Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany.
Department of Statistics and Applied Probability, National University of Singapore, Singapore.
Stat Med. 2019 May 30;38(12):2206-2218. doi: 10.1002/sim.8104. Epub 2019 Feb 5.
In recent years, quality control charts have been increasingly applied in the healthcare environment, for example, to monitor surgical performance. Risk-adjusted cumulative (CUSUM) charts that utilize risk scores like the Parsonnet score to estimate the probability of death of a patient from an operation turn out to be susceptible to misfitted risk models causing deterioration of the charts' properties, in particular, the false alarm behavior. Our approach considers the application of power transformations in the logistic regression model to improve the fit to the binary outcome data. We propose two different approaches of estimating the power exponent δ. The average run length (ARL) to false alarm is calculated with the popular Markov chain approximation in a more efficient way by utilizing the Toeplitz structure of the transition matrix. A sensitivity analysis of the in-control ARL against the true value δ shows potential effects of incorrect choice of δ. Depending on the underlying patient mix, the results vary from robustness to severe impact (doubling of false alarm rate).
近年来，质量控制图在医疗保健环境中得到了越来越多的应用，例如，用于监测手术绩效。利用风险评分（如 Parsonnet 评分）来估计患者因手术而死亡的概率的风险调整累积（CUSUM）图容易受到不合适的风险模型的影响，从而导致图表特性的恶化，特别是误报警行为。我们的方法考虑了在逻辑回归模型中应用幂变换来改善对二项结果数据的拟合。我们提出了两种不同的方法来估计幂指数 δ。通过利用转移矩阵的 Toeplitz 结构，以更有效的方式利用流行的马尔可夫链逼近来计算误报警的平均运行长度（ARL）。对控制状态下 ARL 对真实值 δ 的敏感性分析表明 δ 选择不正确可能会产生影响。根据基础患者组合的不同，结果从稳健性到严重影响（误报警率翻倍）不等。
