A polytomous conditional likelihood approach for combining matched and unmatched case–control studies

In genetic association studies it is becoming increasingly imperative to have large sample sizes to identify and replicate genetic effects. To achieve these sample sizes, many research initiatives are encouraging the collaboration and combination of several existing matched and unmatched case–control studies. Thus, it is becoming more common to compare multiple sets of controls with the same case group or multiple case groups to validate or confirm a positive or negative finding. Usually, a naive approach of fitting separate models for each case–control comparison is used to make inference about disease–exposure association. But, this approach does not make use of all the observed data and hence could lead to inconsistent results. The problem is compounded when a common case group is used in each case–control comparison. An alternative to fitting separate models is to use a polytomous logistic model but, this model does not combine matched and unmatched case–control data. Thus, we propose a polytomous logistic regression approach based on a latent group indicator and a conditional likelihood to do a combined analysis of matched and unmatched case–control data. We use simulation studies to evaluate the performance of the proposed method and a case–control study of multiple myeloma and Inter‐Leukin‐6 as an example. Our results indicate that the proposed method leads to a more efficient homogeneity test and a pooled estimate with smaller standard error. Copyright © 2010 John Wiley & Sons, Ltd.