Investigating non-linear volume-outcome relationships in total knee arthroplasty based on a sample of more than 60,000 hospital cases from Germany, 2020-2023.

Due to established volume-outcome relationships, total knee arthroplasty (TKA) is subject to minimum volume regulation in Germany. However, the appropriateness of past (50 cases per year for TKA) and current (150 cases per year for primary TKA) minimum volume thresholds at the hospital level is unclear. In particular, there is a lack of statistical modeling studies accounting for potential nonlinearities in volume-outcome associations. Utilizing statutory health insurance data, we analyzed a large sample of German hospital cases with TKA from the period 2020–2023. We considered revision TKA and surgical complications within one year after TKA as outcomes. To capture potentially nonlinear relationships, we applied logistic regression models with natural cubic splines of hospital case volume. For each outcome, we estimated models including splines with one to ten degrees of freedom and selected the model with the best fit according to the Akaike information criterion (AIC). Based on the selected models, we predicted outcome probabilities with 95%-prediction intervals (95%-PIs) for a representative patient (i.e. a patient with average values of all covariates). Sensitivity analyses included the use of the average number of TKA cases of the three preceding years as volume indicator and estimation of regression models with smoothing splines. We included 64,911 TKA cases that were treated in 964 hospitals. Hospital case volume was lower than 250 for 76.6% of all hospitals, which treated 45.3% of all cases in 2023. Within one year after TKA, we observed revision TKA for 2.9% and surgical complications for 1.5% of all cases. Spline-based regressions revealed strong, nonlinear volume-outcome relationships at low hospital case volumes. Predicted probabilities of revision TKA were 3.6% (95%-PI: 3.1%;4.1%) for a hospital case volume of 50 and 2.6% (95%-PI: 2.3%;2.8%) for a hospital case volume of 250. For surgical complications, predicted probabilities were 1.9% (95%-PI: 1.6%;2.3%) and 1.3% (95%-PI: 1.2%;1.5%) for case volumes of 50 and 250, respectively. The results of sensitivity analyses were in line with these findings. Our results suggest that increasing the minimum volume threshold to 250 cases per year may have had reduced the risks of revision TKA and surgical complications for almost half of all patients undergoing TKA in Germany.