this is not an outrageous thing to do, it is not quite as efficient. The Poisson regression model has to fit all of the counts well, not just the count at 0. Revista Română de Statistică nr. 12 /

4 In a linear regression model, the slope represents the estimated average change in the dependent variable when the independent variable increases by one unit. In a Poisson regression model, the antilog of the slope represents the estimated average change in the count when the independent variable increases by one unit. An important difference is that the change is a multiplicative change. Since exp( ) = 0.82, we would say that the estimated average count significantly declines by a factor of 0.82 (18% decline) when time increases by one month. The results show that there is significant time (seasonal) effect on the number of infected people for chickenpox in. A negative slope in a Poisson regression model corresponds to a multiplicative change less than 1. This is an exponential decline. Table 2 indicates the P-values of goodness of fit of different criteria for Poisson regression [1] where we attempt to test the hypothesis that the model fitted well. Since all the criteria s p-value >0.05 which indicate our hypothesis not rejected that is the model is fitted the data very well and there is no evidence of model lack of fit. Conclusion The infectious diseases are severe case now-a-days in the world. The public health and disease related organization in the development of strategies to avert outbreak of the disease. In this study, we applied Poisson regression model for this chickenpox dataset to detect the seasonal effect. It was found that there is significant (p=0.0001) seasonal effect of chickenpox in. It was also observed that the disease is decline on average about 18% every month in a year. The most number of infected people lies between March and May and in these period individuals have more chance to receive varicella than other periods in a year. In this paper we did not considered more data and we have restricted our analysis only on parametric approach. This study can be useful to make awareness of the people in as well as other countries which belongs to same weather like. Further analysis can be conducted using more data with different approaches. Acknowledgements We are giving thanks to the staffs of the Infectious Diseases Hospital at Sylhet in to help us providing the dataset. 64 Romanian Statistical Review nr. 12 / 2009

5 Bibliography 1. Agresti, A. Categorical Data Analysis, John Wiley & Sons, New York. 2. Cameron, A.C. and Trivedi, P.K. Regression Analysis of Count Data, Cambridge University Press, Cambridge. 3. Chaves, S.S., Gargiullo, P., and Zhang. J.X. Loss of Vaccine-induced Immunity to Varicella over Time. N. Engl. J. Med. 2007, 356: Chickenpox in Pregnancy. Royal College of Obstetricians and Gynaecologists, ( 4. Chickenpox (varicella). New Zealand Dermatological Society, ( General questions about the disease. Varicella Disease (Chickenpox), ( 6. Infectious disease. McGraw-Hill Encyclopedia of Science and Technology, 2005.( 7. Somekh, E., Dalal, I., Shohat, T., Ginsberg, G.M. and Romano, O. The Burden of Uncomplicated Cases of Chickenpox in Israel. J. Infect. 2002, 45: Table 1: Results of Poisson regression Variable df Estimate Standard error Wald Chisquare P-value Intercept Time Table 2: P-values of different criteria of goodness of fit Criterion df Value P-value Deviance Scaled deviance Pearson Chi-square Scaled Pearson Chi-square Revista Română de Statistică nr. 12 /

6 Figure 1: Number of chickenpox over time Number of infected people Count Month Figure 2: Histogram of Cont (number of chickenpox people) Histogram of count Frequency count 66 Romanian Statistical Review nr. 12 / 2009