Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

Background: Multi-state models are appropriate for cancer studies such as gastrectomy which have highmortality statistics. These models can be used to better describe the natural disease process. But reaching thatgoal requires making assumptions like Markov and homogeneity with time. The present study aims to investigatethese hypotheses. Materials and
Methods: Data from 330 patients with gastric cancer undergoing surgery atIran Cancer Institute from 1995 to 1999 were analyzed. To assess Markov assumption and time homogeneity inmodeling transition rates among states of multi-state model, Cox–Snell residuals, Akaikie information criteria andSchoenfeld residuals were used, respectively.
Results: The assessment of Markov assumption based on Cox–Snellresiduals and Akaikie information criterion showed that Markov assumption was not held just for transitionrate of relapse (state 1gstate 2) and for other transition rates - death hazard without relapse (state 1gstate 3)and death hazard with relapse (state 2gstate 3) - this assumption could also be made. Moreover, the assessmentof time homogeneity assumption based on Schoenfeld residuals revealed that this assumption - regarding thegeneral test and each of the variables in the model - was held just for relapse (state 1gstate 2) and death hazardwith a relapse (state 2gstate 3).
Conclusions: Most researchers take account of assumptions such as Markov andtime homogeneity in modeling transition rates. These assumptions can make the multi-state model simpler butif these assumptions are not made, they will lead to incorrect inferences and improper fitting.