An integer programming model to limit hospital selection in studies with repeated sampling

Health Services Research, June, 1995 by Michael Shwartz, Ronald K. Klimberg, Melinda Karp, Lisa I. Iezzoni, Arlene S. Ash, Janelle Heineke, Susan M.C. Payne, Joseph D. Restuccia

3. Area-specific rates of hospitalization for each condition were estimated using empirical Bayes techniques (Efron and Morris 1975). This approach also accounts better for the greater unreliability associated with estimates from areas with small populations.

Two criteria were used to select study conditions: (1) differences in the amount of systematic variation in hospital admission rates across areas, as measured by the maximum likelihood estimates (in particular, we wanted to select some conditions with high variation, some with medium variation, and some with low variation); and (2) conditions that represented a substantial proportion of Medicare discharges or dollars.

After reviewing a range of candidate conditions, we focused on respiratory and cardiac conditions. In particular, the following ADRGs were selected: angina (DRG 140); atherosclerosis (DRGs 132-133); coronary artery bypass graft surgery (DRGs 106-107); percutaneous transluminal coronary angioplasty (DRG 112); cardiac catheterization (DRGs 124-125); acute myocardial infarction (DRGs 121-123); asthma (DRGs 96-98); respiratory infection (DRG 79); chronic obstructive pulmonary disease (DRG 88); and pneumonia (DRGs 89-91). For evaluating appropriateness, angina and atherosclerosis were combined; respiratory infection and pneumonia were combined; and asthma and COPD were combined. Appropriateness will be evaluated by applying condition-specific criteria developed by expert physician panels to hospital medical records.

The Sampling Problem

For each of the five cardiac and two respiratory conditions, areas were ranked based on their empirical Bayes-estimated area-specific rates of hospitalization, using data from 1989-1991. Because of the small number of cases in individual areas for specific conditions, we decided to classify areas into three nonexhaustive categories: high-rate areas (the top 15 areas in terms of their hospitalization rates), medium-rate areas (areas with ranks 28 to 42, where 35 is the midpoint of the ranks); and low-rate areas (ranked in the bottom 15).

The most straightforward sampling plan is to randomly sample discharges from the population of all discharges within a certain time period from high-, medium-, and low-rate areas, respectively. However, we were concerned that this would require a review of records at numerous hospitals, sometimes involving only a few records from low-volume facilities. We wanted to concentrate the medical record reviews in hospitals that were major providers of treatment for residents of the areas under consideration. Therefore, for each condition in each area, we identified major hospitals by ranking hospitals from highest to lowest in terms of the percentage of discharges and then selecting the smallest subset of hospitals for which the cumulative percentage of discharges was at least 75 percent. In this way we were able to associate a small number of hospitals with each area for each condition (in most cases two to five hospitals per area, with the exception of several of the areas in Boston, where up to eight hospitals were associated with the area).