Augmented transfer regression learning for completely missing covariates

Large-scale population-level datasets, such as the UK Biobank and the All of Us Research Program, often lack covariates needed for a specific analysis, such as genetic or lifestyle measures, while related studies measure them. This creates a cross-population missing data problem in which covariates are completely unobserved in the target population, rather than partially missing within one dataset. We propose an augmented transfer regression learning method for this setting. The key identifying condition is a sub-population shift assumption: the joint distribution of the outcome and observed covariates may differ across source and target populations, but the conditional distribution of the missing covariates given observed variables is invariant. We combine importance-weighted estimating equations with imputation terms for first- and second-order moments of the missing covariates. The resulting estimator is doubly robust, remaining consistent if either the density ratio model or both imputation models are correctly specified. It is $n^{1/2}$-consistent and asymptotically normal, and attains the semiparametric efficiency bound when both nuisance models are correctly specified.

Debiased high-dimensional regression calibration for errors-in-variables log-contrast models

Motivated by the challenges in analyzing gut microbiome and metagenomic data, this work aims to tackle the issue of measurement errors in high-dimensional regression models that involve compositional covariates. This paper marks a pioneering effort in conducting statistical inference on high-dimensional compositional data affected by mismeasured or contaminated data. We introduce a calibration approach tailored for the linear log-contrast model. Under relatively lenient conditions regarding the sparsity level of the parameter, we have established the asymptotic normality of the estimator for inference. Numerical experiments and an application in microbiome study have demonstrated the efficacy of our high-dimensional calibration strategy in minimizing bias and achieving the expected coverage rates for confidence intervals. Moreover, the potential application of our proposed methodology extends well beyond compositional data, suggesting its adaptability for a wide range of research contexts.