A short note revisiting the concentration index: Does the normalization of the concentration index matter?
Bibliographic record
Abstract
The concentration index, including its normalization, is prominently used to assess socioeconomic inequalities in health and health care. Wagstaff's and Erreygers' normalizations or corrections of the standard concentration index are the most suggested approaches when analyzing binary health variables encountered in many health economics and health services research. In empirical applications of the corrected or normalized concentration indices, researchers interpret them similarly to the standard concentration index, which may be problematic as this ignores their underlying behaviors. This paper shows that the empirical bounds of the standard concentration index, including the corrected indices, depend not only on the sample size directly but also on the sampling weight. Notably, the paper highlights critical challenges for assessing and interpreting the popular Wagstaff's and Erreygers' corrected concentration indices with binary health variables. Specifically, it shows that it might be misleading, for example, to assess socioeconomic health inequalities using the magnitude of the "symmetric" Erreygers' corrected concentration index in the face of progressive improvements in the binary health variable. Also, Wagstaff's normalized concentration index may give a spurious "concentration" of the binary health variable among the rich or the poor in certain rare instances.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.022 | 0.124 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.003 | 0.011 |
| Scholarly communication | 0.010 | 0.014 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.004 | 0.016 |
| Insufficient payload (model declined to judge) | 0.006 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".