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 Departement 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 Departement is an optimal measure of Departement-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. (C) 2013 Elsevier Ltd. All rights reserved.