Estimating the risk of recurrent or multiple events in longitudinal studies

Background. Longitudinal studies usually evaluate risk by modelling time to first event using standard Cox's regression. However this method fails to utilize further outcome information after the first event. In patients with Chronic Kidney Disease repeated events of the same type (recurrent events) and or different type (multiple events) occur frequently. Risk estimation based on partial information may be inaccurate and imprecise. Yet, the analytical tool must take into account the lack of independence of the failure times. -- Methods. To determine whether other methods of analysis are more informative and powerful than standard Cox's regression I re-evaluated data from previous research I had undertaken in Chronic Kidney Disease patients. Data from a multi-centre dialysis access study of incident hemodialysis patients were used as an example of recurrent failure events. Data from a cohort of pre-dialysis patients were used as an example of multiple competing events (dialysis start and death). Correlation in the data was accounted for using either robust variance methods or incorporating frailty effects into the model. Different approaches were used more or less free from distributional assumptions, including generalized models for counts, and using the robust version of the Cox's model as reference estimation method. -- Results. The work shows that standard survival techniques that disregarded further information after the first event have limitations, in terms of power (precision of each estimate and number of estimated effects) and possibly of accuracy (bias). For example, the hazard ratio (HR) of primary failure of the first arterio-venous access for dialysis was 1.96 (95% Confidence Intervals 0.93 to 4.1) in presence of both history of heart failure and nephrology follow-up shorter than 3 months before dialysis start (effect of the interaction controlling for the main effects and other covariates). The estimate was more precise in the corresponding extended Cox's model for recurrent events (HR 2.02, 95% CI 1.11 to 3.65). Similar fits were obtained using variance corrected parametric models. However, all these variance corrected models did not take into account any random effects. This may have induced underestimation of the true effects if the frailty models were true (HR from the frailty Weibull model 3.5, 95% CI from 1.34 to 9). Improvement of model efficiency and more flexibility in model building were observed also using competing risk models for multiple events. -- Conclusion. Analytical techniques for repeated events exist that make more efficient the use of longitudinal data while accounting for their correlation. These methods help address research questions about risk (and some also survival time) considering the entire course of a disease process or multiple possible outcomes, and have implications on design, implementation and costs of clinical research