Assessing misspecification of individual homogeneity assumption in multi-state models based on asymptotic theory

Background Aim: Multi-state models can help better understand the process of chronic diseases such as cancers. These models are influenced by assumptions like individual homogeneity. This study aimed to investigate the effect of lack of individual homogeneity assumption in multi-state models. Methods Materials: To investigate the effect of lack of individual homogeneity assumption in multi-state models, tracking model as well as frailty factor with gamma distribution were used. Accordingly, without any simulation and only based on asymptotic theory, the bias of mean transition rate which is among the basic parameters of the multi-state models was studied. Results: Analysis of the effect of individual homogeneity assumption misspecification revealed that for different number of follow-ups as well as censoring time, the mean transition rate and its variance were underestimated. In addition, if there is a lot of heterogeneity in reality and if the individual homogeneous multi-state model is fitted, a significant bias will exist in the estimated mean transition rate and its variance. The results of this study also showed that the intensity of bias increases with an increase in the degree of heterogeneity. But with an increase in the number of follow-ups, the intensity of bias decreases, to some extent. Conclusion: Disregarding individual homogeneity assumption in a heterogeneous population causes bias in the estimation of multi-state model parameters and with an increase in the degree of heterogeneity, the intensity of bias will increase too.