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Objective(s): In survival analysis because are still unknown some of the important factors related to disease, it is too difficult or impossible measure all the appropriate factors and related diseases. Not consider these common unknown risk factors causes dependence among survival times, the results from Cox proportional hazard model and parametric models are not reliable. In this case, we use to confront the above problem of frailty models. The purpose of this study was to examine factors affecting survival of patients with gastric cancer using the log-logistic parametric model with gamma frailty and to compare these results with Cox model.
Methods: This study includes Information of 110 cases with gastric cancer was collected from Babol cancer registry during 1990 through 1991, who were followed up for a period of 15 years by the year 2006. In order to explore factors affecting survival of patients, Cox model and also parametric model Log-logistic with gamma frailty were examined and the Akaike information criterion (AIC) was considered as a criterion to select the best model (s). For the statistical analysis, the statistical softwares SAS 9.1 and STATA 8.0 were used. All P<0.05 were defined as statistical significance.
Results: Sample of subjects encompassed 75.4% men and 24.6% women. The mean age at diagnosis was 60.2 yr for men and 57.5 yr for women. The median survival time reached 8.6 months, and survival rates in 1, 3, and 5 years following diagnosis were 25%, 18%, and 17%, respectively. Multivariate analysis showed that family history of cancer might increase significantly the risk of death from cancer according to Cox and parametric models by including and not including heterogeneity effect. According to AIC criterion and the nature of the data (hazard rate is non-monotonic), parametric model (with and without gamma frailty) had better performance when compared to Cox model. And among, log logistic model with gamma frailty seemed more appropriate. In this model, age and family history of cancer were significant predictors.
Conclusion: Results indicated that early preventative care for patients with family history of cancer might be of importance to decrease the risk of death in patients with gastric cancer, and being younger, on the other hand, would cause a potential decline in the corresponding risk of death. According to our findings, based on the Akaike criterion and also the nature of the data (the hazard rate is hump-shaped), log logistic model with gamma frailty could be considered as a useful statistical model in survival analysis of patients with gastric cancer rather than Cox model.

Keywords: Gastric cancer, Survival analysis, Log normal distribution, Frailty model

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