Each hospital's 30-day risk-standardized readmission rate (RSRR) is computed in several steps. First, the predicted 30-day readmission for a particular hospital obtained from the hierarchical regression model is divided by the expected readmission for that hospital, which is also obtained from the regression model. Predicted readmission is the number of readmissions (following discharge for heart attack, heart failure, or pneumonia) that would be anticipated in the particular hospital during the study period, given the patient case mix and the hospital's unique quality of care effect on readmission. Expected readmission is the number of readmissions (following discharge for heart attack, heart failure, or pneumonia) that would be expected if the same patients with the same characteristics had instead been treated at an "average" hospital, given the "average" hospital's quality of care effect on readmission for patients with that condition.
This ratio is then multiplied by the national unadjusted readmission rate for the condition for all hospitals to compute an RSRR for the hospital. So, the higher a hospital's predicted 30-day readmission rate, relative to expected readmission for the hospital's particular case mix of patients, the higher its adjusted readmission rate will be. Hospitals with better quality will have lower rates.
The formula follows:
(Predicted 30-day readmission/Expected readmission) * U.S. national readmission rate = RSRR
For example, suppose the model predicts that 10 of Hospital A's heart attack admissions would be readmitted within 30 days of discharge in a given year, based on their age, gender, and preexisting health conditions, and based on the estimate of the hospital's specific quality of care. Then, suppose that the expected number of 30-day readmissions for those same patients would be higher—say, 15—if they had instead been treated at an "average" U.S. hospital. If the actual readmission rate for the study period for all heart attack admissions in all hospitals in the United States is 12 percent, then the hospital's 30-day RSRR would be 8 percent.
RSRR for Hospital A = (10/15) * 12% = 8%
If, instead, 9 of these patients would be expected to have been readmitted if treated at the "average" hospital, then the hospital's readmission rate would be 13.3 percent.
RSRR for Hospital A = (10/9) * 12% = 13.3%
In the first case, the hospital performed better than the national average and had a relatively low RSRR (8 percent); in the second case, it performed worse and had a relatively high rate (13.3 percent).
Hospitals with relatively low-risk patients whose predicted readmission is the same as the expected readmission for the average hospital for the same group of low-risk patients would have an adjusted readmission rate equal to the national rate (12 percent in this example). Similarly, hospitals with high-risk patients whose predicted readmission is the same as the expected readmission for the average hospital for the same group of high-risk patients would also have an adjusted readmission rate equal to the national rate of 12 percent. Thus, each hospital's case mix should not affect the adjusted readmission rates used to compare hospitals.
Adjusting for Small Hospitals or a Small Number of Cases. The hierarchical regression model also adjusts readmission rate results for small hospitals or hospitals with few heart attack, heart failure, or pneumonia cases in a given reference period. This reduces the chance that such hospitals' performances will fluctuate wildly from year to year or that they will be wrongly classified as either a worse or a better performer. For these hospitals, the model not only considers readmissions among patients treated for the condition in the small sample size of cases, but pools together patients from all hospitals treated for the given condition, to make the results more reliable.
In essence, the predicted readmission rate for a hospital with a small number of cases is moved toward the overall U.S. national readmission rate for all hospitals. The estimates of readmission for hospitals with few patients will rely considerably on the pooled data for all hospitals, making it less likely that small hospitals will fall into either of the outlier categories. This pooling affords a "borrowing of statistical strength" that provides more confidence in the results. For classifying hospital performance, extremely small hospitals will be reported separately.
