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Updated: Sep 21, 2025

Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index

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Published on: January 8, 2020

The CUSUM Slope Equals Observed Minus Expected Mortality and Can Be Visualized by a "Slope-Meter".

Ruyun Jin¹, Mansen Wang¹, Lian Wang¹

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Summary

The Risk-Adjusted CUSUM (RA-CUSUM) chart

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Area of Science:

Medical Statistics
Healthcare Quality Improvement
Clinical Performance Monitoring

Background:

The Risk-Adjusted CUSUM (RA-CUSUM) chart is a statistical tool used for monitoring healthcare quality.
Quantifying performance over time is crucial for effective quality improvement initiatives.

Purpose of the Study:

To highlight an additional advantage of the RA-CUSUM chart: the quantification of its slope.
To demonstrate that the RA-CUSUM slope is equivalent to Observed (O) minus Expected (E) mortality.
To introduce a graphical tool, the Slope-Meter, for approximating this mortality difference.

Main Methods:

Analysis of the RA-CUSUM chart's mathematical properties.
Equating the chart's slope to the difference between observed and expected mortality.
Development and presentation of the Slope-Meter graphical tool.

Main Results:

The slope of the RA-CUSUM chart directly quantifies Observed (O) minus Expected (E) mortality over a selected interval.
The height of the RA-CUSUM chart represents the cumulative O minus E deaths since the series began.
The Slope-Meter provides a visual method for estimating the O minus E mortality difference.

Conclusions:

The RA-CUSUM chart offers a dual measure of performance: cumulative O-E deaths (height) and interval-specific O-E mortality (slope).
The Slope-Meter enhances the interpretability of RA-CUSUM charts for assessing performance trends.
This quantification of mortality difference provides valuable insights for healthcare quality assessment.