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Risk-adjusted CUSUM charts under model error.

Sven Knoth1, Philipp Wittenberg1, Fah Fatt Gan2

  • 1Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany.

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Summary
This summary is machine-generated.

Improving healthcare quality control charts requires better risk models. This study enhances risk-adjusted cumulative (CUSUM) charts using power transformations to reduce false alarms, crucial for accurate surgical performance monitoring.

Keywords:
Markov chain approximationParsonnet scoreToeplitz matrixaverage run length to false alarmbinary logistic regressionpower transformation

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Area of Science:

  • Healthcare Quality Improvement
  • Statistical Process Control
  • Biostatistics

Background:

  • Quality control charts are increasingly used in healthcare for monitoring performance, such as surgical outcomes.
  • Risk-adjusted cumulative (CUSUM) charts, using scores like Parsonnet, can be unreliable due to misfitted risk models, impacting false alarm rates.

Purpose of the Study:

  • To improve the fit of logistic regression models in healthcare risk-adjusted CUSUM charts.
  • To investigate the impact of power transformations on the false alarm behavior of these charts.

Main Methods:

  • Applied power transformations to logistic regression models for binary outcome data.
  • Developed two methods for estimating the power exponent (δ).
  • Calculated average run length (ARL) to false alarm using Markov chain approximation with Toeplitz matrix structure.

Main Results:

  • Power transformations can improve model fit, potentially enhancing CUSUM chart properties.
  • Sensitivity analysis revealed that incorrect choice of δ can significantly impact false alarm rates, from robustness to doubling the rate.
  • The efficiency of ARL calculation was improved by exploiting matrix structure.

Conclusions:

  • Power transformations offer a promising approach to mitigate misfitted risk models in healthcare CUSUM charts.
  • Careful selection or estimation of the power exponent δ is critical for reliable false alarm control.
  • Optimized statistical methods enhance the practical application of CUSUM charts in surgical performance monitoring.