Regression inference for multiple populations by integrating summary-level data using stacked imputations

There is a growing need for flexible general frameworks that integrate individual-level data with external summary information for improved statistical inference. This paper proposes an imputation-based methodology where the goal is to fit an outcome regression model with all available variables in the internal study while utilizing summary information from external models that may have used only a subset of the predictors. The method allows for heterogeneity of covariate effects across the external populations. The proposed approach generates synthetic outcome data in each population, uses stacked multiple imputation to create a long dataset with complete covariate information, and finally analyzes the imputed data with weighted regression. This flexible and unified approach attains the following four objectives: (i) incorporating supplementary information from a broad class of externally fitted predictive models or established risk calculators which could be based on parametric regression or machine learning methods, as long as the external model can generate outcome values given covariates; (ii) improving statistical efficiency of the estimated coefficients in the internal study; (iii) improving predictions by utilizing even partial information available from models that uses a subset of the full set of covariates used in the internal study; and (iv) providing valid statistical inference for the external population with potentially different covariate effects from the internal population. Applications include prostate cancer risk prediction models using novel biomarkers that are measured only in the internal study.