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 high mortality statistics. These models can be used to better describe the natural disease process. But reaching that goal requires making assumptions like Markov and homogeneity with time. The present study aims to investigate these hypotheses. Materials and Methods: Data from 330 patients with gastric cancer undergoing surgery at Iran Cancer Institute from 1995 to 1999 were analyzed. To assess Markov assumption and time homogeneity in modeling transition rates among states of multi-state model, Cox-Snell residuals, Akaikie information criteria and Schoenfeld residuals were used, respectively. Results: The assessment of Markov assumption based on Cox-Snell residuals and Akaikie information criterion showed that Markov assumption was not held just for transition rate of relapse (state 1 -> state 2) and for other transition rates - death hazard without relapse (state 1 -> state 3) and death hazard with relapse (state 2 -> state 3) - this assumption could also be made. Moreover, the assessment of time homogeneity assumption based on Schoenfeld residuals revealed that this assumption - regarding the general test and each of the variables in the model - was held just for relapse (state 1 -> state 2) and death hazard with a relapse (state 2 -> state 3). Conclusions: Most researchers take account of assumptions such as Markov and time homogeneity in modeling transition rates. These assumptions can make the multi-state model simpler but if these assumptions are not made, they will lead to incorrect inferences and improper fitting.