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Introduction: In cohort studies, the time to a particular non-terminal event, such as disease onset, occurrence of infection or hospitalization, is often of main interest. For proper modeling, death as a competing risk should be accounted for. Especially, the “semi-competing” character of the data has to be acknowledged: The non-terminal event process can be observed before death (the terminal event), but not vice versa¹. Consequently, the two time-to-event endpoints might be correlated when both events are observed on the same individual. An additional challenge in this setting arises when study individuals experience the non-terminal event of interest, e.g., multiple hospital admissions, repeated epileptic seizures or successive heart attacks, repeatedly over time. Thus, for valid statistical inference, it is essential to adjust for dependencies between the two types of events while considering repeated occurrences of the non-terminal event. Li et al.² suggest a joint frailty-copula model estimated in a Bayesian framework to this task. However, a prior distribution specification in complex Bayesian models may require careful consideration and extensive sensitivity analysis, which can hamper the straightforward application of the model in practice.

Methodology: We define a copula model that constructs the joint distribution of the time to both events, considering in addition the recurrent nature of the non-terminal process and estimate it in the frequentist paradigm. A flexible parametric framework is implemented by assuming Weibull and Gompertz distributions for the recurrent and terminal events, respectively. Further, we apply an AFT model, allowing for a simple interpretation of the model parameters in terms of acceleration factors.

Results: The model is illustrated using a randomized controlled study investigating the efficacy of a nurse coordinated disease management program versus usual care for patients readmitted due to systolic heart failure. In this context, hospital readmission is considered a recurrent non-terminal event, while death serves as the competing terminal event. Our findings indicate that patients in the nurse coordinated disease management program tend to live longer on average than those in the usual care group. Additionally, the treatment group experiences a longer duration before readmission compared to the control group, indicating that the nurse-coordinated disease management program may offer advantages in terms of both longer life expectancy and the time until hospital readmission.

Conclusion: In many clinical trials individuals are followed up for an event, that could occur repeatedly over time, but can be stopped by a terminal event such as death. In this situation, dependent censoring is encountered due to the potential correlation between the two event type processes. Thus, we adopt a flexible copula model and construct the joint distribution of the terminal and non-terminal event, while also considering the repeated instances of the non-terminal event. The model provides results that are intuitively interpretable, facilitating its application within the medical field.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.

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