Abstract
In most clinical studies, the evaluation of the effect of a therapy and the impact of prognostic factors is based on relapse-free survival. Relapse free is a net survival, since it is interpreted as the relapse-free probability that would be observed if all patients experienced relapse sooner or later. Death without evidence of relapse prevents the subsequent observation of relapse, acting in a semi-competing risks framework. Relapse free survival is often estimated by standard regression models after censoring times to death. The association between relapse and death is thus accounted for. However, to better estimate relapse free survival, a bivariate distribution of times to events needs to be considered, for example by means of copula models. We concentrate here on the copula graphic estimator, for which a pertinent regression model has been developed. No direct parametric estimation of the regression coefficient for the covariates is available and the evaluation of the impact of covariates on relapse free survival is based on graphical representation for each covariate singularly. The advantage of this approach is based on the relationship between net survival, and crude cumulative incidences. Regression models can be fitted for the latter quantities and the estimates can be used to compute net survival through a copula structure. Our proposal is based on flexible regression transformation model on crude cumulative incidences based on pseudo-values. An overall view of the joint association among covariates and relapse free survival is obtained through Multiple Correspondence Analysis. Moreover cluster analysis on MCA coordinates was used to synthesize covariate patterns and to estimates the corresponding relapse free survival curve. This approach has been applied to a large “historical” case series of patients with breast cancer.
Highlights
The evaluation of the effect of a therapy or the impact of prognostic factors is based on the time elapsed form the date of disease diagnosis or the beginning of treatment and the occurrence of different events related to the disease progression
The aim of the analysis is to evaluate the effect of covariates on relapse free survival
To evaluate treatment or covariate effects on specific events, common regression models are based on cause specific hazards (e.g., Cox regression model) or on sub distribution hazard (e.g., Fine regression model)
Summary
The evaluation of the effect of a therapy or the impact of prognostic factors is based on the time elapsed form the date of disease diagnosis or the beginning of treatment and the occurrence of different events related to the disease progression.A first analysis on event free survival is often based on the comprehensive end-point in which all possible events are considered. The evaluation of the effect of a therapy or the impact of prognostic factors is based on the time elapsed form the date of disease diagnosis or the beginning of treatment and the occurrence of different events related to the disease progression. Tumour recurrence is a composite end-point in which the occurrence of local relapses, contralateral tumours and distant or local metastases are frequently considered. The occurrence of death not related to the disease or secondary tumours different from breast cancer (defined as absorbing events) may be observed for some patients before tumour relapse and prevent the observation of the main end-point. On the contrary the occurrence of relapses does not prevent the observation of absorbing events. This situation is usually referred to as “semi-competing risks” [1]. In the absence of independent censoring, times to absorbing events are always observable and the incomplete observation relies only to relapse
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