Risk-Adjusted Exponentially Weighted Moving Average for Poisson Data and Application in Healthcare

Abstract

<p>The Risk-Adjusted Exponentially Weighted Moving Average (RA-EWMA) for Poisson data is developed in detail. The method is useful to monitor healthcare or to other counts that are generated dynamically over time. The approach used is motivated by and follows closely the approach used by Grigg and Spiegelhalter (2007) for dynamic binary outcomes. In simple terms, a Bayesian approach is applied that uses conjugate priors (gamma in the case of Poisson data) utilized iteratively to provide the method estimates as the posterior expected means. The main application is counts with covariates. The thesis provides the necessary formulas to update the method's estimates. Numerical calculations are presented to illustrate the use of the methods and to compare it to the Standard Exponentially Weighted Moving Average (Standard EWMA), which is a standard monitoring method used in industrial applications. The numerical evidence provided in the thesis suggests that the RA-EWMA method is more sensitive than the Standard EWMA method to the presence of the underlying covariates. This was shown clearly on real data, specifically in the UK's death counts from lung diseases.</p>