title: A Bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model.
abstract: When multicentre clinical trial data are analysed, it has become more and more popular to look for possible heterogeneity in outcome between centres. However, beyond the investigation of such heterogeneity, it is also interesting to consider heterogeneity in treatment effect over centres. For time-to-event outcomes, this may be investigated by including a random centre effect and a random treatment by centre interaction in a Cox proportional hazards model. Assuming independence between the random effects, we propose a Bayesian approach to fit our proposed model. The parameters of interest are the variance components sigma(0) (2) and sigma(1) (2) of these random effects, which can be interpreted as a measure of centre and treatment effect over centres heterogeneity of the hazard. These variance components are estimated from their marginal posterior density after integrating out the fixed treatment effect and the random effects. As this integration cannot be performed analytically, the marginal posterior density is approximated using the Laplace integration technique. Statistical inference is then based on the characteristics of the posterior marginal density, such as the mode and the standard deviation. We demonstrate the proposed technique using data from a pooled database of seven EORTC bladder cancer clinical trials. Substantial centre and treatment effect over centres heterogeneity in disease-free interval was found.
authors.affiliation: European Organisation for Research and Treatment of Cancer, Brussels, Belgium. catherine.legrand@eortc.be
authors.forename: Catherine
authors.initials: C
authors.lastname: Legrand
authors.forename: Vincent
authors.initials: V
authors.lastname: Ducrocq
authors.forename: Paul
authors.initials: P
authors.lastname: Janssen
authors.forename: Richard
authors.initials: R
authors.lastname: Sylvester
authors.forename: Luc
authors.initials: L
authors.lastname: Duchateau
mesh_terms: D001499:Bayes Theorem; D005060:Europe; D006801:Humans; D015233:Models, Statistical; D015337:Multicenter Studies as Topic / Q000706:statistics & numerical data*; D016016:Proportional Hazards Models