A STATISTICAL METHOD FOR UNDER-REPORTED CHILD DIARRHEA

A STATISTICAL METHOD FOR ESTIMATING UNDER-REPORTED INCIDENCE RATES WITH APPLICATION TO CHILD DIARRHEA IN THAI PROVINCES BORDERING

Sulawan Yotthanoo1 and Chamnein Choonpradub2

1Department of Statistics, School of Science and Technology, Naresuan University, Phayao; 2Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani,

Abstract. Diarrhea is a major health problem in Thailand, but reported data of disease incidence are known or suspected to be under-reported. This study aimed to develop a statistical model for estimating the annual incidence of hospital diarrhea cases among children under five years. Data regarding diarrhea patients 0-4 years old were col- lected for the National Notifiable Disease Surveillance (Report 506) about Thai prov- inces bordering Cambodia during 1999-2004 by the Ministry of Public Health. A log- linear regression model based on the prevailing seasonal-trend pattern was used for diarrhea incidence as a function of quarter, year and district, after imputing rates where under-reporting was evident, using populations obtained from the 2000 population census. The model also takes any spatial correlation between districts into account, using the generalized estimating equation (GEE) method. Diarrhea incidence had sea- sonal peaks in the first quarter (January to March) and the trend steadily increased from 1999 to 2004. Results from such studies can help health authorities develop pre- vention policies. Key words: child diarrhea, statistical model, BEE method, linear regression

INTRODUCTION third of all deaths in this age group are as- sociated with diarrhea. Approximately 1.5 Diarrhea is one of the world’s top five billion diarrhea episodes and 4 million infectious disease causes of death (Brownlie deaths occur annually among children age et al, 2006) and remains a major cause of less than five years (Vargas et al, 2004). morbidity and mortality among children in As in other developing countries, diar- developing countries (Carlos and Saniel, rhea in Thailand is a major health problem 1990; Parashar et al, 2003). Children under and accounts for approximately 50% of all five years of age have an average of 3.3 diar- hospital-reported infectious diseases (Thai rhea episodes per year, and more than one- Working Group on Burden of Disease and Injuries, 2002). The Bureau of Epidemiology Correspondence: Chamnein Choonpradub, De- (2002) reported that while diarrhea-related partment of Mathematics and Computer Science, Faculty of Science and Technology, Prince of mortality declined from 1.11 per 100,000 in Songkla University, Pattani Campus, Pattani 1988 to 0.23 per 100,000 in 2002, morbidity 94000, Thailand. increased from 1,488 cases per 100,000 in Tel: 66 (0) 89 4660 803; Fax: 66 (0) 7331 2729 1993 to 1,687 cases per 100,000 in 2002. In E-mail: [email protected] 2002, there were 1,055,393 cases of diarrhea in

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Thailand, of which one-third occurred among Data analysis children under five years of age and 12% re- Although the registry included the vil- quired hospitalization (Jiraphongsa et al, 2005). lage of residence and date of hospitalization Given that diarrhea morbidity remains of the patient, we used districts (statistical high in Thailand, there is a need to improve regions containing up to hundreds of vil- treatment to prevent the disease, especially lages ranging in population from 795 to in provinces bordering Cambodia where 21,409). We did this to substantially reduce cross-border migration may be a factor correlations between annual incidence out- (Thimasarn et al, 1995; Konchom et al, 2003). comes in successive periods of time and in We investigated a statistical model neighboring locations, while still enabling based on linear regression for estimating the trends for place and time to be identified. extent of under-reporting. We then classified Data from the Thai infectious disease regis- patterns of child diarrhea in Thai provinces try are known, or suspected, to be seriously bordering Cambodia using the GEE model. under-reported (Lumbiganon et al, 1990; Saengwonloey et al, 2003; Intusoma et al, 2008). MATERIALS AND METHODS We first calculated disease incidence in cells defined by district (i) and month (j) of Study area and data source year (t) as the ratio of the number of reported The border between Thailand and Cam- cases (n ) to the district population in 1,000s bodia is approximately 800 km long, stretch- ijt (P ). For reasons evident from a detailed ing along the provinces of the lower north- i study of monthly disease counts (Table 2), east area of Thailand from a point known as any occurrence of zero cases in a cell was “Chong Bog” in Province considered as a possible instance of under- and ending in the Had Lek Subdistrict of reporting, and an additive linear model was Khlong Yai in Province (Fig 1). Due to fitted to the logarithms of the remaining in- its stronger economic growth, Thailand at- cidence rates, namely, tracts many migrant workers from Cambo- dia. Cross-border migration has been con-  nijt  nected with health problems, including in- ln  = y = µ+ + α + β γ (1)  P  ijt i j t . fectious diseases (Thimasarn et al, 1995;  i  Konchom et al, 2003). In this model µ is a constant and αi, βj Data regarding diarrhea cases from 1999 and γt are the effects of district i=1,2,...,106, to 2004 in the border provinces of interest month j=1,2,...,12 and year t=1,2,...,6, respec- were taken from the National Notifiable Dis- tively, with zero means. After examining the ease Surveillance Report (506), Bureau of plot of standardized residuals, this model Epidemiology, Ministry of Public Health. was refitted after further omission of cells Each record contains the type of infectious corresponding to residuals below a specified disease, age, gender, subdistrict of residence, cut-off value. Having thus obtained an ac- date of hospitalization, and disease severity ceptable fit, the omitted occurrences were of the patient. The resident population de- then imputed using the model. Next, we nominator used to compute the annual inci- aggregated the monthly data into quarterly dence was obtained from the Population and incidence rates and fitted a model similar to Housing Census of 2000, performed by the (1) with j now representing quarter instead National Statistics Office of Thailand. of month, and the residuals from this model

204 Vol 41 No. 1 January 2010 A STATISTICAL METHOD FOR UNDER-REPORTED CHILD DIARRHEA were used to compute correlation coeffi- above. These estimated proportions for lev- cients between different districts. The aver- els of each factor after adjusting for the other ages of the correlation coefficients within factors in the model were again computed by each province were then used to fit a gener- requiring the weighted average of the ad- alized estimating equation (GEE) model justed proportions match the overall propor- (Liang and Zeger, 1986; Yan and Fine, 2004) tion, using a Newton-Raphson iteration pro- having a fixed block-diagonal correlation cedure with Marquardt damping, and stan- structure with the blocks corresponding to dard errors for differences between indi- provinces. Residuals from this model were vidual proportions and the overall mean. examined using normal quantile plots after All statistical analysis was carried out filtering to remove their estimated correla- using the R program (R Development Core tion. Team, 2007). To obtain unbiased estimates of inci- dence rates in cells we used the formula RESULTS

Preliminary analysis rˆ = exp ( yˆ + c) , ijt ijt (2) Preliminary analysis indicated gender was not a major factor influencing diarrhea where y ˆ ijt is the fitted value of yijt and c is a constant chosen to match the total num- incidence (Ardkeaw and Tongkumchum, ber of observed cases with the total given 2009), therefore it was not included in the by the model. After fitting the model, unbi- model. Children less than five years old had ased incidence rates for levels of each factor the highest age-specific annual incidence adjusted for other factors were calculated rate (Bureau of Epidemiology, 2007), so this similarly. Standard errors for these adjusted group was selected for study. incidence rates were obtained using sum Data from were not avail- contrasts (Venables and Ripley 2002) to com- able for 2002 and so were excluded from the pare the incidence rates for each level of a analysis. factor with the overall mean incidence rate. During the study period from January Since the confidence intervals for fac- 1999 to December 2004, 260,522 cases of di- tor-specific incidence rates and proportions arrhea were reported from district hospitals obtained from this model (using the sum in the Thai-Cambodia border provinces contrasts) divide naturally into three groups among children less than 5 years old. The according to their location entirely above the number of cases reported in a month for each mean, around the mean, or entirely below district varied from zero to 578 (average an- the mean, we used this trichotomy to create nual incidence rate 69.4 per 1,000). Among schematic maps of districts according to their the six provinces, Surin (78.8 per 1,000) and estimated diarrhea annual incidence rates Buri Ram (78.2 per 1,000) had relatively high and under-reporting percentages. rates (Table 1). We also estimated the extent of under- Under-reporting reporting data by district, quarter and year, Table 2 shows the number of monthly by fitting a simple logistic regression model reported diarrhea cases in ten selected dis- (Hosmer and Lemeshow, 2000; Kleinbaum tricts. Six of these districts Pho Si Suwan, and Klein, 2002) to the corresponding propor- Chan, Ban Mai Chaiyaphot, Sila Lat, tions imputed using the method described Nam Kliang and Chalermphrakiet, had

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Laos

Surin Si Sa Ket Buri Ram Ubon Ratchathani

Sakaeo

Cambodia Chanthaburi

Trad

Gulf of Thailand

1 Mueang Chantchaburi 23 Nang Rong 45 Tha Tum 67 Khun Han 89 Nam Yuen 2 Khlung 24 Nong Ki 46 Chom Phra 68 Rasi Salai 90 Buntharik 3 Tha Mai 25 Lahan Sai 47 Prasat 69 Uthumphon Phisai 91 Trakan Phuet Phon 4 Pong Nam Ron 26 Prakhon Chai 48 Kap Choeng 70 Bung Bun 92 Kut Khaopun 5 Makham 27 Ban Kruat 49 Rattanaburi 71 Huai Thap Than 93 Mueang Sam Sip 6 Laem Sing 28 Phu Thai Song 50 Sanom 72 Non Khun 94 Warin Chamrap 7 Soi Dao 29 Lam Plai Mat 51 Sikhoraphum 73 Si Rattana 95 Phibun Mangsahan 8 Kaeng Hang Maeo 30 Satuek 52 Sangkha 74 Nam Kliang 96 Tan Sum 9 Na Yai Am 31 Pakham 53 Lamduan 75 Wang Hin 97 Pho Sai 10 Khao Khitchakut 32 Na Pho 54 Samrong Thap 76 Phu Sing 98 Samrong 11 Mueang Sa Kaeo 33 Nong Hong 55 Buachet 77 Mueang Chan 99 Don Mot Daeng 12 Khlong Hat 34 Phlapphla Chai 56 Phanom Dong Rak 78 Benchalak 100 Sirindhorn 13 Ta Phraya 35 Huai Rat 57 Si Narong 79 Phayu 101 Thung Si Udom 14 Wang Nam Yen 36 Non Suwan 58 Khwao Sinarin 80 Pho Si Suwan 102 Na Yai 15 Wattana Kakhon 37 Chamni 59 Non Narai 81 Sila Lat 103 Na Tan 16 38 Ban Mai Chaiyaphot 60 Mueng Si Sa Ket 82 Mueang Ubon Ratchathani 104 Lao Suea Kok 17 Khao Chakan 39 Non Din Daeng 61 Yang Chum Noi 83 Si Mueang Mai 105 Sawang Wirawong 18 Khok Sung 40 Ban Dan 62 Kanthararom 84 Khong Chiamk 106 Nam Khun 19 Wang Sombun 41 Khaen Dong 63 Kantharalak 85 Khueang Nai 20 Mueang Buri Ram 42 Chaloem Phra Kiet 64 Khukhan 86 Khemarat 21 Khu Mueang 43 Mueang Surin 65 Phrai Bueng 87 Det Udom 22 Krasang 44 Chumphon Buri 66 Prang Ku 88 Na Chaluai Fig 1–Districts of Thai provinces bordering Cambodia (excluding Trad).

206 Vol 41 No. 1 January 2010 A STATISTICAL METHOD FOR UNDER-REPORTED CHILD DIARRHEA

Table 1 Number of reported diarrhea cases and population in each province.

Province No. districts Diarrhea cases Population Annual Incidence Rate

Chanthaburi 10 12,552 33,108 63.2 Sa Kaeo 9 18,849 42,560 73.8 Surin 23 64,574 136,634 78.8 Buri Ram 17 58,940 125,642 78.2 Si Sa Ket 22 42,798 130,875 54.5 Ubon Ratchathani 25 62,809 153,410 68.2

Standardized residuals Standardized residuals Standardized residuals

n = 6983 n = 6377 n = 7632 r2 = 0.399 r2 = 0.542 r2 = 0.561

Normal quantiles Normal quantiles Normal quantiles Fig 2–Plots of standardized residuals against normal quantiles with zero cell counts omitted (left panel), further cells with low residuals omitted (middle panel) and imputed using the fitted model (right panel). stretches of successive unusually low case ther 606 cells with residuals less than -1.4 counts. In contrast, the four remaining se- were omitted (7.9%), as the middle panel lected districts (Na Yai Am, Khwao Sinarin, shows. We thus used this latter model to Khlung, and Chom Phra) showed no such impute cell counts for the omitted data, ob- evidence of under-reporting. Any outcome taining the plot shown in the right panel of of zero or an extremely low number of re- Fig 2. ported cases was considered as a possible Table 3 lists the estimated proportions case of under-reporting. of under-reported cases. These proportions The method involved first aggregating were highest in the October to December diarrhea cases by district counts for month quarter and lowest in the April to June quar- and year from 260,522 individual cases into ter. Similarly the estimated under-reporting 7,632 records by cross-tabulating 106 dis- rate was lowest in the year 1999 and gradu- tricts over 72 months. The left panel of Fig 2 ally increased to 15.2% in 2001 and then de- shows the plot of standardized residuals creased to 7.7% in 2004. against normal quantiles after omitting the Based on the criterion we used, there 649 cells with zero counts (8.5%) based on were only four districts with no evidence of model (1). The residuals indicated a poor fit, under-reporting (Mueang Sa Kaeo, Ban which improved substantially when a fur- Kruat, Chom Phra and Phrasat). Chom Phra

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Table 2 Number of monthly reported diarrhea cases in ten selected districts.

Month ID Pho Si Mueang Ban Mai Sila Lat Nam Chaloem Na Yai Khwao Khlung Chom Suwan Chan Chaiyaphot Kliang Phra Kiet Am Sinarin Phra

100101805357 88 59 193 200107019242248141 30001903426153788 40031201142183744 5001160950 18 32 59 60042402535333253 7001802621 16 33 43 8004001620 20 33 47 9001185933 21 28 45 10 0 0 3 4 15 16 30 27 33 58 11 0 0 2 5 1 10 17 27 22 73 12 0 0 0 7 0 1 18 45 31 121 13 5 13 3 08874415575101 14 9 25 10 0 64 57 48 51 58 112 15 25 2 4 8 66 62 39 30 41 92 16 18 0 3 12 53 48 34 31 44 45 17 13 0 6 21 55 68 35 47 49 69 18 37 0 2 4 72 69 23 29 54 115 19 0 1 7 10 35 63 23 45 51 110 20 0 0 4 0 21 40 18 27 31 60 21 0 0 2 0 65 31 25 26 38 53 22 0 0 1 0 17 37 20 25 48 62 23 0 0 1 0 28 48 35 29 36 41 24 0 0 0 0 0 59 21 42 31 79 25 17 20 10 0 21 77 34 56 53 91 26 9 17 5 0156143316374 27 6 10 7 0166052483472 28 2 3 2 0 37 64 59 34 29 49 29 0 0 1 0 108 54 26 33 27 57 30 0 0 6 0 160 71 32 53 42 84 31 0 0 2 0 81 32 32 67 37 111 32 0 0 0 0 56 33 39 53 31 118 33 0 0 0 0 45 22 26 33 30 85 34 7 0 0 0 37 20 9 37 27 36 35 9 0 0 0 0 11 34 19 31 39 36 14 0 0 1 0 0 13 37 11 39 37 25 42 3 91 0 0 42 67 55 381 38 51 20 6 60 1 0 70 58 87 173 39 34 4 1 66 1 1 63 49 94 187 40 26 30 5 54 2 3 33 48 61 91 41 2 30 0 16 0 4 38 32 37 113 42 1 24 26 17 0 5 53 38 47 153 43 0 19 31 30 0 7 36 42 46 178 44 2 12 14 31 2 7 37 48 39 178 45 2 22 7 33 5 7 30 41 26 94 46 5 12 3 24 3 0 22 45 27 118 47 6 0 24 20 1 0 24 68 38 136 48 5 0 9 30 2 0 28 28 55 104 49 5 2 13 2 2 18 30 100 68 187 50 16 0 12 4 4 44 65 77 46 217 51 14 1 19 2 6 34 74 46 51 171 52 3 1 14 8 1 48 26 27 32 103 53 1 0 17 5 3 32 38 17 54 105

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Table 2 (Continued).

Month ID Pho Si Mueang Ban Mai Sila Lat Nam Chaloem Na Yai Khwao Khlung Chom Suwan Chan Chaiyaphot Kliang Phra Kiet Am Sinarin Phra

54 0 1 16 4 7 13 47 36 48 91 55 4 0 14 4 2 7 34 37 48 117 56 5 2 10 6 3 9 27 29 51 123 57 1 1 46 7 1 8 32 22 73 56 58 4 0 52 2 2 0 26 36 54 76 59 2 1 87 1 4 0 17 25 45 99 60 516 03 0154811106 61 51 85 111 54 98 0 47 111 60 124 62 48 43 12 48 60 58 45 57 69 116 63 28 81 19 50 57 28 33 60 69 170 64 8 45 12 41 53 27 9 27 45 101 65 10 47 23 47 51 41 24 29 46 115 66 35 31 22 25 32 47 35 29 59 182 67 73 41 35 55 113 62 28 60 45 274 68 64 60 39 54 53 30 20 72 36 219 69 36 31 12 26 0 51 20 56 31 131 70 2 7 17 16 0 8 11 43 42 103 71 0 1 17 2 1 54 22 76 40 125 72 0 0 11 2 0 72 13 39 33 129 Total 745 788 880 1,131 1,734 2,115 2,348 3,011 3,164 7,905 Population 12,306 9,654 14,226 10,926 24,336 20,526 13,128 16,506 21,480 32,658

and Phrasat are located in the . Table 3 The highest estimates were found in Mueang Estimates of under-reporting percentages Chan, Nam Kliang and Ban Mai Chaiyaphot by quarter and year. Districts where the percentages exceeded 50%. Mueang Chan and Nam Kliang are lo- Factor Percent cated in the Si Sa Ket Province (see the left Quarter panel in Fig 5). 1 : Jan-Mar 8.1 2 : Apr-Jun 7.3 Diarrhea incidence 3 : Jul-Sep 9.6 After aggregating the monthly cell 4 : Oct-Dec 21.8 counts (including those imputed from the Mean 11.7 under-reporting model for monthly data), Year we used the generalized estimating equation 1999 6.4 2000 13.0 (GEE) model with a fixed correlation struc- 2001 15.2 ture to account for spatial correlations be- 2002 14.4 tween districts. In this structured correlation 2003 8.9 matrix, correlations between different dis- 2004 7.7 tricts within a given province were specified Mean 10.9 as the common mean of the corresponding residual correlation coefficients after fitting different provinces were similarly fixed at the linear model, unless this value was less the means of the corresponding residual cor- than 0.1, in which case it was taken to be 0. relation, provided these means exceeded 0.1 Correlations between districts in pairs of in magnitude.

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Table 4 Means and standard errors of residual correlations between districts within and between provinces.

Province Chanthaburi Sa Kaeo Surin Buri Ram Si Sa Ket Ubon Ratchathani

Chanthaburi 0.17 (0.04) Sa Kaeo 0.07 (0.03) 0.13 (0.05) Surin 0.03 (0.02) 0.05 (0.02) 0.03 (0.02) Buri Ram -0.06 (0.02) -0.05 (0.02) 0.03 (0.01) 0.17 (0.03) Si Sa Ket -0.06 (0.02) -0.02 (0.02) 0.00 (0.02) 0.09 (0.01) 0.12 (0.01) Ubon Ratchathani 0.02 (0.02) 0.09 (0.02) 0.03 (0.01) 0.03 (0.01) 0.01 (0.01) 0.12 (0.02)

Table 4 shows the means and standard sent the overall mean annual incidence rate errors of the residual correlation coefficients (19.4 per 1,000). The seasonal pattern of di- between different districts in each province. arrhea incidence clearly indicates a peak in These correlations were generally quite the January to March quarters with an ad- small, ranging from 0.03 in Surin to 0.17 in justed annual incidence rate of 29.8 per 1,000 Chanthaburi Province. (95% CI 28.6 - 31.0). The trend steadily in- creased from 17.7 (95% CI 16.5 - 18.9) in 1999 The results obtained by fitting the GEE to 20.0 (95% CI 18.9 - 21.0) in 2002, then drop- model are shown in Fig 3. The left plot shows ping slightly to 18.6 (95% CI 17.8 - 19.4) in observed counts versus expected counts. The 2003 and increasing to 23.4 (95% CI 22.4 - middle plot shows observed annual inci- 24.4) in 2004. The variation between districts dence per 1,000 versus the corresponding was greater, ranging from 3.6 (95% CI 3.0 - model-fitted values. Since both the cell 4.4) in to 58.2 (95% CI counts and the corresponding incidence 50.8 - 66.7) in . The an- rates were strongly right-skewed, they were nual diarrhea incidence rate was general plotted on a cube root scale, which gave a higher than the mean in the districts of Buri squared correlation of 0.65 between the ob- Ram and Surin Provinces, generally lower served and fitted rates on this scale. The right than the mean in Chantaburi and Si Sa Ket plot shows the residuals (after filtering out Provinces, and typical of the whole in Sa the estimated spatial correlations) versus Kaeo and Ubon Ratchathani Provinces. normal quantiles. Apart from a slight tilt, this The particular statistical and graphics plot shows little reason to doubt the normal- methods used to produce Fig 5 enable un- ity assumption. der-reporting and incidence relativities be- Fig 4 shows the fitted annual diarrhea tween districts to be clearly illustrated. The incidence rates based on the GEE model. The right panel shows a thematic map of districts graphs show 95% confidence intervals for with diarrhea incidence coded according to annual diarrhea incidence/1,000 by quarter whether the confidence interval exceeds, (left panel), year (middle panel) and district crosses, or is below the overall mean. Higher (right panel), each adjusting for the effects disease incidence occurred mainly in Buri of the other two factors in the model. The Ram (14 of 23 districts) and Surin (8 of 17 dotted horizontal lines on each graph repre- districts) in the middle of the region.

210 Vol 41 No. 1 January 2010 A STATISTICAL METHOD FOR UNDER-REPORTED CHILD DIARRHEA

Observed counts Observed annual incidence/1000 Filtered residuals

r2 = 0.658

Expected counts Fitted annual incidence/1000 Normal quantiles

Fig 3–Plots of observed versus fitted counts and incidence rates (left panels) and residuals versus nor- mal quantiles after fitting the GEE model.

Chan, Chanthaburi; SK, Sakaeo; Bur, Buri Ram; Si Sa, Si Sa Ket; Ubon, Ubon Ratchathani Fig 4–Confidence interval plots of annual incidence rates for each factor (quarter, year and district).

DISCUSSION tion is discussed in detail in a recent review by Dormann et al (2007). Generalized linear The results show the diarrhea incidence models (GLMs) provide powerful statistical in the Thai provinces bordering Cambodia modeling (Aitkin et al, 1989) and the appli- is a serious health problem (Staff of the De- cation of the GLMs to model epidemiologi- partment of Planning and Health Informa- cal data was recommended by Flanders and tion, 2008). The log-linear model was used Kleinbaum (1995). This method has also to impute cell counts for the omitted data been applied to modeling diarrhea diseases and the generalized estimating equation by Kale and Hinde (2004), HIV/AIDS and (GEE) model with a fixed correlation struc- other infectious disease mortality rates by ture based on quarter, year and district Lim and Choonprabub (2007). which were used for analysis. The use of the The estimated under-reporting of diar- GEE method for modeling spatial correla- rhea case (Table 3) was relatively high dur-

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Laos Laos

Surin Si Sa Ket Surin Si Sa Ket Buri Ram Ubon Buri Ram Ubon Ratchathani Ratchathani

Sakaeo Sakaeo

Chanthaburi Cambodia Chanthaburi Cambodia

Trad Trad Under-reporting Above average Annual incidence rate Average Gulf of Thailand Gulf of Thailand Above average Below average Average None Below average

Fig 5–Schematic map of under-reporting (left panel) and annual diarrheal incidence rates (right panel) in districts of Thailand bordering Cambodia. ing the last quarter and low during the sec- among children under five years old, which ond quarter. One reason for this pattern might is consistent with the findings by Pinfold et have been due to the low number of actual al (1991) who conducted a study of seasonal cases during the last quarter of each year, but effects on the reported incidence of acute may also have been due to health worker fail- diarrhea in Northeast Thailand. They found ure to record and report actual cases for vari- young children were the most affected ous reasons, including computer system group, with a reported annual incidence of problems. During the period 1999 to 2004, 2,952 per 100,000 for children less than five estimated under-reporting was lowest in 1999 years old. Kosek et al (2003) found that diar- and steadily increased in 2001 and then de- rhea accounted for 21% of all deaths of chil- creased by 2004. The highest estimates were dren less than five years old. Early interven- found in the three districts Mueang Chan, tion for this age group could reduce the in- Nam Kliang and Ban Mai Chai Phot, where cidence. our estimates exceed 50%. Evidence of un- According to this study, the diarrhea in- der reporting was also found in most districts cidence during the study period was rela- of Si Sa Ket Province. Possible causes include tively high from January to March. This pe- overworked government personnel, inad- riod mainly overlaps the winter and sum- equate coordination with private hospitals, mer seasons and is associated with a high and inadequate supervision at the central risk of diarrhea (Pinfold et al, 1991). Diarrhea public health level (Saengwonloey et al, 2003). disease was influenced by El Niño (Patz, However, there were four districts with no 2005) in Peru, the number of diarrhea cases evidence of under-reporting. increased with an ambient temperature in- The highest diarrhea incidence occurred crease (Checkley, 2000). Moreover, we dis-

212 Vol 41 No. 1 January 2010 A STATISTICAL METHOD FOR UNDER-REPORTED CHILD DIARRHEA covered the overall trend of diarrhea inci- Rundle and Dr Shanley Chong who cor- dence from 1999 to 2004 was slightly higher. rected the English for our paper. In contrast, the Bureau of Policy and Strat- egy has shown that the diarrhea trend REFERENCES among the overall Thai population remained stable based on statistics from the Ministry Aitkin M, Anderson D, Francis B, Hinde J. Sta- of Public Health (2001). The high, and in- tistical modelling in GLIM. Oxford, En- gland: Claredon Press, 1989. creasing trends of diarrhea incidence oc- curred in the districts in the middle of the Ardkeaw J, Tongkumchum P. Statistical model- region. Possible reasons are as follows: resi- ling of childhood diarrhea in the north-east- ern border region of Thailand. Southeast dents in this area have a relatively low Gross Asian J Trop Med Public Health 2009; 40: 807- Regional and Provincial Product (GRP) per 15. capita (Office of the National Economic and Brownlie J, Peckham C, Waage J, et al. Foresight. Social Development, 2006); residents are Infectious diseases: preparing for the future. more likely to consume raw meats and fer- Future threats. London: Office of Science mented foods (Lee et al, 1993; Somnasang et and Innovation, 2006. al, 1998) and long droughts occur in the re- Bureau of Epidemiology, Department of Disease gion. Control, Ministry of Public Health. Thai- In conclusion, the data analysis model land: Annual epidemiology surveillance re- enables adjustments to be made to compen- port 2001. : War Veterans Organi- sate for under-reporting and should thus zation of Thailand, 2002. provide more accurate estimates of disease Bureau of Epidemiology, Department of Disease incidence. The model may be useful for Control, Ministry of Public Health, Thai- health planning in countries similar to Thai- land: Annual epidemiology surveillance re- land where routine epidemiological reports port 2006. Bangkok: War Veterans Organi- of diarrhea and other disease cases are pro- zation of Thailand, 2007. vided at the district level, because it provides Carlos CC, Saniel CM. Etiology and epidemio- a simple method based on readily available logy of diarrhea. Phil J Microbiol Infect Dis demographic data. The model can also be 1990; 19: 51-3. used to identify an unusually high annual Checkley W. Effect of El Niño and ambient tem- incidence within the period of its occurrence, perature on hospital admissions for diar- and thus enable health authorities to reduce rhoeal disease in Peruvian children. Lancet the severity of ensuing epidemics by imple- 2000; 355: 442-50. menting preventative measures put in place Dormann CF, McPherson JM, Arauújo MB, for the demographic group at risk. et al. Methods to account for spatial auto- correlation in the analysis of species distri- butional data: a review. Ecography 2007; 30: ACKNOWLEDGEMENTS 609-28. This study was funded by the Gradu- Flanders WD , Kleinbaum DG. Basic models for ate School, Prince of Songkla University. We disease occurrence in epidemiology. Int J would like to thank the Ministry of Public Epidemiol 1995; 24: 1-7. Health for giving permission to use the data. Hosmer DW, Lemeshow S. Applied logistic re- We are grateful for Prof Don McNeil and gression. 2nd ed. New York: John Wiley and Dr Vorasith Sornsrivichai for their helpful Sons, 2000. advice and suggestions. We also thank Greig Intusoma U, Sornsrivichai V, Jiraphongsa C,

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