Signature
yX_i = alpha_hat + sum_(j=1)^J [beta_hat_j * x_ji] + sum_(k=1)^K [gamma_hat_k * z_bar_k]
| Inputs | Definition | Unit |
|---|---|---|
alpha_hat | Estimated intercept of the regression of use on need and control variables | units of use |
beta_hat_j | Estimated coefficient on need variable j, read as the appropriate difference in use per unit of that need indicator, summed over the J need variables | units of use per unit of the need variable |
x_ji | Value of need variable j for person i, for example an indicator of fair or poor self-assessed health, a chronic condition, an activity limitation or an age and sex group | unit of the need variable, often an indicator coded 1 or 0 |
gamma_hat_k | Estimated coefficient on control variable k, a non-need correlate of use such as income or insurance cover, summed over the K control variables | units of use per unit of the control variable |
z_bar_k | Sample mean of control variable k, used in place of each person's own value | unit of the control variable |
yX_i | Need-expected use of care by person i: the use predicted from the need regression with that person's need values and every control at its sample mean | units of use, for example doctor visits per person per year |
|---|
Function
Horizontal equity measurement function for health care delivery and finance
Maps data on the use of health care, proxies of need and compulsory health payments, for people ranked by income or another measure of living standards, to measures of horizontal equity: need-expected use from a need regression, need-standardised use, the horizontal inequity index for the delivery of care, its rule-of-75 reading, and the horizontal inequity term in the decomposition of the redistributive effect of health finance. Equal treatment for equal need is judged against the average relationship between need and use in the sample, so the vertical norm is assumed rather than tested. The grouped-data concentration index (HE-FM-HINQ-005 on the Health Inequality page and HE-FM-VEQ-002 on the Vertical Equity page) and the Kakwani index (HE-FM-VEQ-001) have their own records and are not repeated here.
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Implementations
Excel
Need-expected use of health care in one Excel cell
With the intercept in a cell named Intercept, the need coefficients and the person's need values in ranges named NeedCoef and NeedValues, and the control coefficients and control sample means in ControlCoef and ControlMeans, Excel returns need-expected use. Each pair of ranges has the same size and order.
=Intercept+SUMPRODUCT(NeedCoef,NeedValues)+SUMPRODUCT(ControlCoef,ControlMeans)
Assumptions
Observed need indicators capture need in the need regression
Need is proxied by demographic variables plus health status and morbidity, such as self-assessed health, chronic conditions and activity limitations. Variation in use left after these indicators are controlled for is treated as due to non-need factors, so the result is biased if unobserved need is correlated with income.
Average relation between need and use taken as the vertical norm
The fitted need coefficients are taken as the appropriate differences in use between people in different states of need, which assumes that vertical equity holds on average in the sample. No external standard of needed care enters the prediction.
Linear need regression for indirect standardisation
The regression is linear, so setting the controls to their means removes their effect on the distribution of predicted use. In a nonlinear model for counts or binary use, such as a probit, the controls cannot be fully neutralised in this way, and the result depends on the values at which they are set.
Worked examples
Need-expected visits for a person in poor health in an illustrative need regression
Illustrative figures: a need regression has an intercept of 1.5 visits, a coefficient of 5.0 visits on fair or poor self-assessed health and a coefficient of 1.0 visit on insurance cover, and half the sample is insured. A person in poor health then has need-expected use of 7.0 visits a year, whatever their own insurance status.
alpha_hat = 1.5; beta_hat_j = [5.0]; x_ji = [1]; gamma_hat_k = [1.0]; z_bar_k = [0.5]; yX_i = 7.0
Need-expected visits for a person in good health and the quintile means
The same illustrative regression gives 2.0 visits for a person in good health. A quintile in which 60 per cent report poor health then has mean need-expected use of 5.0 visits, and one in which 20 per cent do has 3.0, the poorest and richest figures in the article's worked example.
alpha_hat = 1.5; beta_hat_j = [5.0]; x_ji = [0]; gamma_hat_k = [1.0]; z_bar_k = [0.5]; yX_i = 2.0
Common errors
Leaving non-need controls out of the need regression
If a correlate of use that is not need, such as more generous insurance cover for people in poor health, is left out of the regression, the coefficient on poor health picks up part of its effect. The appropriate need difference is then overstated, and part of a non-need effect is removed from the measured inequity as if it were need.
Predicting need-expected use with each person's own control values
Using individual values of the controls puts their effects into need-expected use, so the part of the inequality carried by income or insurance is standardised away. In the illustrative regression an insured person in poor health would be given 7.5 visits instead of 7.0, and need-expected use would vary with insurance status as well as need.
Sources
World Bank guide on the standardising regression for need-expected use
O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. Washington, DC: World Bank; 2008. Chapter 5, equations 5.1 and 5.2: the indirect standardisation regression with variables to standardise for and controls, and predictions from individual values of the standardising variables with the controls at their sample means.
World Bank guide on need proxies and controls in health care use
O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. Washington, DC: World Bank; 2008. Chapter 15, pages 177 to 179: need proxied by demographics, self-assessed health, chronic conditions and activity limitations; the assumption that vertical equity holds on average; controls that would bias the need coefficients if omitted, with the insurance cover example; and the difficulty of neutralising controls in nonlinear models (equation 15.2).
Canonical Identity
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