When the frontier is drawn by the poorest countries: comparison-set sensitivity in health system efficiency rankings
Abstract
Background: Cross-country league tables of health system efficiency rank countries and are used to argue that one institutional form outperforms another. A country’s score depends on the comparator set. We ask how much of a ranking that choice produces, and what survives when it is made explicit and second-stage inference uses methods suited to bounded DEA scores.
Methods: Input-oriented data envelopment analysis (DEA) was applied to a 2019 cross-section of 70 countries with complete data on four health inputs and one output (life expectancy at birth). Countries were scored against a pooled frontier, an income-group frontier, and a DEA meta-frontier with a technology gap ratio. Bias-corrected scores and confidence intervals came from a non-parametric bootstrap that resampled the decision-making units (B = 1000 replications). Leave-one-out and order-m estimates tested whether the pooled frontier was anchored by one or two observations. Second-stage inference used the Papke-Wooldridge fractional response model and a parametric truncated regression in the Simar-Wilson framework (B = 1000) on three dependent variables (pooled VRS, within-group CRS, meta-frontier TGR), n = 58.
Results: Two of 70 countries defined the pooled CRS frontier (Gambia, Papua New Guinea). China scored 0.158 against pooled CRS (34th of 70) and 0.997 against pooled VRS (25th of 70; 23 of 70 countries sit on the VRS frontier with score = 1.000, so China is close to the VRS frontier). Within its upper-middle-income group it scored 0.491 (14th of 17), with a technology gap ratio of 0.322. Removing both frontier countries together moved China’s CRS score to 0.169 (rank 33 of 68) while leaving the country ordering nearly intact (Spearman rho = 0.993). The out-of-pocket share was not associated with efficiency on any of the three primary dependent variables (all p > 0.30). System-type coefficients did not reverse sign under VRS, and their 95% confidence intervals included zero on the TGR dependent variable; marginal VRS associations in one control set did not survive the other control set. The United States market-based coefficient was negative in direction but imprecise in the bounded-outcome model. Common support was poor (mean GDP per capita US$4813 vs. US$58842 across fragmented and national-health-service groups).
Conclusions: Comparison-set sensitivity is the main result. The out-of-pocket association and system-type effects reported in earlier pooled-CRS work do not survive methodologically appropriate re-estimation; they reflect that a pooled CRS frontier spanning all income groups is defined by the lowest-spending countries. China’s financing projections are exploratory.
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BibTeX
@article{ma2026when,
title = {{When the frontier is drawn by the poorest countries: comparison-set sensitivity in health system efficiency rankings}},
author = {Hongwei Ma},
journal = {BMC Public Health},
year = {2026},
month = oct,
doi = {10.1186/s12889-026-30061-0},
url = {https://link.springer.com/article/10.1186/s12889-026-30061-0},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - When the frontier is drawn by the poorest countries: comparison-set sensitivity in health system efficiency rankings
AU - Hongwei Ma
PY - 2026
DA - 2026/10/28
JO - BMC Public Health
DO - 10.1186/s12889-026-30061-0
UR - https://link.springer.com/article/10.1186/s12889-026-30061-0
AB - Background: Cross-country league tables of health system efficiency rank countries and are used to argue that one institutional form outperforms another. A country’s score depends on the comparator set. We ask how much of a ranking that choice produces, and what survives when it is made explicit and second-stage inference uses methods suited to bounded DEA scores. Methods: Input-oriented data envelopment analysis (DEA) was applied to a 2019 cross-section of 70 countries with complete data on four health inputs and one output (life expectancy at birth). Countries were scored against a pooled frontier, an income-group frontier, and a DEA meta-frontier with a technology gap ratio. Bias-corrected scores and confidence intervals came from a non-parametric bootstrap that resampled the decision-making units (B = 1000 replications). Leave-one-out and order-m estimates tested whether the pooled frontier was anchored by one or two observations. Second-stage inference used the Papke-Wooldridge fractional response model and a parametric truncated regression in the Simar-Wilson framework (B = 1000) on three dependent variables (pooled VRS, within-group CRS, meta-frontier TGR), n = 58. Results: Two of 70 countries defined the pooled CRS frontier (Gambia, Papua New Guinea). China scored 0.158 against pooled CRS (34th of 70) and 0.997 against pooled VRS (25th of 70; 23 of 70 countries sit on the VRS frontier with score = 1.000, so China is close to the VRS frontier). Within its upper-middle-income group it scored 0.491 (14th of 17), with a technology gap ratio of 0.322. Removing both frontier countries together moved China’s CRS score to 0.169 (rank 33 of 68) while leaving the country ordering nearly intact (Spearman rho = 0.993). The out-of-pocket share was not associated with efficiency on any of the three primary dependent variables (all p > 0.30). System-type coefficients did not reverse sign under VRS, and their 95% confidence intervals included zero on the TGR dependent variable; marginal VRS associations in one control set did not survive the other control set. The United States market-based coefficient was negative in direction but imprecise in the bounded-outcome model. Common support was poor (mean GDP per capita US$4813 vs. US$58842 across fragmented and national-health-service groups). Conclusions: Comparison-set sensitivity is the main result. The out-of-pocket association and system-type effects reported in earlier pooled-CRS work do not survive methodologically appropriate re-estimation; they reflect that a pooled CRS frontier spanning all income groups is defined by the lowest-spending countries. China’s financing projections are exploratory.
SN - 1471-2458
ER -