Concept Architecture
Concept
Theoretically, the Theil Index (Health) is an entropy-based measure of inequality that quantifies the distribution of health outcomes across individuals or population groups. Derived from information theory, it measures the extent to which observed health outcomes deviate from perfect equality. In health economics, the index is used to assess health inequalities, decompose inequality into within-group and between-group components, and evaluate changes in population health distributions over time.
Mathematically, the Theil Index is calculated as an entropy measure based on the ratio of each individual's health outcome to the population mean. A value of zero indicates perfect equality, while larger values indicate greater inequality. One of the principal advantages of the index is its exact additive decomposition, allowing total inequality to be partitioned into within-group and between-group components.
In practice, the Theil Index is estimated using individual- or group-level health outcome data, such as life expectancy, mortality rates, disability measures or other health indicators. It is widely applied in studies of socioeconomic health inequalities, geographical variation, and international comparisons, particularly where decomposition of inequality is required.
Purpose
Used to quantify health inequality and decompose total inequality into within-group and between-group components for the evaluation of health disparities, healthcare policies and population health outcomes.
Mathematical Formulae
Primary Formula
T = (1/N) ????? ((y?/?) ln(y?/?))
where:
- T = Theil Index
- N = number of individuals or population units
- y? = health outcome for individual i
- ? = mean health outcome
Supporting Formulae
The additive decomposition of the Theil Index is:
T = T?between? + T?within?
where:
- T?between? = inequality between population groups
- T?within? = inequality within population groups
Related Mathematical Methods
- Entropy Measures
- Gini Coefficient
- Atkinson Index
- Generalised Entropy Indices
- Concentration Index
- Inequality Decomposition Analysis
Example
A study evaluates disability-adjusted life years (DALYs) across five regions with a mean value of 120 DALYs per 1,000 population. Applying the Theil Index formula produces:
T = 0.083
Subsequent decomposition shows:
- Between-region inequality = 0.028
- Within-region inequality = 0.055
Thus, approximately two-thirds of total health inequality arises from variation within regions rather than differences between regions.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| LN | =LN(B2/$B$102) | Calculates the natural logarithm of each health outcome relative to the population mean. |
| AVERAGE | =AVERAGE(B2:B101) | Calculates the mean health outcome used in the Theil Index. |
| SUMPRODUCT | =SUMPRODUCT((B2:B101/$B$102),LN(B2:B101/$B$102))/COUNT(B2:B101) | Calculates the Theil Index from individual health outcome data. |
VBA (Optional)
A VBA macro can automate calculation and decomposition of the Theil Index across multiple populations and reporting periods.
Sources
- Theil, H. (1967). Economics and Information Theory. North-Holland Publishing Company.
- Shorrocks, A. F. (1980). The Class of Additively Decomposable Inequality Measures. Econometrica.
- Cowell, F. A. Measuring Inequality. Oxford University Press.
- O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data. World Bank.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
Related Concepts (2)
Library
Publications
1
Fair Society, Healthy Lives: The Marmot Review (Strategic Review of Health Inequalities in England Post-2010) — Michael Marmot, Peter Goldblatt, Jessica Allen, et al., 2010 Edition ed., 2010 (The Marmot Review / UCL Institute of Health Equity)
The landmark strategic review of health inequalities in England, articulating the social determinants of health and the "social gradient" and setting out six policy objectives for reducing inequalities — the defining reference for health-inequalities policy in the UK.
Frequently Asked Questions (6)
What is the health Theil index?
An information theory based inequality measure applied to a health outcome's distribution, decomposable into inequality within and between population subgroups.
Source: Theil 1967
What is the Theil index applied to health?
The health Theil index is an inequality measure, drawn from information theory, applied to the distribution of a health outcome across a population. It summarises inequality in a single figure, where zero indicates that the outcome is equally distributed and higher values indicate greater inequality. Its distinctive feature is that it can be decomposed into inequality within population subgroups and inequality between them, which many other inequality measures cannot do cleanly.
Source: Theil 1967
How is the Theil index decomposed?
The Theil index can be split additively into a within-group component, the inequality that exists inside each subgroup, and a between-group component, the inequality between the subgroup averages. This decomposition shows how much of total inequality arises from differences within groups, such as regions or socioeconomic strata, and how much from differences between them. It is this additive decomposability that distinguishes the Theil index and makes it useful for locating the sources of inequality.
Source: Theil 1967
Why is the decomposability of the Theil index useful?
Decomposability is useful because it shows where inequality originates: separating within-group from between-group inequality reveals whether disparities lie chiefly between defined groups, such as areas or income strata, or within them. This informs where action might reduce inequality, since a large between-group component points to differences across groups, while a large within-group component points to variation inside them. Many summary measures cannot be split this way, so the Theil index adds analytical value.
Source: Theil 1967
How is the health Theil index applied?
Applied to health, the Theil index measures inequality in a health outcome, such as mortality or a health-state score, across individuals or areas, and decomposes it to show how much reflects differences between groups, for instance regions or socioeconomic classes, and how much reflects variation within them. This supports the study of the structure of health inequality, distinguishing disparities between defined populations from dispersion inside them, which guides where efforts to reduce inequality might focus.
Source: Theil 1967
What are the limitations of the health Theil index?
The Theil index is less intuitive than measures such as the Gini, since its information-theory basis gives it no simple graphical interpretation, which can make it harder to communicate. Its value depends on how the health outcome is measured, and outcomes must be on a scale where the calculations are meaningful. Like any single index, it summarises the distribution in one figure, and the decomposition depends on how the subgroups are defined.
Source: Theil 1967
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 27 Aug 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/theil-index-health
- Term code
- HE-EE-HE-017
Stable URI · Machine-readable · Resolvable · CC BY 4.0