Estimating Relapse Free Survival as a Net Probability : Regression Models and Graphical Representation : An Application of a Large Breast Cancer Case Series
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 relapsefree
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 \u201chistorical\u201d case
series of patients with breast cancer
