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

The intent of the integer programming model is to identify hospitals that can be used in several of the condition-specific analyses. Theoretically, each hospital could be associated with the high and low category for each condition, appearing a total of 14 times for the seven actual conditions studied. In fact, several of the large Boston teaching hospitals did appear 13 or 14 times. On average, hospitals selected by the model appeared over 4 times out of the 14 possibilities, versus hospitals not selected, which appeared slightly over 1.8 times.

We compared the number of hospitals selected by the initial run of the integer programming model (41 hospitals) to the expected number of hospitals resulting from a sampling plan in which areas were randomly sampled from the three area categories, high, medium, and low, for each condition and then records reviewed at the set of major hospitals associated with each area selected. Because of random selection of areas, this latter plan would result in more generalizable results. The expected number of hospitals resulting from the random selection of areas was determined by simulating 3,500 iterations of the sampling plan. The average number of hospitals at which it would be necessary to review records was 64, one-third more than the 41 hospitals identified by the integer programming model. Reviews at 64 hospitals would have been infeasible, given the budget and time constraints for the project.

Sampling Medical Records and the Question of Bias

Of the 48 hospitals identified from the final model, 42 agreed to participate in the study. To secure support and ensure continued participation, it was necessary to limit the number of medical records selected at individual hospitals to 150. This caused us to modify somewhat our plan for sampling medical records from participating hospitals.

For each study condition, areas were ranked from highest to lowest in terms of their relative hospital admission rates, and then the areas were divided into septiles, with septile 1 representing the ten areas with the lowest hospitalization rates and septile 7 the ten areas with the highest rates. The actual sampling plan was extremely complex, reflecting the fact that only a limited number of hospitals performed revascularization procedures (we decided to combine CABG and PTCA in the analysis) and cardiac catheterization. Essentially, however, cases were randomly sampled, one from septile 7, then one from septile 1 until the constraint on number of records at individual hospitals was met, in which case no more records were sampled from that hospital.

In Table 1, we address the question of the generalizability of our hospital selection model and our final sampling plan along the one dimension that was available, given that we only had confidentially coded hospital identifiers - the volume of discharges of the hospitals from which records were selected. Based on the total number of discharges for all conditions in 1990, hospitals in the state were divided into quintiles, where quintile 1 consisted of the 20 percent of hospitals with the largest number of discharges. For those condition-specific area septiles from which records were sampled (mostly septiles 1 and 7 for all conditions but catheterization, where a large number of cases were also selected from septiles 2 and 6), Table 1 portrays the following: (1) the distribution, over the hospital size categories, of major hospitals associated with the areas comprising the septiles and the distribution of hospitals in our sample; and (2) the percentage of patients in each hospital size category in the population, the percentage in each hospital size category in the hospitals in our sample, and the percentage in each size category among patients in the final sample.