Flexible regression models are useful tools to calculate and assess threshold values in the context of minimum provider volumes.
OBJECTIVE
The aim was to review different approaches for the derivation of threshold values and to discuss their strengths and limitations in the context of minimum provider volumes.


METHODS
The following methods for the calculation of threshold values are compared and discussed: The value of acceptable risk limit, the value of acceptable risk gradient, the benchmark value proposed by Budtz-Jørgensen and Ulm's breakpoint model. The latter is extended to account for two different breakpoints. The methods are applied to German quality assurance data concerning total knee replacement.


RESULTS
The discussed methods for calculating threshold values differ in the kind of information that has to be specified beforehand. For the value of acceptable risk limit approach an absolute number, the acceptable risk, has to be predetermined. The value of acceptable risk gradient approach and the method of Budtz-Jørgensen require the specification of a relative change expressed in gradient and in odds, respectively. On the other hand, the threshold value according to the method of Ulm is defined as a parameter of a statistical model and no a priori specification is required.


CONCLUSIONS
Each of the proposed methods has benefits and drawbacks. The choice of the most appropriate approach depends on the specific problem and the available data.
Grouven
Ulrich
U
Institute for Quality and Efficiency in Health Care, Cologne, Germany. ulrich.grouven@iqwig.de
Küchenhoff
Helmut
H
Schräder
Peter
P
Bender
Ralf
R
D000368:Aged; D019645:Arthroplasty, Replacement, Knee / Q000592:standards / Q000706:statistics & numerical data; D019985:Benchmarking; D005260:Female; D005858:Germany / Q000453:epidemiology; D006302:Health Services Research / Q000379:methods; D006761:Hospitals / Q000592:standards / Q000706:statistics & numerical data*; D006801:Humans; D016015:Logistic Models; D008297:Male; D011785:Quality Assurance, Health Care / Q000379:methods*; D018570:Risk Assessment / Q000379:methods; D013530:Surgical Wound Infection / Q000453:epidemiology; D016896:Treatment Outcome