Flexible regression models are useful tools to calculate and assess threshold values in the context of minimum provider volumes

Abstract 

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.

Study Design and Setting

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.

Conclusion

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.

Keywords: Threshold values, Benchmark values, Minimum provider volume, Volume–outcome data, Logistic regression models, Generalized estimating equations