A pseudo-values regression model for non-fatal event free survival in the presence of semi-competing risks

During follow-up patients may experience non-fatal events related to disease progression and death. This is a “semi-competing risks” setting, as the occurrence of death before non-fatal events prevents the observation of the latter, but not vice versa. We developed a regression model for non-fatal event free survival in the presence of semi-competing risks based on pseudo-values. It is estimated in three steps: estimate non-parametrically non-fatal event free survival under a defined copula representing the joint distribution of time to fatal and non-fatal events; compute non-fatal event free survival pseudo-values for every individual at predefined time points; fit a GEE model using pseudo-values as a response variable. A simulation study is performed and two clinical examples are analysed. The proposed method provides covariate coefficient estimates almost unbiased, with standard errors slightly higher than those obtained with methods based on maximum likelihood estimation. However, pseudo-values regression, being based on estimation functions, has the advantage of enabling adjusted covariate effects estimation without convergence problems and allowing a direct smoothed estimate of the hazard function. Moreover, standard routines computing pseudo-values and GEE are available in statistical software.