Abstract
We propose a nonparametric risk-adjusted cumulative sum chart to monitor surgical outcomes for patients with different risks of post-operative mortality due to risk factors that exist before the surgery. Using varying-coefficient logistic regression models, we accomplish the risk adjustment. Unknown coefficient functions are estimated by global polynomial spline approximation based on the maximum likelihood principle. We suggest a bisection minimization approach and a bootstrap method to determine the chart testing limit value. Compared with the previous (parametric) risk-adjusted cumulative sum chart, a major advantage of our method is that the morality rate can be modeled more flexibly by related covariates, which significantly enhances the monitoring efficiency. Simulations demonstrate nice performance of our proposed procedure. An application to a UK cardiac surgery dataset illustrates the use of our methodology.
Highlights
Monitoring surgical outcomes of clinical trials is a critical task for doctors to timely detect patient deterioration
To alleviate the modeling bias problem and to cope with possible interaction effect among the patient characteristics, we propose the following varying-coefficient logistic regression (VCLR) model: logitðptÞ 1⁄4 m þ Xt0bðUtÞ; ð4Þ
We propose a bisection search algorithm and a bootstrap method to determine the nonparametric risk-adjusted CUSUM chart limit value
Summary
Monitoring surgical outcomes of clinical trials is a critical task for doctors to timely detect patient deterioration. To adjust the risk factors in the UK cardiac surgery example, a linear logistic regression was used to model the relationship between the surgical outcome and the Parsonnet score [8]. If the null hypothesis is rejected, it indicates a significant increase in the mortality rate By using this method, the Parsonnet score was found to significantly affect the mortality rate, and it was claimed [8] that this procedure could detect changes in surgical performance earlier than the non-adjusted CUSUM. The Parsonnet score was found to significantly affect the mortality rate, and it was claimed [8] that this procedure could detect changes in surgical performance earlier than the non-adjusted CUSUM This approach is based on the assumption in model (1) that the log odds ratio of mortality rate is a linear function of the Parsonnet score. Through simulations and a real data example, we illustrate nice performance and the use of the proposed methodology
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