title: Description of an approach based on maximum likelihood to adjust an excess hazard model with a random effect.
abstract: 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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Hospices Civils de Lyon, Service de Biostatistique, F-69003 Lyon, France.
authors.forename: Cyrielle
authors.initials: C
authors.lastname: Dupont
authors.forename: Nadine
authors.initials: N
authors.lastname: Bossard
authors.forename: Laurent
authors.initials: L
authors.lastname: Remontet
authors.forename: Aurélien
authors.initials: A
authors.lastname: Belot
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D016000:Cluster Analysis; D015179:Colorectal Neoplasms / Q000453:epidemiology*; D005260:Female; D005602:France / Q000453:epidemiology; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D016016:Proportional Hazards Models; D012042:Registries; D012044:Regression Analysis; D013964:Thyroid Neoplasms / Q000453:epidemiology*; D055815:Young Adult