Relationship between Gamel-Boag and Cox regressions in survival analysis of gastric cancer

Background: As an increasing number of cancer patients have been cured of the disease in recent decades, clinicians need to determine whether cancer therapies will actually cure the disease or merely prolong time to death and what percentage of patients will be cured. These questions can be answered by the Boag model (parametric cure model) with its three parameters including the cure rate and mean log survival time, whereas conventional Cox model fails to distinguish between cure and delayed death. One may argue, however, that the Boag model compared with the Cox one-parameter model may have superfluous parameters. We assess the redundancy of the Boag model and the relationship between its regression coefficients with that of the Cox model. Methods: We used follow-up data from 1410 gastric cancer patients who were randomized to receive high-dose or low-dose adjuvant chemotherapy after curative gastrectomy. Each of 18 explanatory variables were converted to a binary covariate and entered into three modifications of the Gamel-Boag regression models and into the Cox regression model, to obtain maximum likelihood estimates of regression coefficients representing the covariate effects on the cure rate, mean survival time and hazard ratio. The adequacy of the Gamel-Boag models was assessed by the Akaike information criterion and the relationship between the Gamel-Boag and Cox regression coefficients was examined by regression analysis. Results: The assumption that chemotherapy and other factors affect the cure rate alone is comparable with the assumption that chemotherapy affects both the cure rate and survival time. The Gamel-Boag regression coefficients for cure rate were highly correlated with and proportional to the Cox regression coefficient for hazard ratio (|r|= 0.99, P < 0.0001); the Gamel-Boag regression coefficients for survival time were less strongly correlated with the Cox regression coefficient. Conclusion: In curable subsets of cancer patients, the hazard ratio may be used to test whether or not treatment is curative; the Gamel-Boag regression coefficient for survival time may be a superfluous parameter. To assess the survival benefits of treatment, however, the Gamel-Boag parametric analysis should be done.