Flexible risk‐adjusted surveillance procedures for autocorrelated binary series

Risk‐adjusted cumulative sum (RACUSUM) charts are popular for the surveillance of binary health care outcomes such as 30‐day mortality rates following cardiac surgery. RACUSUM charts are built on the assumptions that the binary outcomes are independent and the baseline rates are known constants. However, these two assumptions are often violated, thus undermining the validity of the surveillance procedure. In this paper, the authors propose risk‐adjusted surveillance procedures using a binary logistic regression model which allows AR ( p ) ‐type autocorrelations among the binary outcomes. Two versions are presented: one with known, the other with estimated baseline parameters. The authors use Monte Carlo experiments to evaluate the power and the probability of false alarm (Type I error) of the surveillance procedures. Data on 30‐day mortality rates following cardiac surgery are used for illustration. The Canadian Journal of Statistics 43: 403–419; 2015 © 2015 Statistical Society of Canada