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 2p + 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. Copyright © 2016 John Wiley & Sons, Ltd.

We propose a semiparametric approach to estimate the existence and location of a statistical change-point to a nonlinear multivariate time series contaminated with an additive noise component. In particular, we consider a p-dimensional stochastic process of independent multivariate normal observations where the mean function varies smoothly except at a single change-point. Our approach involves conducting a Bayesian analysis on the empirical detail coefficients of the original time series after a wavelet transform. If the mean function of our time series can be expressed as a multivariate step function, we find our Bayesian-wavelet method performs comparably with classical parametric methods such as maximum likelihood estimation. The advantage of our multivariate change-point method is seen in how it applies to a much larger class of mean functions that require only general smoothness conditions.

When a multivariate control chart raises an out-of-control signal, several diagnostic questions arise. When did the change occur? Which components or quality characteristics changed? For those components for which the mean shifted, what are the new values for the mean? While methods exist for addressing these questions individually, we present a Bayesian approach that addresses all three questions in a single model. We employ Markov chain Monte Carlo (MCMC) methods in a Bayesian analysis that can be used in a unified approach to the diagnostics questions for multivariate charts. We demonstrate how a reversible jump Markov chain Monte Carlo (RJMCMC) approach can be used to infer (1) the change point, (2) the change model (i.e., which components changed), and (3) post-change estimates of the mean.

We propose a semiparametric approach to infer the existence of and estimate the location of a statistical change-point to a nonlinear high dimensional time series contaminated with an additive noise component. In particular, we consider a p dimensional stochastic process of independent multivariate normal observations where the mean function varies smoothly except at a single change-point. Our approach first involves a dimension reduction of the original time series through a random matrix multiplication. Next, we conduct a Bayesian analysis on the empirical detail coefficients of this dimensionally reduced time series after a wavelet transform. We also present a means to associate confidence bounds to the conclusions of our results. Aside from being computationally efficient and straight forward to implement, the primary advantage of our methods is seen in how these methods apply to a much larger class of time series whose mean functions are subject to only general smoothness conditions.

We prospectively monitor a stochastic process x1, x2, … in an effort to detect quickly some statistical change to the process mean. Initially, the process is monitored with a classic control chart equipped with statistical control limits indicating the process is in control or signaling an alarm sometime after a statistical change occurs. Once the alarm signals, we would then like to ‘look back’ and determine at which point the process changed. To this end, we apply and compare three change‐point detection methods under a variety of different assumptions. In particular, two classic methods of Bayesian and maximum likelihood estimation change‐point detection are compared with a technique that first applies the discrete wavelet transform to the series and then applies Bayesian methods directly to the wavelet details. Copyright © 2013 John Wiley & Sons, Ltd.