Modelling recurrent event data: a comparison of the Cox proportional hazards model and three of its extensions to estimate the risk of recurrent healthcare-associated infections in critically ill patients

Background: Intensive-care unit (ICU) patients are prone to healthcare-associated infections which are often recurrent. Such infections are influenced by previous occurrences and hence correlation between events needs to be taken into account when modelling the risk of infection recurrence. Objective: To compare five different survival-time models, the Cox proportional hazards model (CPH) and three of its extensions to recurrent event data: Andersen-Gill (AG), Prentice-Williams-Peterson (PWP) and Frailty models. Methods: The models were empirically assessed by direct application to data from a cohort study of 550 patients with ICU-acquired infections. Covariate data included patients sex, age, Glasgow, Apache-II and comorbidity scores, and exposures to medical devices, treatment appropriateness and infection site and resistance to carbapenems. Models were compared using accuracy criteria and goodness-of-fit statistics. Results: 180/550 (33%) patients had infection recurrence, of whom 128 had a first, 40 a second and 12 a third recurrence. All models agreed in the direction of effect for all covariates. However, the CPH model for the risk of first recurrence disregarded data on 64 (26%) of infections, produced the more pronounced hazard ratio estimates, and presented the poorest data fit and accuracy measures. Model fit and accuracy improved in all extended models, with PWP performing best in terms of log-likelihood, Akaike and Bayesian information criteria. Conclusion: The PWP model is based on plausible assumptions in the context of modelling the risk of infection recurrence and was shown in this study to outperform alternative extensions for modelling recurrent events.