Comparison of Bayesian and Classical Methods for Exploring the Important Factors regarding Maternal and Child Health Care

The literature contains a number of studies to analyze the important factors relating to maternal and child health care (MCH). However, the earlier contributions have employed classical models for the analysis. We have proposed Bayesian models for exploring the factors regarding MCH in Pakistan. The latest data, from Pakistan Demographic and Heath Survey (PDHS) conducted in 2017-18, have been used for analysis. The performance of Bayesian methods have been compared with classical methods based on various goodness-of-fit criteria. The performance of Bayesian methods was observed to be better than the classical methods. The results advocated that 86.20% of mothers received antenatal care (ANC), while only 51.40% of the mothers received it at least for ANC visits during the whole pregnancy period. Further, 68.90% of the mothers were protected against neonatal tetanus. More than 30% of women neither delivered in the health facility place nor they were in receipt of postnatal checkups. Additionally, only three out of five newborns were availed with postnatal checkup (PNC) within two days of their births. About 66.89% of women reported problems in accessing the MCH in the country. The study also suggested the presence of severe disparities among different socio-economic groups in availing MCH. There is immediate need to reduce these disparities among various socio-economic groups in the country.


Introduction
e access to the ANC and PNC is fundamental. At present, Pakistan is far behind the Millennium Development Goal (MDG) number 5 to diminish maternal mortality ratio (MMR) by three quarters [1,2]. e MMR for Pakistan in 2015 was 178 per 100,000 live births, that is substantially more than the MDG target of less than 140 per 100,000 MMR. e reduction in the maternal mortality rate is a part of in Sustainable Development Goal (SDG) number 3, and it is a real challenge for Pakistan [3]. e rise in the maternal deaths has been reported in the country [4]. e adequate access to ANC and PNC is fundamental in reduction of MMR [5,6]. Unfortunately, there is a lack of accessibility to the MCH services among pregnant women in Pakistan [7]. e literature contains numerous studies for determination of important factors regarding access to MCH in the country. e health care by skilled professionals before, during, and after child birth can save the lives of women and their babies [8]. However, the majority of women in the country do not have access to MCH [9]. Poverty has been considered to be a major barrier in access to maternal healthcare services in Pakistan [10,11]. Unfortunately, the women with lower education levels are also less likely to get ANC in the country [11][12][13][14]. e lack of knowledge about ANC, high transport costs, and traditional attendants were also the common causes for insu cient utilization of maternal healthcare services in the country [15,16]. Comparatively lower levels of MCH utilization were identi ed in women with less education, lower income levels, and higher birth order in the country [17]. An inflexibly controlled caste ladder also restricts the females from the well-deserved MCH services [18]. e communities' attitude and the health system in rural areas are also important in order to access the maternal health care in the country [19]. e knowledge of women regarding health played an important role in their use of maternal health care [13]. Improving education, nutrition, and the standardized implementation of protocols of obstetric care are required in Pakistan for better maternal and neonatal health [14]. e socio-economic factors are closely related to the delivery of maternal health services in the country [17]. e exploration of such socio-economic factors is important for policy making. Although literature contains a number of earlier contributions, some of them used old data [12,13,20] and [17] some others contain limited number of respondents and areas [20,21]. e contribution by Ref. [17] has considered the detailed investigation regarding factors of the MCH services in Pakistan, using nationally representative data. But the said contribution contained only three dependent variables, namely, number of visits for ANC, delivery in the healthcare facility, and delivery assistance by skilled health provider. e said contribution used the data from Pakistan Demographic and Health Survey (PDHS) 2012-13, which have been updated in PDHS 2017-18. In addition, the PNC is a very important component of the maternal health care, which was not discussed in the said contribution. e identification of specific problems in receipt of MCH is also important. On the other hand, the detailed studies regarding child health care in connection with maternal health care are also very important for the country. We have considered a more detailed study including twelve output variables that explore vital factors of ANC and PNC in the country. e detailed investigation of the child health care has also been considered. e earlier studies have employed classical models, such as logistic regression and chi-square tests, for the analysis of MCH facilities in Pakistan. It is worth mentioning here that the Bayesian methods often produce better results as compared to classical estimation methods [22][23][24].
ough corresponding estimates can be biased, they are associated with smaller amounts of mean square errors as compared to their classical counterparts. ey include additional information (prior) about the model parameters [25] and are applicable even in case of correlated parametric estimates [26,27]. Despite these features, the Bayesian models have not yet replaced the conventional models in their application in different fields [28]. For modeling the binary response data, the Bayesian methods have shown better results than the classical methods [29,30]. An improvement in the Bayesian methods for modeling binary response data was also proposed [31]. Further, Workie and Belay [32] also employed the Bayesian methods to analyze the categorical data regarding study of dental caries.
ough the literature contains a number of studies to explore MCH in the country, some of them have used old data and some others contain a limited number of respondents and areas. Most of the earlier studies have considered the exploration of important determinants of antenatal care; however, the investigation of PNC in the country is equally important. Further, all of the previous studies have employed classical methods for identifying the factors related to MCH in the country. We have proposed improved models for identification of important factors regarding maternal and child health care in the country, using latest nationally representative data. We have considered a more detailed study including twelve output variables to explore vital factors regarding ANC and PNC. e study has explored that there are high inequalities in access to MCH across different socio-economic and demographic sectors of the society. e results from the study will be helpful for the policy makers in order to device strategies for improving the MCH in the country by reducing the observed inequalities among various socioeconomic groups in society. e data regarding problems in access to MCH were obtained from ever-married women aged 15-49. e said information was collected from 12,365 eligible women.

Methodology
e Bayesian logistic regression has been used to identify the vital factors for MCH facilities in Pakistan. e prior distribution for modeling the said response has been assumed to be normally distributed. e comparison between Bayesian and classical methods has also been reported. e Akaike information criteria (AIC) and Bayesian information criteria (BIC) has been used for the said comparison.
Let "L" denote the log-likelihood function for a model f(x) and "k" be the number of parameters involved in f(x), then AIC and BIC can be defined as AIC � −2L + 2k and BIC � −2L + k * Ln(n), where Ln denotes the natural logarithmic value and "n" is the sample size. e following response variables were considered in the study: (i) ANC from a skilled provider, (ii) medical drugs during pregnancy, (iii) protection against neonatal tetanus, (iv) counseling during the pregnancy, (v) delivery in health facility place, (vi) delivery by a skilled provider, (vii) checkup during the first two days of delivery, (viii) skilled postnatal checkup during the first two days of delivery, (ix) checkup of newborn baby during the first two days of birth, (x) the first skilled postnatal checkup for newborn babies, (xi) at least one signal (cord examination, temperature measurement, counseling on danger signs, counseling on breast feeding, observation of breast feeding, and weight) performed within two days of birth, and (xii) at least one problem, in accessing the maternal and child health care, faced by the mothers. On the other hand, age of mother at birth (MAB), order of birth (BO), residence (RES), level of education (EDU), wealth status (WQ), and region (REG) of the respondents has been considered as exploratory variables in the study. All the results have been obtained using R software. In case of Bayesian methods, the normal prior has been used for the posterior estimation. e rstanarm package in R software has been used for numerical computations. e advantage of using this package as compared to other packages such as lme4 is that (i) it provides better estimates for the uncertainty and (ii) it allows users to incorporate prior information.

Results
e reduction in the maternal mortality is the Millennium Development Goal (MDG) 5. Pakistan is also signatory of Sustainable Development Goals (SDGs) 2015-30. e MCH is a major feature of SDG 3. e compliance of SDGs needs even more efforts than those for MDGs. Being a responsible country, Pakistan has already started efforts to come close to MDG 5 and SDG 3. e country has already installed the National Maternal Neonatal and Child Health (MNCH) program in 2007 to speed up the progress on MDG 5 and SDG 3. e country has also determined a National Health Vision (NHV) 2016-2025. A monitoring and evaluation mechanism has also been established for the NHV. e current situation of MCH services in the country has been investigated using data from PDHS 2017-18. e survey included the women aged 15-49 years having a live birth in five years preceding the said survey. e results reported in PDHS 2017-18 revealed that 86.20% of mothers accessed antenatal care (ANC) from the skilled provider. e major contributors for the skilled ANC were doctors (82%). Only 51.40% of the mothers received at least four ANC visits during the whole pregnancy period, while 6 out of 10 (60.32%) of the mothers used medical drugs during the most recent pregnancy. About one-third (30%) of the mothers did not even receive any counseling during the whole period of pregnancy. e major cause of neonatal deaths in developing countries is neonatal tetanus. However, in Pakistan, approximately seven out of ten (68.90%) were protected against neonatal tetanus. e delivery by skilled attendant in a clean and safe environment is fundamental in reducing the complications for mothers and newborn babies. In Pakistan, 66.16% of the mothers delivered in a health facility place, and 69.34% received assistance from a doctor, nurse, midwife, or lady health worker during the delivery. e postnatal period is often considered very risky for the mothers. In order to reduce the chances of complications during this period, the mothers should receive recommended postnatal care visits. However, only three out of five (61.61%) women who gave birth in last two years got the PNC facility within two days after the delivery. PNC for the newborn is also very important to minimize the neonatal complications and mortalities. e percentage of newborn babies with PNC within the first two days of birth is 63.91% in the country. Additionally, 56.86% of the mothers availed the skilled PNC during the first two days after birth, while 59.35% of the newborn babies were in receipt of PNC within two days after birth. At least one signal (cord examination, temperature measurement, counseling on danger signs, counseling on breast feeding, observation of breast feeding, and weight) was performed for newborns within two days of birth in 58% of the cases. A high number (66.89%) of the mothers faced problem in accessing the MCH in the country. In addition, there are high disparities in access to MCH across different socio-economic sectors of the society. e comparison between proposed Bayesian logistic models and classical logistic models has been made using the values of AIC and BIC. e smaller values of AIC and BIC indicate a better model. is comparison is shown in Table 1. From these results, it can be seen that amounts of AIC and BIC are relatively smaller in case of Bayesian logistic regression models, as compared to classical logistic regression models. Similarly, the comparison between Bayesian and classical methods based on widths of 95% CI for ORs is shown in Table 2.
e results, presented in Table 2, also advocate the improved performance of Bayesian methods.
is is owing to the fact that a width of 95% CI for ORs using Bayesian methods is smaller than those under classical methods.
Since the results under Bayesian logistic regression models are superior to those under classical logistic regression models, we have reported the ORs and associated 95% CIs for Bayesian logistic regression models only. ese results are shown in Tables 3 and 4. e ORs and respective 95% CIs for the delivery of ANC is shown in Table 3. For each explanatory variable, the reference group has been represented by letter "R.". e results from this  Table 4.
e graphical results for all twelve response variables are shown in Figure 1. Figure 1(a) represents the magnitudes of the ORs for age groups (at the time of birth) regarding all twelve variables. is figure shows that access to MCH is significantly higher for the mothers within the age group 20-34 as compared to those in the age group 35-49 throughout. However, OR for the problem faced by mothers (represented by variable 12) are lower for the mothers within the age group 20-34. e ORs for the availability of MCH services, with respect to birth order isshown in Figure 1(b).    is figure elucidates that likelihood for the access to the MCH is more than double at the first birth as compared to that for the sixth (and above) birth. e access to the said services tends to decrease with the increase in the birth order, with few exceptions. On the other hand, the ORs for the problems faced in receipt of the said services are lower for lower birth orders. Similarly, the ORs for availability of MCH services are almost half in rural areas as compared to urban areas of the country (Figure 1(c)). Figures 1(d) and 1(e) show that access to MCH is highly skewed towards the mothers with high levels of education and incomes. Likewise, the ORs for problems faced in access to these facilities are much lower for women with more education and higher wealth.
Figure 1(f ) shows the likelihood of MCH services across different regions of the country. From this figure, it can be assessed that the utilization of said services is considerably low in different regions of the country as compared to the capital city Islamabad. e availability of the said services is the least in KPK, Balochistan, and Gilgit Baltistan. Additionally, the hurdles in access to MCH are the highest in KPK, Balochistan, and Gilgit Baltistan.

Discussions
e results from the analysis revealed that the odds of MCH facilities in the country are in favor of mothers with lower ages, lower birth orders, urban residences, higher education, higher wealth quintiles, and the residents of capital city Islamabad. e utilization of the said services is drastically different among different socio-economic sectors of the society. Hence, the future policies regarding delivery of the   Figure 1: Graphs of ORs for age at birth, birth order, residence, education levels, wealth quintiles, and provinces. e response variables have been placed along x-axis with the following codes: the availability of ANC (1), the use of medical drugs during pregnancy (2), protection against tetanus (3), counseling during the pregnancy (4), delivery at the health facility place (5), delivery by the skilled attendant (6), postnatal checkup of mother during the first two days after delivery (7), skilled postnatal checkup of mother during the first two days after delivery (8), postnatal checkup of newborns during the first two days of birth (9), skilled postnatal checkup of newborns during the first two days of birth (10), at least one performed for newborn within two days of birth (11), and at least one problem faced by the mothers in access to maternal health services (12 [29] reported the improved performance of Bayesian models as compared to classical models in modeling trends of awareness about Hepatitis in Pakistan. In the similar way, Feroze et al. [30] advocated the better performance of Bayesian models as compared to classical models for analyzing the binary responses.

Conclusions
e improvement in the MCH is still receiving central importance in the global health initiatives. Unfortunately, Pakistan remains behind many developing countries to provide adequate maternal and child health services. Given the importance of these services, there has been number of contributions dealing with exploration of important factors related to the utilization of the said services in the country. However, the earlier contributions have employed classical models for the analysis. We have employed the Bayesian logistic regression models for exploration of the important factors regarding access to MCH services. e performance of Bayesian logistic regression models has been compared with the most frequently used classical logistic regression models.
e detailed analysis has been carried out using twelve response variables.
e results under the proposed Bayesian logistic regression models were superior to those under classical logistic regression models. is argument was supported by large number of AICs and BICs. e results from the study elucidate that access to maternal and child health care, in the country, is still far behind the desired levels. e finding of the study advocated that there are high disparities in access to MCH across different socio-economic sectors of the society. Any healthcare initiative in the country should target the reduction of these disparities. e results from the study will be helpful for the policy makers in order to plan and implement various strategies to improve the MCH in the country by reducing the observed inequalities for various socio-economic groups in society.

Strengths and Limitations of the Study
e proposed Bayesian models for exploring the important determinants of the maternal and healthcare services in the country used latest nationally representative data. e proposed models provided improved results as compared to the most frequently used classical logistic models. However, the study has some limitations as well. Since self-reporting mothers were the main source of information regarding MCH services, the obtained information may include social desirability biases. e current information is based on the MCH utilization for the most recent birth; hence, the previous patterns regarding access to the said services remained unknown.

Data Availability
All data used in this study areincluded within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.