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

• Main Authors: Ali Zare, Mahmood Mahmoodi, Kazem Mohammad, Hojjat Zeraati, Mostafa Hosseini, Kourosh Holakouie-Naieni
• Format: Article
• Language: English
• Published: Tehran University of Medical Sciences 2015-10-01
• Series: Journal of Biostatistics and Epidemiology
• Subjects: asymptotic theory; frailty; individual homogeneity; gamma distribution; misspecification; multi-state model
• Online Access: https://jbe.tums.ac.ir/index.php/jbe/article/view/1

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.