عنوان مقاله [English]
Health Services Research (HSR) is of great importance to communities because decision makers and the public consider the HSR as the primary source of information to determine how well health systems are meeting their specifications. Nowadays, in healthcare, there are many therapeutic processes which their results obtained by some related stages. For studying these kind of processes, so called multi-stage processes, two concepts are important: one is risk adjustment and the other is considering the cascade property. An example of a multi-stage therapeutic process is thyroid cancer surgery, which is usually performed on patients in two stages and part of the cancerous tumors are removed at each stage. In two-stage thyroid cancer surgery, the quality of the second surgery will be affected by the results of the first stage operation. For monitoring these processes, various control charts are used including model-based control charts. In order to designing these kind of charts, an appropriate model should be identified at first; then control charts could be proposed based on the identified model. In this research, a risk-adjusted time-varying linear state space model is introduced for analysis the multi-stage therapeutic processes. The state space models are statistical models that many researchers have used them to analyze the multi-stage processes. These models are based on engineering knowledge and the physical laws of real systems. Then, the model order and its parameters is estimated by Hankel Singular Value Decomposition (HSVD) and Prediction Error Minimization (PEM) methods, respectively. This is called input-output identification. For evaluating the proposed model, the model performance is investigated on the simulated data and the real two-stage thyroid surgery data set. Considering the acceptable results, Since the risk adjustment, the cascade property, the transmission error, and the test error can be considered simultaneously by using the linear state space modeling of the multi-stage processes, the proposed identified model can be used for simulating, forecasting and monitoring the multi-stage therapeutic processes.