طراحي اقتصادي آماري يك نمودار كنترل به منظور پايش مدت زمان بقاي بيماران

THE ECONOMIC-STATISTICAL DESIGN OF A CONTROL CHART FOR MONITORING PATIENTS' SURVIVAL TIME

در سال‌هاي اخير استفاده از نمودارهاي كنترل در سيستم‌هاي سلامت توجه محققين را به خود جلب كرده است. در اين نوشتار طراحي يك نمودار كنترل جمع تجمعي تعديل ريسك شده براي پايش مدت زمان بقاي بيماران پيشنهاد مي‌شود. در اين نمودار، تعديل ريسك با هدف در نظر گرفتن تاثير ريسك‌هاي قبل از عمل هر بيمار بر روي زمان بقاي او انجام مي‌گيرد. به منظور به‌كارگيري نمودار كنترل پيشنهادي لازم است پارامترهاي طراحي به‌گونه‌يي تعيين شود كه خواص مطلوب اقتصادي و آماري به‌طور هم‌زمان برآورده شوند. از اين رو، يك مدل چندهدفه پيشنهاد شده كه حل آن توسط يك الگوريتم چندمرحله‌يي انجام مي‌پذيرد. سپس، عملكرد رويكرد پيشنهادي در يك مركز جراحي قلب مورد بررسي قرار گرفته است. در پايان، نتايج حاصله با مدل طراحي اقتصادي خالص مقايسه شده است كه نتايج نشان مي‌دهد طراحي چندهدفه‌ي نمودار كنترل با افزايش نسبتا اندك هزينه، ويژگي‌هاي آماري بهتري دارد.

In recent years, the development of control charts has attracted the attention of researchers in healthcare systems. The purpose of this paper is to design a risk-adjusted cumulative sum (CUSUM) control chart to monitor the survival time of patients after performing a surgical operation. In this control chart, risk adjustment is conducted to consider the impact of each patient's preoperative risks on survival times. It should be noted that the Parsonnet score has been calculated and recorded for each patient before undergoing a surgical operation. Moreover, a class of survival analysis regression models called accelerated failure time models has been employed for risk-adjustment. However, the implementation of the RACUSUM control chart requires determining the design parameters such as the lower control limit and coefficient for optimal design of CUSUM control chart. These parameters should be selected in an optimal way putting the desired statistical and economic considerations into service. To this end, a multi-objective model, including three objectives of cost, the in-control ARL and the inverse of out-of-control ARL, has been proposed and the model is solved with the help of a multi-stage algorithm based on the data envelopment analysis (DEA) method. Then, to show the performance of the proposed procedure, a real case study has been considered in the cardiac surgery center in Iran. Doing so, a special kind of operation called coronary artery bypass grafting (CABG) surgery was selected, and the information associated with 100 patients was collected over time. Finally, a comparison has been made between the multi-objective design model and a pure economic design model. The results clearly reveal that with a relatively small increase in the cost function, the multi-objective design of the RACUSUM chart has better statistical performance. Therefore, it is advisable to implement the proposed multi-objective model to design the risk-adjusted CUSUM control chart in healthcare systems.