prevalence of diarrhoea and acute respiratory infection at...

Proceedings of the 5th International Conference on Natural Sciences and Technology (ICNST’18) March 30 - 31, 2018, Asian University for Women, Chittagong, Bangladesh

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Prevalence of Diarrhoea and Acute Respiratory Infection at District Level in Bangladesh using Small Area Estimation Method

Bappi Kumar*, Sumonkanti Das, Abdullah Al Islam, Luthful Alahi Kawsar

Shahjalal University of Science & Technology, Department of Statistics

Kumargaon, Sylhet, 3114, Bangladesh *E-mail: [email protected]

Abstract

Acute respiratory infection (ARI) and diarrhoea are two major causes of child mortality in Bangladesh. National level prevalence of ARI and diarrhoea can be calculated from a nationwide survey, however prevalence at micro-level administrative units is not possible due to lack of data. In such case, small area estimation (SAE) methods are applied by combining a survey data with a contemporaneous census data. Using a SAE method for dichotomous response, this study aims to estimate the proportions of under-5 children experienced with ARI and diarrhoea separately as well as either ARI or diarrhoea within a period of two-week. The ARI and diarrhoea information extracted from the Bangladesh Demographic and Health Survey 2011 are used to develop a random effect logistic model for each of the indicators, and then the prevalence is estimated following the World Bank SAE approach using 5% data of the Census 2011. The estimated prevalence of each indicator significantly varied by district: ARI 2.5-7.2%, diarrhoea 4.7-7.5%, and ARI/diarrhoea: 7.4-13.2%. In a number of districts, the proportions are found significantly higher than the national level. Spatial distributions of the indicators observed from this study might help the policy makers to identify the vulnerable districts.

Keywords: Child morbidity; Dichotomous variable; Random Effect Logistic Model; World Bank SAE Method.

1. Introduction

Acute respiratory infection (ARI) and diarrhoea are the two important determinants of child morbidity and mortality all over the world. Diarrhoea is one of the leading causes of global child morbidity and mortality after pneumonia [1]. While ARI is one of the early symptom of pneumonia and the number of deaths due to pneumonia can be reduced by the early diagnosis and treatment of ARI. To improve the global child health, the UN has set a target under the third sustainable development goal (SDG) to end the epidemics of water-borne diseases and other communicable diseases by 2030 (target 3.3) with the aim of achieving the SDG target of ending preventable deaths of children under-5 to reduce under-5 mortality to below 25 per 1,000 live births (target 3.2).

The prevalence of ARI and diarrhoea at national and divisional levels are estimated usually either from Bangladesh Bureau of Statistics (BBS) or Bangladesh Demographic and Health Survey (BDHS) data. The information of diarrhoea and ARI are collected by asking mothers whether their children are experienced with diarrhoea episode or ARI symptom during a two-week period preceding the survey. In the BDHS surveys, the episodes of ARI and diarrhoea were found to vary over the years (ARI and Diarrhoea for 1993-94: 24% & 13%; for 1996-97: 13% & 8%; for 1999-2000: 19% & 6%; for 2004: 21% & 8%; for 2007: 5% & 10%; for 2011: 6% & 5% and for 2014: 5% & 5%, respectively) [2-8]. Though at present the national level estimates of diarrhoea and ARI prevalence seems around 5%, it is expected that there are significant inequality at the disaggregated administrative units. The ARI and diarrhoea prevalence at disaggregated level are not estimable solely from the survey data due to lack of observation at the desired level. Thus a proper indirect statistical technique is required to analyze the spatial distribution of the prevalence of ARI and diarrhoea at micro-level administrative units.

Small area estimation (SAE) is a statistical technique to obtain estimates of a target parameter with better precision at any desired disaggregated administrative units of a country. The basic idea of SAE method is to combine a survey data with a recent census or administrative data via a statistical model [9]. Survey data consist of the target variable and a regression model is specified with some explanatory variables which are common in both survey and census data. The World Bank has been utilising an SAE method known as ELL [10] for poverty and nutrition mapping in many developing countries including Bangladesh using a continuous response variable. The basic idea of the methodology is to develop a regression model using a continuous response variable (such as weight-for-age Z-score). Since the variable of interest for diarrhoea and ARI prevalence is dichotomous (whether a child has experienced with diarrhoea (or ARI) or not during a fixed time period preceding the survey) instead of continuous, the ELL methodology cannot be implemented. However, the basic idea can be implemented after developing a generalized linear mixed model (GLMM) more specifically a random effect logistic model for the dichotomous response variable [11]. The main difficulty is to develop a



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proper GLMM model incorporating the available survey data with a recent census or administrative data for a country. Also the development process varies over countries due to survey and census data structure. Thus a unique small area study is required to explore the spatial distribution of ARI and diarrhoea in Bangladesh by identifying a proper GLMM model and then utilizing the available census information. Thus the main aim of this study is to estimate the prevalence of ARI and diarrhoea for under-5 children at district level using a SAE technique for dichotomous response variable. In addition, the proportion of children suffering either from diarrhoea or ARI during the 2-week period (hereafter refereed as ARI/diarrhoea) is also aimed to estimate at district level. Finally, the spatial distributions of ARI, diarrhoea and ARI/diarrhoea at district level are portrayed through interactive maps.

2. SAE Method for Dichotomous Response Variable

To explain the small area statistical methodology for the proposed research, let the child-level measurement 𝑌!"#is either 1 (occurrence of diarrhoea during a fixed time period) or 0 (non-occurrence of diarrhoea) and 𝑃!"# = (𝑌!"# = 1) represents the probability of having diarrhoea during the period for 𝑘!! child belonging to 𝑗!! household of 𝑖!! cluster. According to ELL methodology, the first target is to develop a nested-error logistic regression model of 𝑃!"# as below:

( ) ( )logit | , , log 1 Tijk ijk i ij ijk ijk ijk ijP X u P P uη ⎡ ⎤= − = +⎣ ⎦ X β

where 𝑿𝒊𝒋𝒌 is vector of explanatory information, 𝛃 is vector of regression parameters, and 𝑢!" corresponds to cluster specific random errors respectively. The random errors are usually assumed to be independent and identically distributed with mean zero and constant variance. The considered GLMM can be fitted by estimating regression parameters and variance components [9]. The regression model can be extended to higher level, however the ELL methodology assumes heterogeneity at cluster-level rather than higher levels [10]. Following the ELL approach, the small area estimates and their root mean squared error (RMSE) can be calculated via either a parametric or semi-parametric bootstrap procedure. In each bootstrap, response values 𝑃!"#∗ can be predicted for all census children by generating regression parameters and level-specific errors from their parametric (or empirical) distributions. The estimates at target level can be obtained by aggregating 𝑃!"#∗ belong to the corresponding level. The bootstrap procedure can be done for say B=500 times and then the ultimate parameters with their RMSEs can be calculated by taking average and standard deviation of B estimates respectively. 3. Data Collection

The BDHS 2011 children data are aimed to combine with the Bangladesh Population and Housing Census 2011 data to conduct the study. The main reason for using BDHS 2011 instead of recent BDHS 2014 is that the sampling design of BDHS 2011is based on the Census 2011. The survey data is collected following a two-stage stratified sampling design by covering all 7 divisions, 64 districts, and 396 (out of 544) sub-districts (Table 1). In the BDHS 2011, a total of 8341 children were found whose ARI and diarrhoea information were available [7].

The full census data of Bangladesh is unavailable for academic purposes, however, 5% of the full census data is available from BBS. The mean number of children at district level is 11749 in the 5% census data, while the figure is only 137 in the BDHS 2011 data (Table 1). A number of important socio-demographic characteristics such as age, sex, education, schooling, employment, disability and housing characteristics are available in the census data, and consequently some contextual variables at district and sub-district level can be easily created and then can be included in the model specification. 4. Results and Discussion

A number of multilevel logistic models are developed and compared to find the appropriate model as well as the significant explanatory variables. The final models with the corresponding inputs are utilized in the SAE approach to estimate the proportion of each child health indictor with their RMSEs. Table 2 shows that the two-level GLMM are performing better than the fixed effect logistic models (GLM) in terms of AIC, LRT, R2, and area under the ROC curve (AUC) for each of the three child health indicators. In all cases, GLMM can classify children health status more correctly than the GLM, particularly for ARI about three-fourth children are correctly classified. Table 1. Structure of administrative units and children in the Census 2011 and BDHS 2011.

5% of 2011 Census 2011 BDHS Division Zila Upzila EA Division Zila Upzila EA

Administrative Units 7 64 544 291669 7 64 396 600 Mean Children U5 107415 11749 1382 3 1250 137 22 15 Minimum Children U5 43026 2504 41 1 977 15 1 1



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Table 2. Summary statistics and diagnostics of the fitted logistic (GLM) and random intercept logistic (GLMM) models for Diarrhoea, ARI, and for either ARI or diarrhoea prevalence, BDHS 2011.

Health Indicator n p Model AIC logLik 𝜎!! LRT of 𝐻!:𝜎!! = 0

AUC (%)

R2

(%)

Diarrhoea 8341 10 GLM 3122.6 -1551.3 - 𝜒!: 4.0968 53.69 6.18

GLMM 3120.5 -1549.2 0.176 p-value: 0.0215 71.43 10.94

ARI 8341 10 GLM 3678.9 -1829.5 - 𝜒!: 9.3277 59.39 3.02

GLMM 3671.6 -1824.8 0.2365 p-value: 0.0011 74.16 9.52

Either ARI or Diarrhoea 8341 12 GLM 5363.9 -2669.9 - 𝜒!: 2.8804 57.75 3.99

GLMM 5363.0 -2668.5 0.0815 p-value: 0.0448 65.59 6.32 where n: sample size, p: number of covariates, AIC: Akaike information criterion, 𝝈𝒖𝟐: cluster-level variance component, LRT: likelihood ratio test, AUC: Area under the receiving operating characteristics curve

Though the cluster-specific random errors are assumed to follow the normal distribution, the plots shown in Figure 1 indicates that there may have some lack of normality. Since there is no formal established method to check the normality of the random effects (particularly for GLMM), we are assuming that the residuals are approximately normally distributed. However, to avoid the impact of this non-normality, we utilized non-parametric bootstrap procedure in the prediction of health indicators.

Fig. 1. Q-Q plots of the cluster-level random effects obtained from the random intercept logistic (GLMM) models for

Diarrhoea, ARI, and for either ARI or diarrhoea.

To examine the performance of SAE method at the higher administrative levels, the national and division level estimates for each indicator are also estimated and compared with the design-based direct estimates. Table 3 shows that the SAE method provides very similar estimates of the prevalence with their accuracy measure (RMSE ×100). Both design-based and model-based estimators indicate that the children of Khulna division had less experience with the occurrence of diarrhoea however they were more experienced with ARI. While in Sylhet and Barisal, prevalence of ARI/diarrhoea are found more frequent compared to the other divisions. The RMSE of SAE estimates are found slightly higher than that of direct method estimates for Dhaka and Chittagong division along with national level, which might be due to relatively large sample size in the survey data. Table 3. Prevalence of diarrhoea, ARI, and either ARI or diarrhoea under-5 children at national and division level in Bangladesh with standard errors (RMSE) using direct (DIR) and SAE (ELL) estimators.

Division N n

Diarrhoea ARI ARI /Diarrhoea Prevalence

(%) RMSE ×

100 Prevalence

(%) RMSE ×

100 Prevalence

(%) RMSE ×

100 DIR ELL DIR ELL DIR ELL DIR ELL DIR ELL DIR ELL

Barisal 43026 925 4.93 4.32 1.01 0.42 7.01 6.30 1.19 0.53 10.92 9.86 1.45 0.54 Chittagong 163366 1684 5.93 6.21 0.54 0.69 7.41 7.42 0.59 0.78 12.50 12.29 0.75 0.84 Dhaka 239704 1378 4.00 5.01 0.38 0.50 4.65 5.58 0.41 0.46 8.22 8.41 0.54 0.82 Khulna 70260 947 2.58 2.83 0.57 0.57 6.40 6.94 0.89 0.92 8.86 9.44 1.03 0.55 Rajshahi 88878 1027 4.67 4.30 0.64 0.41 5.47 5.88 0.69 0.49 9.76 9.74 0.90 0.50 Rangpur 83452 1061 4.10 4.09 0.67 0.42 5.43 5.99 0.76 0.50 9.54 9.48 0.98 0.52 Sylhet 63220 1319 6.02 6.69 0.94 0.81 4.95 4.98 0.86 0.69 10.21 11.61 1.20 0.76 National 751906 8341 4.62 4.98 0.23 0.36 5.79 6.18 0.26 0.40 9.91 9.98 0.33 0.44



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Summary statistics of the estimated Diarrhoea, ARI and ARI/Diarrhoea prevalence for the 64 districts and their RMSEs are shown in Table 4. The direct estimates of prevalence vary with higher standard errors due to small sample sizes, while the SAE estimator overcomes these problems by providing significantly lower RMSEs. It is noted that, the proportions (as well as RMSE) are not estimable for about 5 districts by the direct estimator due to smaller number of available children and among them no one was exposed to ARI or diarrhoea. Table 4. Summary statistics of diarrhoea, ARI, and either ARI/diarrhoea prevalence of among under-5 children at district level with their root mean squared errors (RMSE) using direct (DIR) and SAE (ELL) estimators

Statistics Diarrhoea ARI ARI/Diarrhoea

Prevalence (%) RMSE × 1000 Prevalence (%) RMSE × 1000 Prevalence (%) RMSE × 1000 DIR ELL DIR ELL DIR ELL DIR ELL DIR ELL DIR ELL

Minimum 0 2.45 0 4.00 0 4.71 0 4.10 1.05 7.38 7.70 5.20 Q1 1.29 3.75 9.40 4.70 3.20 5.75 16.10 4.60 7.45 8.79 22.10 5.90 Mean 4.38 4.58 17.00 6.00 2.67 0.65 8.20 1.60 9.65 9.71 29.70 7.70 Median 3.66 4.57 16.00 5.50 4.80 5.87 20.50 4.80 9.39 9.26 28.00 7.80 Q3 3.93 1.26 13.60 1.60 7.92 6.98 28.50 7.80 12.74 10.54 35.70 9.10 SD 6.85 5.43 20.90 7.20 3.20 0.75 10.90 1.80 4.08 1.45 11.90 1.80 Maximum 16.03 7.15 60.20 9.80 13.76 7.41 51.70 9.40 19.61 13.13 67.90 12.40

Fig. 2. Estimated prevalence of diarrhoea, ARI, and ARI/diarrhoea among under-5 children at district level with RMSEs

using direct (DIR) and SAE (ELL) estimators against the district-specific population size. The estimated prevalence with the estimated RMSEs are plotted against the district-specific number of children in Fig. 2. The left hand side figures show that the SAE estimates goes through the direct estimates, which indicates the SAE estimator provides approximately unbiased estimates. On the other hand, the SAE estimator provides lower RMSE compared to the direct estimator as expected. The clear gain in RMSE is obvious in case of ARI and ARI/diarrhoea. For the larger districts like Dhaka and Chittagong, the RMSEs are very similar for the SAE and direct estimators due to reasonable sample size in the survey data.

Fig. 3 shows district level maps of Bangladesh for the three indicators in 5% Census and the number of under-5 children. The first map (a) shows where higher number of under-5 children are living, the second map (b) shows that the districts of western-south (Khulna region) had lower diarrhoea prevalence, while the districts of northern (Mymensingh region), north-eastern (Sylhet region) and south-eastern (Chittagong region) had comparatively higher diarrhoea prevalence. More specifically, the highest diarrhoea prevalence is found as about 7% in Sunamgonj and lowest as about 2% in Sathkhira district. Map (c) shows that in case of ARI, the districts of Southern region particularly coastal areas are more vulnerable compared to north-eastern parts of Bangladesh. The districts around Comilla region have more than 7% children exposed to ARI, while the



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proportion is about 5% for Sylhet district. The distribution of ARI/Diarrhoea prevalence shown in the map (d) indicates that the districts around the capital Dhaka (as for example, Gopalgonj – 7.4%) are less vulnerable compared to the districts of other region, particularly the eastern regions (for example, Noakhali – 13%).

Fig. 3. Spatial distribution of the estimated prevalence of diarrhoea, ARI, and ARI/diarrhoea among under-5 children at district level using SAE (ELL) estimators.

5. Conclusion

The study shows the district-level prevalence of ARI and diarrheal episodes with the accuracy measures using a SAE method for dichotomous response variable. The findings suggest that the SAE method for the dichotomous variables is providing unbiased and more accurate estimates compared to the direct estimator. Based on the study, it can be recommended for the policy makers that though the national level estimates seem very low, there is still inequality in health indicators among the districts. The variation can be higher when the target parameters will be estimated at lower administrative units (say, sub-district). The study also attempted to find suitable multilevel models for the three health indicators using the 5% Census data, which can be used more accurately for the lower administrative units if the full census data sets were available. Both ARI and diarrhoea are highly correlated with acute child malnutrition known as wasting. A national target is to reduce the wasting level at 5% by the year of 2025. To reduce this vulnerability, the incidence of ARI and diarrhoea should be estimated at different administrative tiers so that the target of wasting can be reached by the time.

Acknowledgement

We wish to thank the SUST Research Centre, SUST for funding this research project. References

1. WHO. (2013). Diarrheal Disease. Retrieved from World Health Organization: http://www.who.int/mediacentre/factsheets/fs330/en/

2. NIPORT, Associates, M. a., & International, M. (1994). Bangladesh Demographic and Health Survey 1993-1994. Dhaka, Bangladesh, and Calverton, Maryland: National Institute of Population Research and Training (NIPORT), Mitra and Associates, and Macro International.

3. NIPORT, Mitra and Associates, & Macro International. (1997). Bangladesh Demographic and Health Survey 1996-1997. Dhaka, Bangladesh, and Calverton, Maryland: NIPORT, Mitra and Associates, and Macro International.

4. NIPORT, Mitra and Associates, & ORC Macro. (2001). Bangladesh Demographic and Health Survey 1999-2000. Dhaka, Bangladesh, and Calverton, Maryland: NIPORT, Mitra and Associates, and ORC Macro.

5. NIPORT, Mitra and Associates, & ORC Macro International. (2005). Bangladesh Demographic and Health Survey 2004. Dhaka, Bangladesh, and Calverton, Maryland: NIPORT; Mitra and Associates; ORC Macro International.

6. NIPORT, Mitra and Associates, & Macro International. (2009). Bangladesh Demographic and Health Survey 2007. Dhaka, Bangladesh and Calverton, Maryland, USA: NIPORT, Mitra and Associates, and Macro International.

7. NIPORT, Mitra and Associates, & ICF International. (2013). Bangladesh Demographic and Health Survey 2011. Dhaka, Bangladesh and Calverton, Maryland, USA: NIPORT, Mitra and Associates, and ICF International.



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8. NIPORT, Mitra and Associates, & ICF International. (2016). Bangladesh Demographic and Health Survey 2014. Dhaka, Bangladesh and Rockville, Maryland, U.S.A. : NIPORT, Mitra and Associates, and ICF International.

9. Rao, J. (2003). Small Area Estimation. New Jersey: John Wiley & Sons, Inc. 10. Elbers, C., Lanjouw, J. O. & Lanjouw, P., 2003. 'Micro-Level Estimation of Poverty and Inequality'. Econometrica,

71(1), p. 355–364. 11. Haslett, S., Jones, G., Isidro, M. & Sefton, A., 2014. Small Area Estimation of Food Insecurity and Undernutrition in

Nepal, Kathmandu: Central Bureau of Statistics, National Planning Commissions Secretariat, World Food Programme, UNICEF & World Bank.

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