Identifiability of cure models in a competing risk framework

In survival analysis, a competing risk model is a statistical method used to analyze time-to-event data in situations where multiple events of interest may occur and compete for occurrence. The events are considered ‘competing’ because the occurrence of one event prevents the occurrence of other events. Traditional survival analysis focuses on a single event of interest, such as death due to a particular cause. However, in real-world scenarios, there can be multiple events that individuals in a study population might experience. These events can have different causes. For example, in a study involving cancer patients, the events of interest could be death from cancer, death from other causes, and disease recurrence. In survival analysis, a cure model is a statistical model used when a proportion of the study population is considered ‘cured’, meaning they will never experience the event of interest. This concept is particularly important when studying diseases with a good prognosis....Show moreIn survival analysis, a competing risk model is a statistical method used to analyze time-to-event data in situations where multiple events of interest may occur and compete for occurrence. The events are considered ‘competing’ because the occurrence of one event prevents the occurrence of other events. Traditional survival analysis focuses on a single event of interest, such as death due to a particular cause. However, in real-world scenarios, there can be multiple events that individuals in a study population might experience. These events can have different causes. For example, in a study involving cancer patients, the events of interest could be death from cancer, death from other causes, and disease recurrence. In survival analysis, a cure model is a statistical model used when a proportion of the study population is considered ‘cured’, meaning they will never experience the event of interest. This concept is particularly important when studying diseases with a good prognosis. A notable example is paediatric oncology, where patients may be considered cured if they experience long event-free survival. Despite the growing recognition of the significance of considering cured fractions in statistical analysis, there remains limited research on the theoretical aspects of combining competing risks and cure models. The integration of these two approaches has not been extensively studied until now. This research aims to fill the existing gap in the field by focusing on the concept of identifiability. First, a general model that involves two competing events and cause-specific cure for both events is considered. The main objective is to identify the model parameters, particularly the dependence relationship between the two cure status indicators. A logistic model to estimate cure probabilities and a semi-parametric Cox model to assess cause-specific hazards (or subdistribution hazards) are employed. The results demonstrated that, under appropriate assumptions, certain parameters can be effectively identified. However, it is also revealed that the model becomes unidentifiable without these specific assumptions. It is further shown that the models previously proposed in the literature can be seen as special cases of this general model. The thesis presents a novel estimation procedure for the general model, utilizing the EM (ExpectationMaximization) algorithm. The flexibility of this procedure allows it to be applied to special cases of the model. Two simulation studies were conducted to investigate the performance of the estimation procedure and to study the practical identifiability properties of the model for cure and competing risks. The results showed good performance for most parameters of the model. In conclusion, this thesis provides valuable insights into the practical identifiability of parameters 2 through both theoretical and simulation-based analyses. This research significantly contributes to a better understanding of competing risks and cure models. The understanding of these statistical methods enables more accurate analysis of patient outcomes and treatment effects in diverse clinical and non-clinical contexts. Ultimately, this research positively impacts the field, facilitating better decision-making and improving overall outcomes for patients and individuals in various settings.Show less

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Identifiability of cure models in a competing risk framework