Risk-adjusted monitoring of survival times

We consider the monitoring of surgical outcomes, where each patient has a different risk of post-operative mortality due to risk factors that exist prior to the surgery. We propose a risk-adjusted (RA) survival time CUSUM chart (RAST CUSUM) for monitoring a continuous, time-to-event variable that may be right-censored. Risk adjustment is accomplished using accelerated failure time regression models. We compare the average run length performance of the RAST CUSUM chart with the RA Bernoulli CUSUM chart using data from cardiac surgeries to motivate the details of the comparison. The comparisons show that the RAST CUSUM chart is more efficient at detecting a sudden increase in the odds of mortality than the RA Bernoulli CUSUM chart, especially when the fraction of censored observations is relatively low or when a small increase in the odds of mortality occurs. We also discuss the impact of the amount of training data used to estimate chart parameters as well as the implementation of the RAST CUSUM chart during prospective monitoring.