The cohort consisted of 32,354 patients on the ASCTS registry admitted to 18 hospitals from 2001-2009. Patient mean age was 65.5 years (SD 12.5); 27.7% were female. Table includes further patient characteristics. The number of cardiac surgeries ranged from 151 to 5314 across hospitals (Table ). Figure shows that variation in mortality rates across hospitals was considerable with rates in the range 1.0 to 4.1%.
Patient characteristics from a cardiac surgery registry 2001-2009
Total number of cardiac surgeries, median of the annual number of cardiac surgeries, number of deaths within 30-days of surgery, and mortality rates in 18 hospitals 2001-2009 by academic affiliation status
Mortality within 30-days of cardiac surgery in teaching and non-teaching hospitals. The area of their circle is proportional to the number of surgeries in each of the 18 hospitals.
Table contains the odds ratios and 95% CIs for the effects of patient and hospital characteristics from the ordinary, marginal and multilevel logistic regression models. Overall the 95% CIs for hospital-level variables in the marginal and multilevel model were wider than in the ordinary logistic regression, reflecting the between-hospital heterogeneity that is erroneously not accounted for in the latter model (Figure ). In particular the effect of median annual number of cardiac surgeries was statistically significant in ordinary logistic regression, but not in the other models.
Ordinary, marginal and multilevel logistic regression results: Odds ratios, OR, describing associations with 30-day mortality for patient-level and hospital-level characteristics
Odds ratio estimates and 95% CIs derived from conventional, marginal and multilevel logistic regression for 30-day mortality for academic affiliation and median annual number of surgery.
In the marginal model the correlation between mortality outcomes for any two patients from the same hospital was ρ = 0.002 suggesting a weak positive association. The multilevel model estimated that the proportion of the variance in 30-day mortality between hospitals was 1% (ICC = 0.01). From the multilevel model it was estimated that if a patient moved to another hospital with a higher probability of mortality, the median increase in their odds of mortality would be 1.2-fold (MOR = 1.2), a modest effect compared to patient-level risk factor effects in Table but comparable to the hospital-level fixed effects in Figure .
Interpretation of the hospital-level effects estimated from marginal logistic regression (OR = 1.2, 95%CI, (0.9-1.5))was that, on average, the odds of mortality for patients in teaching hospitals increased by 20% compared to that of patients in non-teaching hospitals. In comparison, the multilevel logistic regression odds ratio of 1.3, 95%CI, (0.8-1.9) for the same parameter says that if comparing two patients with identical risk factors, one treated in a teaching hospital and one treated in a non-teaching hospital, and with those hospitals otherwise identical with regard to mortality risk, then the odds of mortality was increased 1.3-fold for the patient in the teaching hospital. The magnitude of these effects may be of high importance clinically but the difficulty in interpretation, particularly with regard to the existence of hospitals with identical underlying mortality risk, may limit their usefulness.
The IOR-80% for academic affiliation was 0.8 to 1.8 which provides the further insight that, when comparing two randomly chosen patients with identical risk factors, one from a teaching hospital, the other from a non-teaching hospital, and those hospitals possibly differing in other ways regarding mortality risk, the odds ratio for the comparison will, with 80% probability, lie between 0.8 and 1.8. In other words, even disregarding the uncertainty inherent in sampling that can be incorporated in confidence intervals, the wide IOR-80% reflects considerable uncertainty in the impact of hospital academic affiliation on patient-level mortality risk due to substantial residual variation in mortality between hospitals that was not accounted for by either academic affiliation or median annual number of cardiac surgeries or patient-level characteristics included in the regression model.
The IOR-80% for the median of the annual number of cardiac surgeries was 0.6 to 1.3. Hence when comparing two randomly chosen patients with identical risk factors except for treatment at respective hospitals which differed by 100 in their median annual number of cardiac surgeries, and possibly differing in ui values, the odds ratio for the comparison will, with 80% probability, lie between 0.6 and 1.3. As for academic affiliation, this is a wide IOR-80%.