شناسايي نقطه‌ي تغيير و مقدار شيب روند در نمودارهاي كنترل تعديل ريسك در فاز 1

Estimating the Change Point and Slope of a Linear Trend in Phase One Risk-Adjusted Control Charts

نمودارهاي كنترل تعديل ريسك كه با در نظر گرفتن ريسك‌هاي پيش از عمل بيماران طراحي مي‌شود، در پايش نرخ مرگ و مير بيماران پس از عمل‌هاي جراحي كاربرد دارند و مديران مراكز درماني در فرايند ارايه‌ي خدمات درماني توسط پزشكان و پرستاران، از آن براي شناسايي نقطه‌ي تغيير بهره مي‌گيرند. شناسايي نقطه‌ي تغيير بدان سبب اهميت مي‌يابد كه كشف علت واقعي تغيير را ميسر مي‌سازد. در اين نوشتار از روش بيشترين درست‌نمايي براي برآورد زمان تغيير و مقدار شيب روند رخ داده در داده‌هاي صفر و 1 (زنده ماندن يا مرگ) بيماران ــ كه با استفاده از نمودار آزمون نسبت درست‌نمايي تعديل ريسك در فاز يك مورد پايش قرار مي‌گيرد ــ استفاده مي‌شود. نتايج حاصله حاكي از آن است كه چنانچه اندازه‌ي تغيير بزرگ باشد زمان تغيير و اندازه‌ي شيب روند با دقت بيشتري برآورد مي‌‌شود.

Using risk adjusted control charts to monitor patients’ surgical outcomes is now popular. Patients have different pre-operation conditions such as age, gender, hypertension –usually called potential risk factors- which form a heterogeneous population. Therefore, there is a need to adjust for patient risk to have homogenous outcomes. In literature, several risk adjustment methods have been applied, including the logistic regression and the Accelerated Failure Time (AFT) models. For the monitoring process, the patients risk adjusted post-surgery outcomes are plotted on an appropriate risk adjusted control chart. Finding the time point at which a change has occurred, provides useful information for the root-cause analysis of the problem, and helps managers to accomplish corrective or preventive actions. There are many articles in this context dealing with this problem in both phases one and two. Most of them, however, have focused on phase two. The risk adjusted Log-likelihood Ratio test (LRT) chart for phase one analysis of data is applied in this paper, to monitor the binary surgical outcomes. This chart is based on the likelihood ratio test derived from a change point model. As a risk adjustment model, logistic regression is used to adjust for patient heterogeneity. This chart is applied to find the time and size of change when a linear trend occurs in patients post-surgery mortality rates. The maximum likelihood estimator (MLE) is used to identify the change point. Knowing the change point, one may apply the Newton-Raphson’s numerical method to find the ML estimate of the slope of the trend. A phase one surgery outcome dataset that is frequently used by other authors is considered for evaluating the proposed method. Simulation data are generated to confirm this approach. The results show that when the change is large, the ML estimation of change point time is more reasonably precise. In addition, the Newton-Raphson method efficiently estimates the slope of the trend.