Phase II monitoring of survival times with categorical covariates

Abstract

AbstractMonitoring surgical outcomes is of paramount importance especially by accounting for health conditions of the patients prior to surgery. However, the problem arises as the effect of some covariates is pronounced but cannot be measured. In this paper, in order to deal with the effect of measured and unmeasured (categorical) covariates simultaneously, a class of survival analysis regression models called accelerated failure time (AFT) model and discrete frailty models is integrated and some Phase II risk‐adjusted control schemes are devised to monitor the patients' lifetime. Three monitoring procedures including the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and probability limits‐based control charts are developed in the presence and absence of censored observations. The performance analysis reveals that the proposed AFT frailty‐based CUSUM control chart outweighs the competing counterparts in detecting shifts under various scenarios. Subsequently, two CUSUM control charts have been constructed corresponding to the cases of neglecting both the unmeasured and measured covariates and ignoring just the unmeasured covariate. The results clearly indicate that the detection ability for both of the mentioned CUSUM control charts declines, and including the unmeasured and measured covariates is critical while monitoring surgical outcomes. Finally, a real case study in a cardiac surgical center in the United Kingdom has been provided to investigate the application of the proposed AFT frailty‐based CUSUM control scheme.