Decomposing differences in acute myocardial infarction fatality in Italian regions

Abstract

The paper develops a general method for evaluating geographical differences in the outcome of acute myocardial infarction patients, by looking at the process of disease occurrence from infarction to hospitalization and possible death or recovery. The method is applied to regional data in Italy, where the long history of geographical diversities in economical, social and cultural fields is reflected in health care. Specific features of AMI, such as high fatality and fast course of the disease, make it a suitable tracer condition to investigate into the differences of regional health systems during the acute phase of hospitalization. The paper combines administrative and official statistics by region and offers a tool providing suggestions to policy-makers where further eventual investigations are needed around the care pathway and also what possible actions might be undertaken to improve the outcomes.

Appendix

Let i _r , h _r , f _r be the attack, hospitalization and in-hospital fatality rates in region r, as defined in Eq. 1. Let F _r be the number of in-hospital deaths and N _r the population of region r. Equation 3 provides a decomposition of the in-hospital deaths in terms of the above mentioned rates. The standardized number of deaths by infarction in the hospitals of region r ($\bar{F}_r$) is then obtained by substituting the regional rates with the corresponding Italian averages ($\bar i, \bar h, \bar f$). Thus, it is possible to compare the regional outcomes in terms of the deviation of in-hospital deaths in region r from the corresponding standardized value:

$$\begin{array}{*{20}l} {{F_{r} - \overline{F} _{r} } \hfill} & {{ = N_{r} \times {\left( {i_{r} \times h_{r} \times f_{r} - \overline{i} \times \overline{h} \times \overline{f} } \right)}} \hfill} \\ {{} \hfill} & {{ = N_{r} \times {\left\{ {{\left( {\overline{i} + \Delta i_{r} } \right)} \times {\left( {\overline{h} + \Delta h_{r} } \right)} \times {\left( {\overline{f} + \Delta f_{r} } \right)} - \left. {\overline{i} \times \overline{h} \times \overline{f} } \right)} \right\}},} \hfill} \\ \end{array} $$

(4)

where

$$i_{r} = \overline{i} + \Delta i_{r} ;\,h_{r} = \overline{h} + \Delta h_{r} ;\,f_{r} = \overline{f} + \Delta f$$

After developing the products in Eq. 4, the deviation of the regional in-hospital deaths from the corresponding standardized value decomposes into a series of first-, second- and third-order deviations:

$$F_{r} - \overline{F} _{r} = N_{r} \times {\left\{ {\Delta I + \Delta H + \Delta F + \Delta ^{2} IH + \Delta ^{2} IF + \Delta ^{2} HF + \Delta ^{3} IHF} \right\}},$$

where

$$\Delta I = \overline{h} \times \overline{f} \times \Delta i_{r} ;\,\Delta H = \overline{i} \times \overline{f} \times \Delta h_{r} ;\,\Delta F = \overline{i} \times \overline{h} \times \Delta f_{r} ;\,\Delta ^{2} IH = \overline{f} \times \Delta i_{r} \times \Delta h_{r} ;\,\Delta ^{2} IF = \overline{h} \times \Delta i_{r} \times \Delta f_{r} ;\,\Delta ^{2} HF = \overline{i} \times \Delta h_{r} \times \Delta f_{r} ;\,\Delta ^{3} IHF = \Delta i_{r} \times \Delta h_{r} \times \Delta f_{r} .$$

The first-order deviation ΔH can be interpreted as the deviation referring to hospitalization of the in-hospital deaths from the standardized counterpart, when the regional attack and in-hospital fatality rates are supposed equal to the Italian rates; similarly for the other two first-order deviations.

Furthermore

$$\begin{aligned} & \% \Delta I = \frac{{\Delta I}}{{\overline{F} _{r} }} \times 100 = \frac{{\Delta i_{r} }}{{\overline{i} }} \times 100 \\ & \% \Delta H = \frac{{\Delta H}}{{\overline{F} _{r} }} \times 100 = \frac{{\Delta h_{r} }}{{\overline{h} }} \times 100 \\ & \% \Delta F = \frac{{\Delta F}}{{\overline{F} _{r} }} \times 100 = \frac{{\Delta f_{r} }}{{\overline{f} }} \times 100 \\ \end{aligned} $$

denote the % contribution of each deviation and are used to build the three bars of Fig. 3a and b. Deviations of second and third order are negligible and are not considered in the analysis.