  Meta-analysis, because of both logistical convenience and statistical
efficiency, is widely popular for synthesizing information on common parameters
of interest across multiple studies. We propose developing a generalized
meta-analysis approach for combining information on multivariate regression
parameters across multiple different studies which have varying level of
covariate information. Using algebraic relationships between regression
parameters in different dimensions, we specify a set of moment equations for
estimating parameters of a maximal model through information available from
sets of parameter estimates from a series of reduced models available from the
different studies. The specification of the equations requires a reference
dataset to estimate the joint distribution of the covariates. We propose to
solve these equations using the generalized method of moments approach, with
the optimal weighting of the equations taking into account uncertainty
associated with estimates of the parameters of the reduced models. We describe
extensions of the iterated reweighted least square algorithm for fitting
generalized linear regression models using the proposed framework. Based on the
same moment equations, we also propose a diagnostic test for detecting
violation of underlying model assumptions, such as those arising due to
heterogeneity in the underlying study populations. Methods are illustrated
using extensive simulation studies and a real data example involving the
development of a breast cancer risk prediction model using disparate risk
factor information from multiple studies.
