  In clinical follow-up studies with a time-to-event end point, the difference
in the restricted mean survival time (RMST) is a suitable substitute for the
hazard ratio (HR). However, the RMST only measures the survival of patients
over a period of time from the baseline and cannot reflect changes in life
expectancy over time. Based on the RMST, we study the conditional restricted
mean survival time (cRMST) by estimating life expectancy in the future
according to the time that patients have survived, reflecting the dynamic
survival status of patients during follow-up. In this paper, we introduce the
estimation method of cRMST based on pseudo-observations, the construction of
test statistics according to the difference in the cRMST (cRMSTd), and the
establishment of the robust dynamic prediction model using the landmark method.
Simulation studies are employed to evaluate the statistical properties of these
methods, which are also applied to two real examples. The simulation results
show that the estimation of the cRMST is accurate and the cRMSTd test performs
well. In addition, the dynamic RMST model has high accuracy in coefficient
estimation and better predictive performance than the static RMST model. The
hypothesis test proposed in this paper has a wide range of applicability, and
the dynamic RMST model can predict patients' life expectancy from any
prediction time, considering the time-dependent covariates and time-varying
effects of covariates.
