**2. Materials & Methods**

The data for this study include the most recent DHS survey between 2010 and 2022 for 56 countries (see Appendix A). DHS surveys are nationally representative and all contain data at the individual-level on coverage for eight key routine vaccines against four antigens, which are utilized in this assessment. The vaccines assessed include: Bacillus Calmette–Guerin (BCG), Diphtheria–Tetanus–Pertussis-containing vaccine doses 1 through 3 (DTP1–3), polio vaccine doses 1–3 (Polio1–3), and the measles-containing vaccine first dose (MCV1), as well as an indicator for being fully immunized for age with each of these vaccines. Data on vaccination coverage, as well as socio-demographic covariates, are used alongside the VERSE multivariate vaccination equity assessment toolkit to measure both wealth-based and multivariate equity in vaccination coverage within each country over each vaccine outcome. A complete list of variables from the DHS surveys that are used in the multivariate equity assessment is presented in Appendix B.

The primary outputs of the VERSE toolkit and the featured outcomes of this study are a multivariate concentration index, a relative measure of equity, and an absolute equity gap in coverage, an absolute (level) measure of equity. These measures are derived from literature on the measurement of socioeconomic equity by Wagstaff and Erreygers, combined with measures of "direct unfairness"—a term borrowed from social choice theory, which has been applied to healthcare access in the works of Fleurbaey, Schokkaert, Cookson, and Barbosa [15–21]. The multivariate concentration index takes the form of a traditional concentration index over vaccination coverage where, instead of ranking individuals by income, individuals are ranked by multivariate unfair disadvantage in access. Multivariate unfair disadvantage, as parameterized in the VERSE model, is measured as an individuallevel propensity score for unfair disadvantage, netting out the effect of fair sources of variation in coverage. For the purposes of this study, the only fair source of variation in coverage status is whether a child is underage to receive the vaccine according to the national immunization schedule of the country examined. Unfair sources of variation included in this assessment are the sex of the child, maternal education level, socioeconomic status derived from the DHS wealth index, coverage by health insurance, urban or rural designation, and geopolitical sub-unit of residence. These factors were chosen based on standardized and near-universal data collection across all demographic and health surveys (DHS) [22]. Complete mathematical details of the quantification of unfair disadvantage, as well as the multivariate equity metric produced by the VERSE toolkit, can be found in the VERSE toolkit's methodological publication [3].

In addition to the multivariate concentration index produced in the VERSE Toolkit, an absolute equity gap is also produced [19,20]. The AEG is a measure of the absolute difference in vaccination coverage achieved by the top 20% compared with the bottom 20% of the population, where the population is ranked based on their propensity score for unfair disadvantage. Mathematically, this is equivalent to isolating the top and bottom quintiles from the Lorenz curve used to estimate the Wagstaff (direct) concentration index [20]. In most equity studies, socioeconomic status as measured by either income or, in the case of the DHS surveys, wealth index, is the sole variable used to rank or group individuals prior to computing a concentration index, slope index, Gini coefficient, Kakwani index, Atkinson index, absolute equity gap, or relative equity gap. In keeping with this convention, we also compute the Wagstaff (direct) concentration index, as well as the AEG between the top and bottom quintile, utilizing the DHS's wealth index as the only criterion to rank individuals. Concentration indices and AEGs derived from both the multivariate and traditional approaches are computed for 56 countries utilizing the same DHS dataset. The concentration indices and AEGs are then compared directly within countries with one another to provide empirical evidence of the degree of inequity, stemming from multiple factors known to be related to disadvantage in being vaccinated, that is missed by using only the traditional approaches for equity measurement.

#### **3. Results**

#### *3.1. Full Immunization for Age*

Among the 56 countries included in the analysis, the average multivariate concentration index for the fully immunized for age status was 0.125 (95% confidence interval: 0.109, 0.140), not weighting by population size. Meanwhile, the average wealth-based concentration index was estimated only at 0.014 (0.004, 0.024)—a difference of 0.110, representing that traditional concentration indices captured, on average, 89% less inequity compared with multivariate concentration index (see Table 1).


**Table 1.** Average inequities among 56 studied countries, by vaccine.

The countries with the most significant difference in concentration index between the two approaches were Chad (0.31), Gabon (0.26), Afghanistan (0.25), Angola (0.25), Ethiopia (0.24), Nigeria (0.22), Papua New Guinea (0.21), Yemen (0.20), Guinea (0.19), and Madagascar (0.18). These countries also have among the lowest full immunization coverage of countries with eligible DHS surveys, ranging from 16% to 50%, and the highest multivariate concentration indices, ranging from 0.205 to 0.331 (see Table 2). When considering wealth-based concentration indices, most of these countries either indicate very slight inequity, or none at all. However, comparing the two types of concentration indices illustrates that, among this group of countries, the traditional wealth-based concentration index misses between 67% and 107% of the coverage inequity for full immunization for age.

Furthermore, nine of these ten countries had the largest AEG values in the data set, ranging from a 33 to 59 percentage point gap in coverage between the most and least advantaged quintiles. The differences between the multivariate and wealth-based AEGs range from 3 to 36 percentage points, highlighting the importance of including multiple criteria when assessing disadvantage and equity.



**Table 2.**Inequities in fully immunized status, by country.







Countries presenting modest differences between concentration indices and equity gaps were typically also among those with the highest levels of coverage for the fully immunized for age status (ranging from 55.6% and 92.1%). While high coverage is likely to be correlated with higher levels of equity utilizing either wealth-based or multivariate approaches—due to fewer individuals missing out on vaccines—it is not always true that a higher performing country will have a higher degree of equity. For instance, Pakistan achieved a full immunization for age coverage level of 65.1% in 2016, yet its multivariate concentration index indicates significant inequity: 0.152, which is 0.123 points higher than its corresponding wealth-based concentration index. Additionally, low coverage does not always lead to inequity, depending on how that coverage is distributed with respect to the assessed characteristics. For example, Uganda achieved a full immunization coverage level of 50.9% in 2016, and yet presented significantly lower multivariate and wealth-based concentration indices, estimated respectively at 0.092 and −0.044, compared with Pakistan. This indicates that while there is a large proportion of children who did not receive the full course of immunization as per Uganda's immunization schedule, these children are more randomly distributed throughout the population in terms of both geographic and socio-demographic parameters (sex, wealth, education, insurance status) than in Pakistan.

Examining the absolute equity gaps using the multivariate metric, full immunization coverage among the bottom quintile of the population would need to increase by approximately 28.8 percentage points (95% confidence interval: 25.1, 32.6) to achieve a similar level of the fully immunized for age status as the most advantage quintile of the population (see Table 1). When utilizing only the wealth-based approach, the AEG for the fully immunized for age status was estimated as only a 13.8 percentage point gap (95% confidence interval: 9.5–18.2). This indicates that wealth-based measures significantly underestimate the fully immunized coverage gap between the most and least advantaged by 15.0 percentage points, on average, across all datasets (see Table 1).
