*Limitations*

This analysis is subject to a number of limitations. First, this study focuses on changes in geographic inequalities at the second administrative level or higher, which results in representing only one of many critical factors that contribute to inequities in immunization delivery [19]. While geographic location can serve as a proxy for determinants also associated with location (e.g., district-level program funding levels, relative remoteness) [58], geography on its own cannot appropriately approximate the mechanisms by which gender, ethnicity, education, wealth, religious affiliation, and other individual, household, or community characteristics affect childhood vaccination [4,8,12–14,16,18]. It is also very possible that reductions in geographic inequalities do not consistently correspond with decreases in vaccination inequalities by these other key drivers of disparities across locations or do so consistently over time. Accordingly, it is critical to prioritize future research and analyses that explicitly assess how these trends in inequality may correlate with each other.

Second, focusing on the second-administrative level likely masks important differences experienced at more granular levels (e.g., within communities), [38,54] and thus potentially could obscure a more nuanced understanding of the localized sociocultural and/or

economic contributors to higher levels of zero-dose children. Future analyses should explore alternative geographic levels or areal operationalizations (e.g., 5 × 5 km pixel estimates rather than administrative boundaries) to further characterize the distribution and magnitude of vaccination inequalities in a given location.

Third, country-to-country comparisons of subnational gaps and changes in these gaps over time may be affected by a country's total number of second-level administrative units rather than meaningful differences in vaccination equity at comparable areal units. For instance, subnational gaps in no-DTP may seem higher among in a country divided into more second-level administrative units than those with fewer units [59]. At least for the present analysis, having more (or fewer) second-level administrative units does not appear to be strongly related to 5th/95th percentile gap measures (i.e., *r* = 0.47 in 2000 and *r* = 0.38 in 2019) or change metrics from 2000 to 2019 (i.e., *r* = −0.17 for absolute change and *r* = 0.03 for percentage change). Since first- or second-level administrative units are often meaningful for health program implementation (e.g., district health authorities), we viewed using country administrative units as having more benefits and relevance than the potential drawbacks around variable subnational geographies. However, exploring alternative units of analysis (e.g., standardized pixel units) could be beneficial for future work.

Fourth, we opted to use estimates from IHME for this analysis rather than administrative data sources (e.g., DHIS2) or alternative sources (e.g., WUENIC estimates). Because the primary goal of this study was to be able to directly compare national and subnational levels and trends in no-DTP across countries, IHME estimates provided the greatest number of countries with subnational estimates for the full time period (2000–2019).

Fifth, DTP estimates draw from household surveys and other data sources in which groups or communities with higher rates of unvaccinated children may be systematically under-represented (e.g., displaced or highly mobile populations). Accordingly, current no-DTP estimates may not fully capture the 'true' magnitude or trends in zero-dose children among populations with disproportionately high vulnerabilities and risks for not being vaccinated.

Sixth, the time period of analysis focused on 2000 to 2019, and thus the identification of potential exemplars may be sensitive to estimated levels of childhood vaccination at either end of the 19-year range. Importantly, this analysis does not account for the ongoing effects of the COVID-19 pandemic, of which has had differential impacts across countries and communities since March 2020 [3,60,61]. Relatedly, these analyses do not reflect improvements in or worsening of conflict since 2019, such as in the Tigray region in Ethiopia [62].

Lastly, these analyses currently lack deeper contextual information from and by the communities most affected by higher rates of un- and under-vaccination. Our aim is to receive critical feedback on the potential applications of these positive-outlier methods for cross-country learning and synthesis around what works to reduce high rates of zero-dose prevalence, and to work with country and regional leadership to improve these approaches going forward.
