Continuous monitoring of long‐term outcomes with application to hip prostheses

The CUSUM continuous monitoring method could be a valuable tool in evaluating the performance (revision experience) of prostheses used in hip replacement surgery. The dilemma when applying the CUSUM in this context is the choice of statistical model for the outcome (revision). The Bernoulli model is perhaps the most straightforward approach but the Poisson model is a plausible, and could be argued, preferable alternative for long-term outcomes such as this, provided the rate of revision with time from surgery can be assumed to be constant. However, a rate (or hazard) varying according to the Weibull distribution appears to be a better representation of a prosthesis lifetime. We show how to adapt the Poisson approach to allow for the hazard to vary according to the Weibull model as well as other parametric survival models. Application to data on a known poorly performing prosthesis shows both the Poisson and Weibull CUSUMs could have given early warning of the poor performance, with the Weibull chart alerting before the Poisson. Simulation work to investigate the robustness of the Poisson and Weibull CUSUM to departures from the underlying survival model highlights the need for correct specification of the model for the outcome.