# Analysis of the Joint Distribution of Disproportionate Share Hospital Payments. Composite Index

We constructed a composite index based on four indicators of financial vulnerability: total margin net of DSH payments, current ratio, cash flow to total debt, and fixed asset turnover. This index is an ordinal measure (shows only the order in a sequence) that ranks all hospitals in the sample according to the extent of their financial vulnerability. This rank is not an indicator of the absolute magnitude of hospitals' financial vulnerability.

We constructed the composite index both for 1998 and for three years overall. For 1998, we derived the index by averaging each hospital's rank according to each of the four indicators of financial vulnerability. For example, if a hospital ranks 10 for total margin (lower ranks always implying weaker positions), 200 for current ratio, 100 for cash flow to total debt, and 50 for fixed assets turnover, the composite rank would be (10+200+100+50)/4 = 90. We derived the final index (hospital ordering) by ranking these averages in the ascending order. For the overall 3-year index, one more step is added: a hospital's rank for each year for the same indicator is averaged before the same procedure is applied to the three-year averages.

Two important assumptions underlie the construction of this composite index. First, we assume all four indicators contribute equally to the overall financial health of hospitals (i.e., they have the same importance and thus are weighted equally). Second, we assume that each of the individual indicators conveys separate information that is not duplicative of the other indicators. The validity of these assumptions can be examined based on their substantive meaning for the hospitals, but the definitions of each indicator, as well as the statistical properties of the obtained series, do not appear to contradict these assumptions.

Technically, we calculated the composite index in three steps. First, we calculated the composite index for those hospitals for which all four indicators of financial pressure were available (96.5% of the hospitals that have any indicators calculated). Second, we excluded about one percent of the observations for having outlier values. The outlier cut-offs are:

• Total margin net of DSH payments: absolute value exceeds 70%;
• Current ratio: absolute value exceeds 12;
• Cash flow to total debt: absolute value exceeds 4;
• Fixed asset turnover: absolute value exceeds 18.

Third, we predicted values for the hospitals that had missing values for one or more of the indicators (3.5%) using a regression analysis model that used the available values of indicators for these hospitals as independent variables.

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