Using multiple timescale models for the evaluation of a time-dependent treatment

In survival analysis, the absolute measure of cumulative risk provided by the Kaplan-Meier estimator is still the most used quantity for its easy calculation and direct interpretability. However, for describing the survival after an intervention that may occur at different times from baseline observation, the Kaplan-Meier estimator generally yields to biased results if intervention is considered as fixed at baseline. The main focus of the present paper is to extend the use of a multiple timescale model in the presence of a time dependent intervention. The aim is to obtain 1) an estimate of treatment effect in terms of hazard ratios by flexible modeling, 2) a valid prediction tool, i.e. estimate of prognosis for a patient who changes treatment later in time, and 3) an appropriate graphical representation of survival in the presence of a time dependent treatment change, accounting for different timescales. We will show the advantages of this approach on the comparison of chemotherapy versus transplant in children with high-risk acute lymphoblastic leukemia in first remission. We considered a model with two timescales that accounts for the change in treatment at different times in the disease course. An alternative approach to survival estimates is also proposed which has some advantages over the traditional landmark approach: it uses all the data available to plot survival from the date of remission, it avoids the arbitrary choice of a landmark time and explicitly models the change in hazard due to transplant.