Equity-Adjusted Net Health Benefit Tool

Equity-Adjusted Net Health Benefit Tool

This app computes the equity-adjusted Net Health Benefit of health policies, comparing them while accounting for society's aversion to health inequality. It implements the health-benefit component of Distributional Cost-Effectiveness Analysis (DCEA) : unlike conventional cost-effectiveness analysis, which treats all health gains equally, it applies equity weights that give greater value to health gains accruing to worse-off groups.

What this app does
  • Data Input: Enter your own group-level data (baseline QALE and policy effects) or use built-in examples based on Dutch income quintiles.
  • Overall Results: Compare policies using the Equally Distributed Equivalent (EDE) of health, which summarises social welfare in a single number. The EDE is always at or below the mean and reflects the penalty society places on inequality.
  • Group-Level Results: Examine Indirect Equity Weights (IEWs) and equity-weighted Net Health Benefits for each group, showing how the social decision maker values marginal gains across the distribution.
  • Sensitivity Analysis: See how the policy recommendation changes as inequality aversion varies, and identify the crossover point where the preferred policy switches.

Scope: This version focuses on the equity-adjusted health-benefit side. A full Distributional Cost-Effectiveness Analysis — incorporating intervention costs and inequality-adjusted ICERs — is planned for a future release (see the Changelog tab).

Default parameters

The app is pre-loaded with inequality aversion parameters elicited from a representative sample of the Dutch adult population. The default Atkinson parameter (ε = 5.36) and Kolm-Pollak parameter (α = 0.074) correspond to the median preferences elicited in the study. At these values, a marginal QALY gain for the poorest fifth (QALE = 62) is weighted 2.58 times more than a gain for the richest fifth (QALE = 74). You can adjust all parameters freely to explore how results change under different levels of inequality aversion.

Citation & Data
Based on

Robson, M., Harlass, M. & Brück, C.C. (2026). Health Inequality Aversion and Rank-Dependent Income Weights in the Netherlands. Working Paper, Erasmus University Rotterdam.

Study sample

A representative sample of 1,101 Dutch adults from the LISS panel (Longitudinal Internet studies for the Social Sciences) completed a two-phase Benefit Trade-Off experiment in June 2025. After applying data quality criteria (graph literacy, normative comprehension, timing, and monotonicity checks) and inverse probability weighting by age, sex, and education, the analytical sample comprises 472 participants.

The majority of participants (89%) are willing to trade off total health gains to prioritise the worse-off. The median Atkinson aversion parameter is ε = 5.36, implying that marginal health gains to the worse-off are weighted 2.6 times more than gains to the better-off.

Resources
Key references

Asaria, M., Griffin, S. & Cookson, R. (2016). Distributional Cost-Effectiveness Analysis: A Tutorial. Medical Decision Making, 36(1), 8–19.

Cookson, R., Griffin, S., Norheim, O.F. & Culyer, A.J. (2020). Distributional Cost-Effectiveness Analysis: Quantifying Health Equity Impacts and Trade-Offs. Oxford University Press.
Input Data

Policy A — EDE

Policy B — EDE

Recommendation
Aggregate Comparison
EDE vs Mean QALE
Equity-Weighted vs Unweighted Net Health Benefit by Group
Individual / Group-Level DCEA Results
Download Group Results
Indirect Equity Weights by Group
QALE Under Each Policy
Sensitivity of Policy Recommendation to Inequality Aversion
The red dashed line marks your current parameter value; the purple dot-dash line marks the Dutch median for the selected SWF (ε = 5.36, α = 0.074, or γ = 1.42; Robson, Harlass & Brück, 2026). The horizontal dashed line at 0 separates the region where Policy A is preferred (above) from where Policy B is preferred (below).
Sensitivity Table
Download Sensitivity Results
Methodology

Distributional Cost-Effectiveness Analysis

Distributional Cost-Effectiveness Analysis (DCEA) extends conventional cost-effectiveness analysis by formally integrating equity considerations into decision-making. Rather than treating all health gains equally, DCEA applies equity weights that reflect society's aversion to health inequality.

This tool implements the equity-weighted net-health-benefit component of DCEA. A full DCEA incorporating intervention costs and inequality-adjusted ICERs is planned for a future version.

Atkinson Social Welfare Function

The Equally Distributed Equivalent (EDE) level of health is:
hEDE = (Σ ωi hi1-ε)1/(1-ε)

where ε is the inequality aversion parameter and ωi are group weights.
ε = 0: No inequality aversion (health maximisation)
ε > 0: Prioritarian (willing to sacrifice total health for equity)
ε → ∞: Maximin (only the worst-off matters)

Kolm-Pollak Social Welfare Function

An alternative SWF capturing aversion to absolute health inequalities:
hEDEK = -(1/α) ln(Σ ωi exp(-α hi))

Extended Gini (Rank-Dependent) Social Welfare Function

A rank-dependent SWF in which a group's weight depends on its position in the health distribution rather than its level. Ordering groups worst-off first and letting Sk be the cumulative population share up to group k:
vk = (1 - Sk-1)γ - (1 - Sk)γ,  hEDEG = Σ vk h(k)

where γ is the rank-aversion parameter.
γ = 1: No aversion (rank weights equal population shares; EDE = mean)
γ > 1: Progressive (greater weight on the worse-off); the standard Gini is γ = 2
The IEW for group k is its rank weight per capita relative to the reference group, (vk/pk) / (vref/pref).

Rank-Dependent Income Weights

Under the Atkinson and Kolm-Pollak SWFs, the group weights ωi can be made asymmetric by income. Letting r(xi) denote the income rank of group i (1 = poorest, N = richest) in a population of N ranks:
ωi = ((N - r(xi) + 1)/N)β - ((N - r(xi))/N)β

where β is the rank-dependent income-weight parameter.
β = 1: Income-neutral (ωi equals population share; ωp = 0.5)
β > 1: Pro-poor (more weight to lower-income groups; the Concentration Index is β = 2)
0 < β < 1: Pro-rich.
ωp = ωpoor/(ωpoor + ωrich) summarises the relative weight on the poorest vs richest group.

Indirect Equity Weights

The IEW for group i relative to group j:
IEWij = (ωi/ωj) × (hj/hi)ε

This indicates how much a QALY for group i is worth, relative to group j.

Policy Evaluation

Policy A is preferred over Policy B if:
hEDEA > hEDEB

Without equity weighting, a conventional CEA compares mean QALE only.

Dutch Parameters
Default Parameter Values

Parameters elicited from a representative sample of the Dutch adult population (n = 472):

Parameter Value Interpretation
Median ε 5.36 Substantial inequality aversion (Prioritarian 5)
Median α (Kolm) 0.074 Equivalent to Prioritarian 5 for absolute inequalities
Median γ (Gini) 1.42 Rank-dependent health aversion; implies a bottom-vs-top quintile IEW of 2.67
Median IEW (h=62 vs h=74) 2.58 QALY gains for worst-off weighted 2.58× more
Modal ωp (β) 0.50 (β = 1) Rank-dependent income weight: 51.7% income-neutral, 30.6% pro-poor (β > 1), 17.6% pro-rich (β < 1)
Category Mapping
Changelog
v1.0.0 2026-06-24
  • Initial public release.
  • Equity-adjusted Net Health Benefit (NHB) analysis using empirically elicited Dutch inequality aversion parameters.
  • Atkinson, Kolm-Pollak and Extended Gini social welfare functions, with Indirect Equity Weights, EDE-based policy comparison and sensitivity analysis.
  • Full Distributional Cost-Effectiveness Analysis (incorporating costs and inequality-adjusted ICERs) is reserved for a future version.