The 2010 derivation cohort consisted of 8,700 patients, 14.1% of whom were readmitted within 30 days of any index admission. The 2011 validation cohort consisted of 8,189 patients, with a 14.8% readmission rate. ► shows characteristics of demography and healthcare utilization of the 2010 and 2011 groups, with the twelve candidate predictor variables denoted with an asterisk. The patients were overwhelmingly white (92.7% in both groups), half were married (49.5%), and less than half male (39.1%). Approximately 55% in both cohorts were Medicare. The median length stay was three days in both groups. The validation cohort had higher age (65 versus 60.6 years), more comorbid conditions (median mCCI scores (seven versus six), were on more inpatient medications (16 versus 14), and were more likely to live alone (18.1% v. 9%).
Descriptive characteristics of study cohorts
Univariate analyses were performed with each of the twelve candidate predictor variables to test for statistically significant differences between patients who were readmitted within 30 days and those who were not, as shown in ► . The only two characteristics that were not statistically significantly different were uninsured status (p = 0.35) and the number of ambulatory medications (p = 0.67). Demographically and socially, readmitted patients were older (p<0.0001) and more likely to be male (p<0.0001), unmarried (p<0.0001), and living alone (p = 0.001). From a healthcare utilization standpoint, they had more ED visits (p<0.0001), more admissions and observation visits (p<0.0001), more unplanned (acute) admissions (p<0.0001), longer lengths of stay (p<0.0001), more medications on their inpatient medication list two days prior to discharge (p<0.0001), and had higher mCCIs (p<0.0001).
Univariate analysis of variables assessed for association with 30-day readmission for the 2010 derivation cohort (n = 8,700).****
The multivariate binary logistic regression results are summarized in ► . The overall percentage of variance accounted for was 14% (Nagelkerke R2) and the Hosmer-Lemeshow had an X2 of 21.6, (p = 0.006).
Table 3 Multivariate binary logistic regression results using the 2010 derivation cohort (n = 8,700) and with all variables maintained in the model. A patient’s RRS score is calculated by multiplying the variable value by its beta coefficient. However, (more ...)
Eleven of twelve candidate variables were significantly associated with 30-day readmission when all twelve predictors were simultaneously entered into the regression equation. One variable, living alone, that had been significant in the univariate analysis became non-significant in the multivariate analysis (p = 0.80). On the other hand, two non-significant univariate predictors became significant as part of the multivariate equation. Uninsured status predicted readmission in the multivariate analysis (p = 0.03). Patients with six or more ambulatory medications were significantly less likely to be readmitted (p<0.0001). The other nine variables remained significant across the analyses: age, being married, being male, being acutely admitted, experiencing more ED visits and hospital stays, having longer lengths of stay, being on more inpatient medications, and having a higher mCCI.
Living alone, although a significant univariate predictor was not a significant multivariate predictor. The number of ambulatory medications was a non-significant univariate predictor but was a significant negative multivariate predictor of 30-day readmission. Both ambulatory and inpatient medications share variance with several other variables, including age, hospital stays, uninsured status, length of stay, and the mCCI. Therefore, the unique variance, not accounted for by other predictors, may be identifying healthier patients who are appropriately medicated, as only revealed when other risk factors are held constant.
A Risk of Readmission Score was created for each patient by multiplying the values for each of the significant variables by the beta coefficient for each variable. Beta coefficients of the categorical variables are multiplied by one instead of a raw value. The mean RRS was 1.7 and ranged from -0.17 to 4.89. The area under the receiver operating characteristic curve (c-statistic) was 0.74 (95% CI 0.73-0.75) for the derivation cohort. The c-statistic for our modification of the LACE model (0.71, 95% CI 0.70-0.72) as applied to this population was comparable to the value of 0.68 reported by its developers. The c-statistic of the validation cohort was 0.70 (95% CI 0.69-0.71). The ten stratified risk groups had probabilities of readmission ranging from a low of 3% to a high of 38%, as shown in ► . ► shows sensitivity, specificity, and positive and negative predictive values with 95% CIs for the 2010 derivation and 2011 validation cohorts using two different Risk of Readmission Scores. One is the mean RRS, and the second is a higher-risk cutoff score in the second-highest risk decile. For a clinical example of a patient with that high risk score, following the format of Billings et al. [13
], see ► . Measures of test performance were similar for both populations, with somewhat lower values observed in the validation population.
Risk of Readmission Score grouped into ten deciles and assigned to probability of 30-day readmission.
Risk of readmission score cutoffs, sensitivity, specificity, positive and negative predictive values with 95% CI for 2010 derivation and 2011 validation populations.
Table 6 Calculation of the RRS is for an insured single 51 year-old female who lives with a friend. The patient has congestive heart failure, prior myocardial infarction, moderate to severe liver disease and diabetes, who reports five medications at home, has (more ...)
A multivariate binary logistic regression equation was used to compare the predictive accuracy of the RRS for predicting readmissions in the 2010 derivation and the 2011 validation groups. The 2010 and 2011 samples were combined. Year of Sample, Risk of Readmission and an interaction term representing Year of Sample by Risk of Readmission were entered in a single regression equation with readmission as the dependent variable. As expected, the RRS (p<0.0001) and Year of Sample (0.0002) were highly significant predictors. There were more 30 day readmissions in 2011 compared to 2010. The interaction term was not significant (p = 0.36), indicating no significant difference in the predictive value of the RRS between the two years.
► visually demonstrates the Hosmer-Lemeshow expected versus observed rates of readmission in the validation cohort. ► shows the display of current inpatients’ individual scores, probability of readmission, and other clinical and demographic data in a clinical surveillance site within the hospital’s intranet. Each row represents one patient. Fourteen different columns contain clinical, demographic, and predictive data. The raw score is posted in the “Total” column, and the risk of readmission is the percent value in the rightmost column. With this presentation, current inpatients can be grouped in descending order of readmission risk, by certain diagnoses, etc. by clicking on the column header. The display in ► is sorted by hospital unit. This functionality was chosen to allow users with different roles to drill down into certain subgroups of patients, such as those without insurance or those with certain disease states. Patients’ names have been obscured in this presentation.