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Point Estimator in its Generic Form

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In a general form, all thirteen summary measures of health disparities in HD*Calc can be expressed as a function of health group means and population shares (μj and pj for j =1,...J), given by X = g (μ,p; for j =1,...J), where (.) is a specific differentiable function of μj and pj, corresponding to each of the eleven disparity measures.  Therefore, X is estimated by substituting means and proportions \(({\mu}_{j},p_{j})\) with complex survey estimates \(({\widehat\mu}_{j},\widehat{p}_{j})\), given by

$$\widehat{X}=({\widehat\mu}_{j},\widehat{p}_{j}),$$

where

$$\widehat{\mu}_{j}=\frac{{\sum}_{h=1}^{H}{\sum}_{\alpha=1}^{t_{h}}{\sum}_{i=1}^{n_{h\alpha}}{\delta}_{h{\alpha}i}{w}_{h{\alpha}i}{y}_{h{\alpha}i}}{{\sum}_{h=1}^{H}{\sum}_{\alpha=1}^{t_{h}}{\sum}_{i=1}^{n_{h\alpha}}{\delta}_{h{\alpha}i}{w}_{h{\alpha}i}}$$

and

$$\widehat{p}_{j}=\frac{{\sum}_{h=1}^{H}{\sum}_{\alpha=1}^{t_{h}}{\sum}_{i=1}^{n_{h\alpha}}{\delta}_{h{\alpha}i}{w}_{h{\alpha}i}}{{\sum}_{h=1}^{H}{\sum}_{\alpha=1}^{t_{h}}{\sum}_{i=1}^{n_{h\alpha}}{w}_{h{\alpha}i}}.$$

 

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