Risk-adjusted Monitoring of Healthcare Quality: Model Selection and Change-point Estimation

Risk adjustment, which is used when healthcare outcomes are monitored, involves taking into account measures of the patient condition and how these measures are related to the outcomes. When the outcome is dichotomous, such as survival/death, the modeling involves logistic regression to assess the relationship between the predictor(s) and the outcome. Most risk‐adjusted control charts are designed to detect a change in the log‐odds of the adverse outcome, but there are a number of possible changes that could occur. For example, there could be an increase in the probability of adverse outcomes for low‐risk patients with no change for high‐risk patients. We address the problem of risk‐adjusted monitoring as a change‐point problem with several possible change‐point models. For p risk variables, there are 2^{p + 1} possible change‐point models, because each of the slope parameters or the intercept in the logistic regression model can change. Our approach generalizes previous risk‐adjusted charts in that we look for changes in any of the parameters. We take a Bayesian approach and find the posterior distribution for the model (i.e., which coefficients changed), the time of the change, and the values of the parameters for those that changed. All three tasks are accomplished in the context of a single model. We apply reversible jump MCMC to account for the variable size of the parameter space.