Estimating the national and regional prevalence of drinking or eating more than usual during childhood diarrhea in Malawi using the bivariate sample selection copula regression

Introduction

Diarrhea in children is defined as the occurrence of three or more loose or liquid stools per day (WHO, 2013). Diarrhea is considered the second killer of under-five children after pneumonia causing an estimated 1.5 million under-five deaths every year (UNICEF/WHO, 2009). The prevalence of diarrhea in Malawi as of 2016 was 22% (National Statistical Office of Malawi, 2017). Diarrhea has a detrimental effect on child’s nutrition status due to decreased food intake caused by anorexia (Huffman et al., 1991). To reduce deaths, dehydration and minimize the effects of diarrhea on nutritional status, mothers are encouraged to improve on feeding practices especially to give children more fluids and food than usual. The prevalence of feeding practices during childhood diarrhea in Malawi from the latest Malawi demographic health survey (MDHS) (National Statistical Office of Malawi, 2017) report is 31% for drinking more fluids and 13% for eating more food.

The estimation of prevalence of feeding practices during childhood diarrhea using demographic health survey (DHS) data is done by focusing on children who had diarrhea in the last two weeks. In this case, the prevalence of either drinking or eating more than usual is the number of children with diarrhea who drink or eat more than usual divided by the total number of children with diarrhea (Croft, Marshall & Allen, 2018). The use of complete case analysis (i.e., children who had diarrhea only) in the estimation of the feeding practices prevalence is biased since the selected sample is not random, that is, selection is more or less like voluntarily, since only children with diarrhea are considered. In addition, some participants who might have had responded that they did not have diarrhea, who are left out of the sample, might have said so due to fear of being ashamed of the disease particularly wealthier people who think they are always hygienic, while in actual sense they might have the disease and their feeding practice status would be better. This would result in underestimation bias of the prevalence. The use of children with diarrhea only can be considered as a missing data problem, where the feeding practice status is not observed for children without diarrhea. Standard or conventional approaches to dealing with missing data are single imputation, multiple imputation, inverse probability weighting or propensity score reweighting (McGovern et al., 2015). However if such methods can be applied in this study, they can be biased since they only account for observed factors and in this study, feeding practice status is not observed for those without diarrhea (McGovern et al., 2015). An alternative method which yield better estimates than the standard methods mentioned is the use of Heckman-style sample selection models (Koné et al., 2019). In this case, two equations are used, where one equation models the sample selection variable, for example, diarrhea status (yes/no) and another equation models the outcome variable of interest, for example, feeding practice status, for example, drinking more fluids or eating more food than usual.

Usually, the presence of diarrhea in a child is associated with poor household characteristics, for example, poor parental education according to Asfaha et al. (2018) (AOR = 2.88, 95% CI [1.70–4.88]) and Manun’Ebo & Nkulu-wa-Ngoie (2020) (AOR = 1.14, 95% CI [0.93–1.40]), and large household size according to Omona et al. (2020) (AOR = 7.185, 95% CI [1.353–38.147]). Such poor household characteristics in turn are associated with poor feeding practices during diarrhea episode, for example, according to Fikadu & Girma (2018), mothers who have one under-five child are 2 times (AOR = 2.11, 95% CI [1.38, 3.23]) more likely to have proper feeding practices during diarrhea episode as compared to those who have two and more under-five children. It is hypothesized therefore that there is a negative association between the presence of diarrhea and feeding practices (drinking or eating more) during childhood diarrhea.

The purpose of this study was to re-estimate the prevalence of drinking or eating more than usual during childhood diarrhea episode using sample selection copula bivariate model. The advantage of copula regression over the standard bivariate normal regression is that it offers flexibility in modelling dependence or association between two outcome variables (Parsa & Klugman, 2011). In this case, the copula regression can even model asymmetric dependence which is not the case with the standard bivariate normal distribution (McGovern et al., 2015). For example, in this study, since the hypothesized association between diarrhea presence and feeding practice status is negative, an exploration of asymmetric copula functions like the Joe copula with 90 degrees rotation which models the negative dependence was made. Specifically, the study sought to find out if diarrhea and drinking or eating more than usual were dependent and also the study aimed at re-estimating the prevalence of eating or drinking more than usual using the sample selection model. The significance of the study is that it would reveal if the estimates of prevalence of eating or drinking more during childhood diarrhea reported in the DHS report (National Statistical Office of Malawi, 2017) were biased or not due to the use of sample with diarrhea only. This would ensure correct policy making using the correct prevalences.

The following is how the article has been organized. First, methods regarding data and statistical analysis, are presented. This is followed by presentation of results, discussion and then conclusion.

Materials and Methods

Results

Table 1 presents the percentage of children under-five in terms of feeding practices during diarrhea as reported from MDHS report (National Statistical Office of Malawi, 2017). Thirty one percent of children with diarrhea were given more than usual fluids and thirty four percent were given less fluids which is a concern. Five percent of the sick children were not given any fluids. Sixty one percent of the sick children were given recommended liquid as compared to fourty five percent children that were given recommended food. These percentages were used as a bench mark as the new percentages using the sample selection model were estimated. The focus however was on the percentage of children feeding or drinking more than usual during diarrhea.

After fitting the bivariate sample selection model using the Joe copula, the estimated national prevalence of drinking more fluids during childhood diarrhea using the conventional imputation method was 28.9% with 95% confidence interval as (27.0, 30.7). Adjusting for sample selection, using the sample selection bivariate model, the estimated prevalence of drinking more fluids was 40.0% with 95% confidence interval (31.7, 50.5). Regarding eating more food, the estimated national prevalence of eating more during diarrhea using the conventional imputation method was 13.1% with 95% confidence interval (12.0, 15.0), and the estimated prevalence using the bivariate sample selection model was 20.46% with 95% confidence interval (9.87, 38.55). The estimated average copula parameter for the bivariate model of diarrhea and drinking more fluids was −1.23 with 95% confidence interval as (−1.53, −1.09) and that of diarrhea and eating more food was −1.29 with 95 % confidence interval as (−2.57, −1.04), both showing negative dependence. The association of drinking and eating more with diarrhea may be considered as weak since the copula parameter values are close to −1.

Figure 1 presents the map of prevalence of drinking more fluids during childhood diarrhea by region. The prevalence estimates by the bivariate sample selection model (Fig. 1B) are relatively higher than the imputation based estimates (Fig. 1A). The copula parameter shows relatively strong negative dependence between diarrhea and drinking more fluids in many districts (Fig. 1C). Figure 2 shows the distribution of prevalence of eating more food. The prevalence estimates by the bivariate sample selection model (Fig. 2B) are also relatively higher than the imputation based estimates (Fig. 2A). The copula parameter distribution shows many areas having weak dependence between diarrhea and eating more food (Fig. 2C).

Discussion

The study has looked at the re-estimation of the prevalence of feeding practices during childhood diarrhea by focusing on drinking and eating more than usual. The standard estimation procedure is prone to be biased as the final selected sample is not random as individuals are selected depending on whether they have diarrhea or not. The study therefore tried to investigate the degree of biasness attached to the estimates if the standard method is used, by re-estimating the prevalences using the novel approach which takes into account sample selection process. Sample selection process was taken into account in estimation by using the bivariate sample selection model where one of the two equations, modeled sample selection variable, diarrhea status (yes/no).

The study found that the prevalence estimates of both drinking more liquids and eating more food using the bivariate model were substantially greater than those estimated by the conventional, imputation method. The increased prevalence was likely, since one international study (Bani et al., 2002) found much higher prevalence of mothers increasing the volume of fluids given during childhood diarrhea episode (75.5%). The observed differences in the prevalence estimated by the bivariate sample selection model and the usual imputation method might be due to the non-randomness of the sample selected (Marra & Radice, 2017a). Non-randomness of the sample would be as a result of selection process, as samples were being selected if they had diarrhea, otherwise they were not selected. The estimates by bivariate sample selection model would be with minor bias as non-randomness was corrected by modelling sample selection variable (diarrhea status) in addition to modelling the outcomes of interest, feeding status variables. The increase in prevalence estimate from standard estimation to sample selection estimation may be due to the fact that those not selected (without diarrhea) were likely to have good education and small number of children since low education and large household size are positively correlated with diarrhea (Asfaha et al., 2018) and this would mean increased drinking and eating more in case sample selection process is corrected as increased education and small household size increase the intake of fluids and food (Fikadu & Girma, 2018). An indication of weak correlation between drinking and eating more food and diarrhea is consistent with Huffman et al. (1991) where having diarrhea did not significantly affect eating habits though there was a decline in eating food as children appetite reduced.

The distribution of estimated prevalence of drinking or eating more by region (Figs. 1 and 2B) shows that there is less variation and most regions especially around the cities show increased intake of fluids and food. Generally, there is reduced intake of food compared to fluids. The reduction in food intake may be due to decrease in appetite in the diarrhea patients as explained by Huffman et al. (1991) and Paintal & Aguayo (2016). Similar distribution of fluid and food intake across all the regions may due to the fact that all regions might have similar spatial determinants of feeding practices during diarrhea, for example, average household size is seen to be similar across the three main regions of Malawi with the following average household sizes: 3.7 (north), 3.6 (central) and 3.7 (south) (National Statistical Office of Malawi, 2017), and household size has been found to be associated with feeding practices (Fikadu & Girma, 2018).

Conclusion

The study finds that both estimated prevalence of drinking and eating more food by the standard method were likely to be biased considering that they deviated greatly from the estimate based on the sample selection model found in this study. There is weak negative correlation between the presence of diarrhea and the feeding practices during diarrhea. The implication of the results is that the prevalence of drinking or eating more food during childhood diarrhea should be estimated by taking into account sample selection process (diarrhea presence) so as to correct for the biasness that may arise due to non-randomness of the sample.

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