From the Southern Association For Vascular Surgery Statistical modeling of the volume-outcome effect for carotid endarterectomy for 10 years of a statewide database

Objective: We aimed to achieve accurate statistical modeling of a putative relationship between carotid endarterectomy (CEA) annual surgeon and hospital volume and in-hospital mortality. Design of Study: We performed a secondary data analysis of 10 years (1994-2003) of the Maryland hospital discharge database. Annual volume was defined as the total number of procedures performed for the time in the dataset divided by the total years in the dataset. Non-linear relationships between death and average volumes were explored with logit-transformed lowess smoothing functions, followed by random effect models and inspection of data likelihood under each combination of spline knots. A marginal model with generalized estimating equations was used to represent population-average response as a function of covariates and to account for clustering in the data. Patient comorbidity was assessed using the Deyo modification of the Charlson Index. Setting: The Maryland hospital discharge database is a 100% sample of all hospitals in the state. Subjects: CEA was identified through ICD-9 and diagnosis codes, using a previously reported algorithm. Main Outcome Measure: Estimated odds ratios predicting in-hospital death, set at 0.05. Results: During the study period, 22,772 patients with surgeon identifiers underwent CEA in Maryland, resulting in 123 in-hospital deaths (0.54%). The crude odds ratio of death for the entire surgeon dataset was 0.9838, meaning that the odds of death decreased by an average of 0.0162 for each additional annual procedure. Surgeon volume of four to 15 CEAs per year was highly significant: for an increase in annual surgeon volume by one procedure per year, the estimated odds of death decreased by 0.065 when controlling for hospital volume, age, and comorbidity (P .351). Surgeons in other volume categories also demonstrated lower odds of death with increased annual volume, but these odds ratios did not attain statistical significance. Surgeons performing <3 CEA per year had an odds ratio of death of 0.802 per additional annual procedure (P .351), whereas those performing >15 CEAs per year had an odds ratio of 0.997 (P .485). Hospitals that saw >130 CEAs per year had an odds ratio of death of 0.945 per additional procedure, or 0.055 decrease in the odds of death (P 0.013), whereas hospitals performing <130 CEAs per year had an odds ratio of 0.998 (P 0.563). Conclusion: We have demonstrated a technique for rigorous statistical analysis of volume-outcome data and have found a volume effect for death after CEA in this 10-year Maryland dataset. Higher volume surgeons had lower estimated odds of death, particularly those performing four to 15 CEAs per year. These data suggest that a patient undergoing CEA by a surgeon performing an average of 16 CEAs annually has a statistically equivalent risk of death compared with one undergoing CEA by a surgeon performing any number higher than this, when controlling for hospital volume, patient comorbidity, and patient age. Hospital volume was not seen to be as significant a predictor of postoperative death in this study, with only high volume hospitals (>130 CEAs per year) showing a statistically significant decrease in the odds ratio of death. As studies on volume-outcome relationships can have important implications for health policy and surgical training, such studies should consider non-linear effects in their modeling of procedural volume. (J Vasc Surg 2008;48:343-50.)