Generalized meta-analysis for multiple regression models across studies with disparate covariate information

Abstract

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.

Assessment of Individual- and Community-level Risks for COVID-19 Mortality in the US and Implications for Vaccine Distribution

“…We modelled the lograte in terms of additive effects of age and race/ethnicity categories and further adjusted for states as fixed effects in the model. We then used data available on age, race/ethnicity and all other risk factors of the model from a combination of health survey data (see below) to estimate joint distribution of all of these factors, and use Generalized Method of Moment (GMM) techniques we have developed earlier 22 to obtain estimates for the effects associated with age and race adjusted for the other risk-factors in the model with their effects being fixed at those available from an underlying fully adjusted model from the UK OpenSAFELY study (Supplementary Methods Section 1.2, Extended Data Table 1).…”

Comparative Validation of Breast Cancer Risk Prediction Models and Projections for Future Risk Stratification

“…Risk projections based on the integrated model assumed that classical risk factors, MD, and PRS act multiplicatively on disease risk. We accounted for known dependencies between classical risk factors, and previous studies support multiplicative effects of classical risk factors or MD with PRS on disease risk (24,64,65). Risk projections based on models with MD accounted for its dependence on age and body mass index, but not on the other risk factors in the model that have weaker associations with MD (66).…”

“…The final analytic samples from the GS and PLCO were 64 874 (863 cases within 5 years) and 48 279 (1008 cases within 5 years), respectively (Supplementary Figure 1, available online). As PLCO was used for the development of iCARE-BPC3 (24), it was used only for validating other models.…”

“…Risk prediction models should be dynamic and flexible in their ability to incorporate additional risk factors and contextspecific incidence rates. However, developing and validating a comprehensive model is challenging because of all the relevant risk factors not being typically measured in a single study and requiring novel methods for data integration from multiple epidemiologic studies (22)(23)(24). Our recently developed Individualized Coherent Absolute Risk Estimation (iCARE) software implements a flexible approach to build absolute risk models for a population combining information on relative risk estimates, age-specific incidence and mortality rates, and risk factor distributions from multiple data sources (25)(26)(27).…”

Enhanced empirical likelihood estimation of incubation period of COVID‐19 by integrating published information

“…A natural question is how to incorporate summarized information with individual level data collected in Zhejiang province to get more efficient estimates for the distribution of forward time or incubation period. Meta-analysis [4][5][6] is a systematic way to utilize the summarized information from several relevant studies. In practice, comprehensive individual-level data may not be publicly available due to privacy concerns or other issues.…”