Description of an approach based on maximum likelihood to adjust an excess hazard model with a random effect

Objective: To adjust an excess hazard regression model with a random effect associated with a geographical level, the Département in France, and compare its parameter estimates with those obtained using a “fixed-effect” excess hazard regression model. Methods: An excess hazard regression model with a piecewise constant baseline hazard was used and a normal distribution was assumed for the random effect. Likelihood maximization was performed using a numerical integration technique, the Quadrature of Gauss–Hermite. Results were obtained with colon-rectum and thyroid cancer data from the French network of cancer registries. Result: The results were in agreement with what was theoretically expected. We showed a greater heterogeneity of the excess hazard in thyroid cancers than in colon-rectum cancers. The hazard ratios for the covariates as estimated with the mixed-effect model were close to those obtained with the fixed-effect model. However, unlike the fixed-effect model, the mixed-effect model allowed the analysis of data with a large number of clusters. The shrinkage estimator associated with Département is an optimal measure of Département-specific excess risk of death and the variance of the random effect gave information on the within-cluster correlation. Conclusion: An excess hazard regression model with random effect can be used for estimating variation in the risk of death due to cancer between many clusters of small sizes.