A unification of multivariate methods for meta-analysis of genetic association studies.

Methods for multivariate meta-analysis of genetic association studies are reviewed, summarized and presented in a unified framework. Modifications of standard models are described in detail in order to be applied in genetic association studies. The model based on summary data is uniformly defined for both discrete and continuous outcomes and analytical expressions for the covariance of the two jointly modeled outcomes are derived for both cases. The models based on the binary nature of the data are fitted using both prospective and retrospective likelihood. Furthermore, formal tests for assessing the genetic model of inheritance are developed based on standard normal theory. The general model is compared to the recently proposed genetic model-free bivariate approach (either using summary or binary data), and it is clearly shown that the estimates provided by this approach are nearly identical to the estimates derived by the general bivariate model using the aforementioned tests for the genetic model. The methods developed here as well as the tests, are easily implemented in all major statistical packages, escaping the need of self written software. The methods are applied in several already published meta-analyses of genetic association studies (with both discrete and continuous outcomes) and the results are compared against the widely used univariate approach as well as against the genetic model free approaches. Illustrative examples of code in Stata are given in the appendix. It is anticipated that the methods developed in this work will be widely applied in the meta-analysis of genetic association studies.