The statistical model for computing 30-day risk-adjusted mortality rate measures is a "hierarchical regression model." This type of model is based
on the assumption that any heart attack or heart failure or pneumonia patients treated at a particular hospital will experience a level of quality of care that
applies to all patients treated for the same condition in that hospital. In other words, the expected risk of death for two similar heart attack or
heart failure or pneumonia patients treated in the same hospital would be more alike than the risk of death for the same two patients treated in two different
hospitals. The likelihood that an individual patient will die is therefore a combination of:
- his or her individual risk characteristics (for example, gender, comorbidities, and past medical history) and
- the hospital’s unique quality of care for all patients treated for that condition in that hospital.
The model estimates the effects of both of these components on mortality.
Each hospital’s “30-day risk-adjusted mortality rate” (also called the “Risk
Standardized Mortality Rate” or RSMR) is computed in several steps. First, the
predicted 30-day mortality for a particular hospital obtained from the
hierarchical regression model is divided by the expected mortality for that
hospital, which is also obtained from the regression model. Predicted mortality is the
rate of deaths from heart attack or heart failure or pneumonia that would be
anticipated in the particular hospital during the 12-month period, given the
patient case mix and the hospital’s unique quality of care effect on mortality.
Expected mortality is the rate of deaths from heart attack or 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 mortality for patients with that condition. This ratio is then
multiplied by the national unadjusted mortality rate for the condition for all
hospitals to compute a “risk-adjusted mortality rate” for the hospital. So, the
higher a hospital’s predicted 30-day mortality rate, relative to expected
mortality for the hospital’s particular case mix of patients, the higher its
adjusted mortality rate will be. Hospitals with better quality will have lower
rates.
(Predicted 30-day mortality/Expected mortality) * U.S. National mortality rate = RSMR
For example, suppose the model predicts that 10 percent of Hospital A’s heart attack patients would die within 30 days of admission in a given
year, based on their ages, gender mix, and pre-existing health conditions, and based on the estimate of the hospital’s specific quality of care.
Then, suppose that the expected rate of 30-day deaths for those same patients were higher – say, 15 percent – if they had instead been treated at
an "average" U.S. hospital. If the actual mortality rate for the 12-month period for all heart attack patients in all hospitals in the U.S. is 12
percent, then the hospital’s risk-adjusted 30-day mortality rate would be 8 percent.
(10%/15%)* 12% = RSMR for Hospital A 8%
If, instead, 9 percent of these patients would be expected to have died if treated at the average hospital, then the hospital’s mortality rate
would be 13.3 percent.
(10%/9%)* 12% = RSMR for Hospital A 13.3%
In the first case, the hospital performed better than the average hospital and had a relatively low risk-adjusted mortality rate (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 mortality rate is the same as the expected mortality rate for the average hospital for
the same group of low-risk patients would have an adjusted mortality rate equal to the national rate (12 percent in this example). Similarly,
hospitals with high-risk patients whose predicted mortality rate is the same as the expected mortality rate for the average hospital for the same
group of high-risk patients would also have an adjusted mortality rate equal to the national rate of 12 percent. Thus, each hospital’s case mix
should not affect the adjusted mortality rates used to compare hospitals.
The hierarchical regression model also adjusts mortality rates results for small hospitals or hospitals with few heart attack or heart failure
or pneumonia cases in a given year. This reduces the chance that such hospitals’ performance will fluctuate wildly from year to year or that they will be
wrongly classified as either a worse or better performer. For these hospitals, the model not only considers deaths 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 result
more reliable. In essence, the predicted mortality rate for a hospital with a small number of cases is moved toward the overall U.S. National
mortality rate for all hospitals. The estimates of mortality 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.
The statistical model for computing the 30-day risk-standardized readmission rates is a "hierarchical regression model."
This type of model is based on the assumption that any heart attack, heart failure, or pneumonia patient
treated at a particular hospital will experience a level of quality of care that applies to all patients
treated for the same condition in that hospital. In other words, the expected risk of readmission for
two similar heart attack, heart failure, or pneumonia patients treated in the same hospital would be more
alike than the risk of readmission for the same two patients treated in two different hospitals. The
likelihood that an individual patient will be readmitted is therefore a combination of:
- his or her individual risk characteristics (for example, gender, comorbidities, and past medical history) and
- the hospital’s unique quality of care for all patients treated for that condition in that hospital.
The model estimates the effects of both of these components on on risk of readmission.
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.
(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
pre-existing 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 were 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 U.S. is 12 percent, then the hospital’s
30-day risk-standardized readmission rate 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 risk-standardized readmission rate (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.
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’ performance 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 result 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, as described below.