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Cluster-Specific Effect of the Hierarchical Logistic Regression Model:

The odds ratios for the individual variables reported in Table 2 are cluster-specific or conditional measures of association or intra-cluster measures of association. It is important to note that the interpretation of the odds ratio is conditional on both the other covariates as well as the cluster-specific random effect [11]. Therefore, they may be interpreted as odds ratios for within-cluster comparisons, that is, state-adjusted associations between the socio-demographic variables of the women and MHC utilization. In examining Model 2, one would interpret the odds ratio for prenatal care as suggesting that, when comparing two subjects who received prenatal care and who do not receive prenatal care, but who share identical values on the remaining 2 covariates and who also share the same state average effect (i.e., the value of the random effect), then the odds of MHC utilization are 8.961 times higher for the woman who received prenatal care compared to the odds of MHC utilization for the woman that do not receive prenatal care. In other words, when comparing two subjects within the same cluster such that one received prenatal care, and the other did not, but shares identical values of the remaining 2 covariates, the likelihood of utilizing MHC for the woman that received prenatal care is 8.961 times higher than the likelihood of utilizing MHC for the woman that did not receive prenatal care. Similarly, the odds of utilizing MHC for a woman having tertiary education, secondary education or primary education are 7.081, 2,153 or 1.375 higher than a woman who has no education respectively, while controlling for individual/state-level variables.

The Effect of Cluster-Level Variables

For this study, we considered the use of Proportion of Opposed Odds Ratios (POOR) proposed by Merlo as a measure of the magnitude of the effect of cluster variables. The POOR is the proportion of such odds ratios with the opposite direction to the overall odds ratio [12]. It can be evaluated as

POOR = (4)

In this case study data, the POOR for residence was 0.45. Thus, in 45% of comparison between an urban residence and a rural residence, the odds ratio for this comparison would be different in direction to that of the overall odds ratio for place of residence. The overall odds ratio was 1.388 (Table 2), denoting the odds of utilizing MHC at an urban residence to be 1.388 times higher than at a rural residence. However, in 45% of pair-wise comparisons, the odds of MHC utilization would be higher at an urban residence than at a rural residence.

Variance Partition Coefficient

In order to estimate the effect of the cluster itself on the subject outcomes, known as the general contextual effect, there is need for measures of heterogeneity and components of variance (e.g., clustering). The Variance Partition Coefficient (VPC), also known as ICC, specifically for hierarchical structures, represents the proportion of the total observed individual variation in the outcome that is attributable to between-cluster variation. Moreover, as this proportion increases, the general contextual effect also increases and vice-versa.

Given a continuous outcome, and if and denote the between-subject and between-cluster variation (e.g., obtained from a variance components model); then it is given that

VPC=. For simple hierarchical structures like women nested within states, the VPC is equivalent to the ICC [13].

Different methods such as the normal response approximation, the simulation method, the Taylor series linearization, and the latent response formulation are being used in the calculation of the VPC. For this study, we employed the latent response formulation based on its popularity and wide acceptance. Under this procedure, it is assumed that the binary outcome variable arises as the dichotomization of an underlying continuous latent variable following a logistic or a probit distribution. That is, the regression uses a logit or a probit link function, respectively. The variance of logistic distribution with scale parameter equal to one is [14].

In this data, the estimate of the between-state variance was 2.237 for Model 1, 0.853 for Model 2, and 0.643 for Model 3. These correspond to VPCs of 0.40, 0.21, and 0.16, respectively. The first of these has an unconditional interpretation, while the latter two have a conditional or residual interpretation. The VPC derived from the null model was 0.40; which implies that 40% of the individual variation in the underlying propensity to utilize MHC is due to systematic differences between states healthcare infrastructure (without considering the possibility of a different woman mix composition when estimating the state variance), while the remaining 60% is due to systematic differences between the women.

The second and third VPCs have a conditional interpretation: of the residual variation in outcomes that remains after accounting for the variables in the model, it is the proportion that is attributable to systematic differences between clusters. Thus, when using Model 2, we would infer that of the residual variation in outcomes that persists after adjusting for 3 EMW demographic variables, 21% is due to systematic differences between states healthcare infrastructure, while the remaining 79% is due to unmeasured differences between the women. However, it should be noted that if the VPC were close to 0, the outcomes for women from the same state would be no more similar than outcomes for a random sample of women from the population. Conversely, if the VPC were close to 1, then all women in the same state would have the same outcome [12].

The Median Odds Ratio as a Measure for Quantifying Variation

Another good measure for quantifying variation or heterogeneity in outcomes between clusters is the

Median Odds Ratio (MOR). The MOR was popularized in the epidemiological literature by Larsen and Merlo [15]. If one were to repeatedly sample at random two subjects with the same covariates from different clusters, then the MOR is the median odds ratio between the subject at higher risk of the outcome and the subject at the lower risk of the outcome (the cluster-specific random effects entirely quantify differences in risk). The MOR can be evaluated as:

MOR = exp (5)

where is the estimated variance of the distribution of the random effects, Φ denotes the cumulative distribution function of the standard normal distribution, while = 0.6745 is the 75th percentile of a standard normal distribution.

In our case study data, the MOR was equal to 4.16 (Model 1), 2.41 (Model 2), and 2.15 (Model 3). In interpreting the MOR from model 2, when comparing two identical women from randomly selected states, the MOR comparing a woman in a state with the higher risk of utilizing MHC to a different woman (but with the same covariate values) in a state with the lower risk of MHC utilization was 2.41. Thus, in half such comparisons, the odds of MHC utilization would be less than 2.41 for a woman in a state at higher risk compared to a different woman (but with the same covariate values) in a state at lower risk. Similarly, the MOR (Model 3) comparing a woman in a state with the higher risk of utilizing MHC to a different woman (but with the same covariate values) in a state with the lower risk of MHC utilization was 2.15. It is expected that states having better healthcare infrastructure will be at a lower risk of MHC utilization while states having poor healthcare infrastructure will be at a higher risk of MHC utilization.

However, the MOR considers only the between-cluster variance, and its value can range from one to infinity. Therefore, the result of this study indicated an MOR of 2.41 as low because it corresponds to a VPC of 0.21. That is, 21% of the total variation in utilizing MHC is due to between state differences in MHC utilization.

Discussion

Multilevel logistic regression models result in odds ratios that have a cluster-specific or within-cluster explanation. Very few multilevel analyses have been done in Nigeria using maternal healthcare utilization binary data, and these analyses have found significant multilevel effects either at the individual levels or higher levels. Findings from Ononokpono and Odimegwu [16] demonstrated a significant association between community-level factors and delivery in a separate healthcare facility. Moreover, it was found that there was a strong association between education, region of residence (community level), and delivery in a health facility. Similarly, for individual-level variables, it was also revealed that educational attainment, occupation, ethnic origin, a woman's autonomy, household wealth index, parity, and religion were significantly associated with delivery care. However, the POOR and MOR measures of utilizing MHC were not assessed.

In support of the findings by Ononokpono and Odimegwu [16], our analysis also reveals evidence (p<0.001) of effects at the states level and the individual level and it also assessed the POOR and MOR measures of utilizing MHC. At the individual level, factors such as education status, wealth index, and prenatal care were significantly associated with MHC utilization in Nigeria. While at the state level, factors such as place of residence and household were also significantly associated with utilization of MHC.

Due to the importance of hierarchical logistic regression in assessing healthcare utilization and interventions, many countries, including those in Africa have utilized this methodology to bridge variations in health utilization at both communities, district, state, and regional levels. Findings show similar observations in Ethiopia [17] where it was found that urban residents in communities with high proportion of educated women and high utilization of antenatal care (ANC) had a significant effect on institutional delivery. Also, the random effects showed that the disparity in institutional delivery service consumption between communities was statistically significant.

A study on two decades of maternity care-fee exemption policies in Ghana found that the rich benefited much more than the poor [18]. Findings from the multilevel analysis recommend that removal of user fees is essential in improving skilled birth care use; however, other obstacles such as distance to facilities, lack of transportation, poor quality of care and lack of information need to be tackled to enhance uptake for the poorest and marginalized women.

In another study that examined the individual and community-level factors associated with the utilization of antenatal care, following the adoption of the focused antenatal care (FANC) approach in Zambia [19], findings show that factors such as the woman's employment status, the actual quality of ANC received and the husband's educational attainment are positively associated with the use of ANC.

In this work, the methods to estimate the marginal or population-average effect of cluster characteristics were described. These result in the formation of 3 different types of models that allow for the formal comparison of outcomes between clusters whose characteristics differ from one another. The POOR, a summary measure of the effects of cluster-level variables, was also described. Findings show that in 45% of pair-wise comparisons between the urban and rural residence, the odds of MHC utilization would be higher at an urban residence than at a rural residence by 1.388 times. The implication of this at the state level is that women residing in urban areas stand a better chance of utilizing MHC than those in rural areas.

The MOR quantifies the magnitude of variation in the utilization of MHC between states. The MOR (Model 2) indicated the odds of MHC utilization was less than 2.41 for a woman in a state at higher risk compared to a different woman (but with the same covariate values) in a state at lower risk. Similarly, the MOR (Model 3) indicated the odds of MHC utilization was less than 2.15 for a woman in a state at higher risk compared to a different woman (but with the same covariate values) in a state at lower risk. The intra-class correlation coefficient (ICC), which is a test of the need for mixed modeling, revealed 40% (Model 1), 21% (Model 2) and 16% (Model 3) chances of utilizing MHC that is explained by between-states differences respectively. A situation where women in one state are at lower/higher risk of utilizing MHC when compared to women in another state is an indication of inequality in assessing MHC services across the Nigerian states. The implication of this is that a sizable proportion of women are automatically denied of MHC as a result of their state of residence.

However, measures such as distance to health facility, to measure accessibility, is not captured in the household survey. Cultural issues are also important factors that influence utilization of MHC, but these are not considered in this study. Although the study accounts for some state-level disparity, based on these women socio-economic and demographic factors, a significant proportion of the disparity remains inexplicable. Consequently, the importance of these women sociocultural barriers needs to be acknowledged for the effective implementation of healthcare interventions.

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