Defining minimum volume thresholds to increase quality of care: a new patient-oriented approach using mixed integer programming.

A positive relationship between treatment volume and outcome quality has been demonstrated in the literature and is thus evident for a variety of procedures. Consequently, policy makers have tried to translate this so-called volume-outcome relationship into minimum volume regulation (MVR) to increase the quality of care-yet with limited success. Until today, the effect of strict MVR application remains unclear as outcome quality gains cannot be estimated adequately and restrictions to application such as patient travel time and utilization of remaining hospital capacity are not considered sufficiently. Accordingly, when defining MVR, its effectiveness cannot be assessed. Thus, we developed a mixed integer programming model to define minimum volume thresholds balancing utility in terms of outcome quality gain and feasibility in terms of restricted patient travel time and utilization of hospital capacity. We applied our model to the German hospital sector and to four surgical procedures. Results showed that effective MVR needs a minimum volume threshold of 125 treatments for cholecystectomy, of 45 and 25 treatments for colon and rectum resection, respectively, of 32 treatments for radical prostatectomy and of 60 treatments for total knee arthroplasty. Depending on procedure type and incidence as well as the procedure's complication rate, outcome quality gain ranged between 287 (radical prostatectomy) and 977 (colon resection) avoidable complications (11.7% and 11.9% of all complications). Ultimately, policy makers can use our model to leverage MVR's intended benefit: concentrating treatment delivery to improve the quality of care.