Bangladesh is a densely populated country in South Asia, with an estimated population of over 170 million [22]. The country has approximately an equal percentage of male and female population (50.5% female versus 49.5% male), with nearly half of the female population (46.9%) in reproductive age (15–49 years) [23]. From being one of the poorest nations at birth in 1971, Bangladesh obtained lower-middle income status in 2015 [22]. There have been improvements in maternal health metrics, such as a significant reduction in MMR over the past twenty years, but challenges persist in ensuring equal access to PNC.
Data and variables
The data for this study was extracted from the 2017–18 BDHS, which is a nationally representative cross-sectional survey. The BDHS 2017–18 employed a two-stage stratified sampling method. Bangladesh was divided into eight administrative divisions. Each division was stratified into three different areas: urban city corporations, urban areas other than city corporations, and rural areas, which gives a total of 22 sampling strata (2 divisions exclude city corporation areas). In the first stage, 675 enumeration areas (EAs) were selected independently with a probability proportional to EA size, with 227 EAs in urban areas and 448 EAs in rural areas. An EA can be a village, a part of a large village, or a group of small villages with an average of approximately 120 households. A complete list of households from the selected EAs was used as a sampling frame for the selection of households in the second stage. A systematic sample of 30 households per cluster (EA) was selected in the second stage using the sampling frame. Among the selected 20,250 households, 20,127 ever-married women aged 15 to 49 years were successfully interviewed about their pregnancies. For this study, we considered mothers whose most recent child was under three years old at the time of the survey. The number of women was reduced to 4899 after filtering the dataset using the above-mentioned criteria and deleting the missing values corresponding to the explanatory variables considered in this study. This figure includes both institutional deliveries (2461 women) as well as deliveries at home (2438 women).
The response variable of interest is the PNC status received by the mothers from medically trained provider (MTP) within two days of delivery. From now onwards PNC for mothers from MTP will indicate PNC received by mothers from MTP within two days of birth. Medically trained providers include qualified doctors, nurses, midwives, paramedics, family welfare visitors, community skilled birth attendants, and sub-assistant community medical officers [11]. The covariates considered in this study are: mother’s age at birth (\(\:\le\:18\), 19–24, 25–34, \(\:\ge\:35\) years), birth order (1, 2–3, 4–5, \(\:\ge\:6\) births), mother’s education level (no, primary, secondary, higher education), gender of child (male, female), place of residence (urban, rural), wealth index (poor, middle, rich), media exposure (low, medium, high), antenatal care visits (0, 1–3, 4–7, \(\:\ge\:8\:\)), mother’s working status (no, yes), and region (Central, Eastern, Western).
Some covariates were not readily available in the BDHS 2017–18 dataset. The wealth index was categorized (based on the cut-points of the wealth score) as poor (\(\:\le\:33.33\)%), middle (33.34–66.66%), and rich \(\:(\ge\:66.67\)%). The frequencies of reading newspapers or magazines, or watching television, or listening radio (0 = not at all, 1 = less than once a week, 2 = at least once a week) were combined using principal component analysis to form scores ranging between 0 and 9 [24]. The principal component scores were categorized as low, medium, and high. According to WHO [25], a minimum of four ANC visits are considered sufficient for safe pregnancy and childbirth for healthy women with no underlying medical problems. Recently, WHO [26] recommended to attend at least eight ANC visits. Hence the number of ANC visits was categorized as no (0), 1–3, 4–7, and \(\:\ge\:8\). Eight administrative divisions was grouped into three regions to reduce geographical heterogeneity. Like some studies in Zambia and Lao PDR [5, 27], we have considered region as a covariate of PNC. The regions are Eastern (Sylhet, Chattogram), Central (Dhaka, Mymensingh, Barishal), and Western (Rajshahi, Rangpur, Khulna), a classification that has been used in previous studies in Bangladesh [28]. The regions were identified based on the map of Bangladesh.
Statistical analysis
We performed univariate analysis (frequency distribution) to observe the fundamental characteristics of the explanatory variables within the sample, and bivariate analysis (chi-square test) to investigate the relationship between the response variable and the selected explanatory variables. The chi-square statistic compares the observed cell counts with their respective expected cell counts, aiming to ascertain the independence or dependence between the response variable and the selected categorical variables. The bivariate analysis served as a foundation for selecting explanatory variables to be included in the multivariate analysis. A binary logistic regression was used to identify the determinants of PNC for mothers from MTP. Finally, dominance analysis, particularly general dominance, was applied to evaluate the relative importance of the determinants of PNC for mothers received from MTP. The statistical software STATA 14 was employed to perform univariate, bivariate, and multivariate analyses. To address the stratified two-stage sampling design, we used the svyset command of STATA in the bivariate and multivariate analyses. For dominance analysis, we considered the survey setting, svyglm() function, in the R programming language. The dominance analysis using a simple random sample is available in R. The R code for calculating general dominance while taking the survey setting into account is available upon request from the corresponding author.
Logistic regression model
Let \(\:{y}_{i}\)(\(\:i=1,\:2,\:\dots\:,\:n\)) be the binary response for the \(\:i\)th individual. The value \(\:{y}_{i}=1\) indicates that \(\:i\)th woman received PNC from MTP and \(\:{y}_{i}=0\) otherwise. Also, let \(\:P\left({y}_{i}=1\right)={\pi\:}_{i}\) is the probability of receiving PNC from MTP for the \(\:i\)th woman. Then the link function of binary logistic regression model is [29]
$$\:g\left({\pi\:}_{i}\right)=\text{l}\text{o}\text{g}\text{i}\text{t}\left({\pi\:}_{i}\right)=\text{log}\left(\frac{{\pi\:}_{i}}{1-{\pi\:}_{i}}\right)={\varvec{x}}_{i}^{\top\:}\varvec{\beta\:}$$
where \(\:{\varvec{x}}_{i}={\left(1,{x}_{i1},{x}_{i2},\dots\:,{x}_{ik}\right)}^{\top\:}\) is a \(\:p\times\:1\) vector of covariates for the \(\:i\)th individual and \(\:\varvec{\beta\:}={\left({\beta\:}_{0},{\beta\:}_{1},{\beta\:}_{2},\dots\:,\:{\beta\:}_{k}\right)}^{\top\:}\) is a \(\:p\times\:1\) vector of regression parameters with \(\:p=k+1\).
Relative importance of predictors
Similar to multiple linear regression, researchers may be interested in identifying the most important predictors among the several predictors in a logistic regression model. Recently, the dominance analysis technique has been extensively used by researchers to examine the predictor importance more accurately in multiple linear regression analysis [30, 31]. Dominance analysis was originally proposed by Budescu [32] and refined and extended by Azen and Budescu [33] to identify the relative importance of variables in a multiple regression analysis. Recently, Azen and Traxel [34] extended the dominance analysis procedure of multiple regression to evaluate the predictor’s importance in logistic regression. Also, Tonidandel and LeBreton [31] proposed the Johnson’s [35] relative weight analogue for logistic regression. In multiple linear regression with \(\:p\) predictors, dominance analysis evaluates the change in\(\:\:{R}^{2}\) to a given subset model due to the addition of a new variable in the model. If the additional contribution of a variable is greater than that of the other predictors for every possible subset model, the variable is said to have complete dominance in the analysis. A predictor is said to have conditional dominance over the other variables if its average additional contribution is greater than the other predictors within each model size. Whereas general dominance refers to the situation in which the average conditional contribution of a variable is greater than that of the other predictors over all possible models. Complete dominance and conditional dominance can rarely happen [33]. Hence, in this research we particularly used the general dominance analysis approach, which is the simplest of the three dominances, to determine the variable importance in logistic regression. One appealing property of general dominance is that the sum of general dominance weights is always equal to model \(\:{R}^{2}\) [36]. The relative importance values proposed by Lindeman et al. [37] (called LMG) are equal to the general dominance values [30, 33, 38]. However, LMG has a simpler arrangement of subset models than general dominance. Hence, we applied the subset models’ arrangement of LMG to evaluate general dominance. Dominance analysis in logistic regression requires an \(\:{R}^{2}\) analogue for logistic regression. According to Azen and Traxel [34], three popular \(\:{R}^{2}\) analogues based on likelihood ratios were proposed by McFadden [39], Nagelkerke [40] and Estrella [41]. These measures satisfied at least three of the four criteria of \(\:{R}^{2}\) analogues namely boundness, linear invariance, monotonicity, and intuitive interpretability [34]. Among them, McFadden and Estrella \(\:{R}^{2}\) satisfies all four criteria while Nagelkerke measure holds only three of four criteria. Azen and Traxel [34] proved algebraically that all three measures produce identical directions of dominance. They illustrated the general dominance analysis in a logistics regression analysis using a dataset that studied teenagers’ attitudes and behavior concerning tobacco. In our study, we applied only McFadden’s \(\:{R}^{2}\), which is the simplest to compute than the others, to evaluate the variable importance (general dominance) of the determinants of PNC for mothers received from MTP.
Suppose\(\:\:{L}_{0}\) represents the likelihood of the intercept-only model and \(\:{L}_{M}\) is the fitted model. Then, according to McFadden [39], the analogous measure of \(\:{R}^{2}\) is
$$\:{R}_{M}^{2}=1-\frac{\text{ln}\left({L}_{M}\right)}{\text{ln}\left({L}_{0}\right)}$$
\(\:{R}_{M}^{2}\:\)varies naturally between 0 and 1 and is independent of the units of measurement of the covariates used in the model. This measure is also monotonic increasing, i.e., it does not decrease with the addition of a covariate and has an intuitively reasonable interpretation [34].
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