Advances in Methods for Integrating Heterogeneous Health Data

In randomized controlled trials (RCTs), leveraging summary information from other RCTs is a powerful strategy for estimation of subgroup-level conditional average treatment effect (CATE). However, most methods have not addressed the common setting where publicly available external estimates—such as single-factor CATEs (e.g., effects stratified by sex)— can be leveraged to estimate the finer subgroups of interest (e.g., sex-by-race interactions). To address this gap, we introduce a novel James–Stein (JS)–type estimator that uses coarser external subgroup summaries while accommodating potential violations of compatibility between external and internal estimates. We theoretically show the proposed estimator uniformly dominates the unconstrained estimator based solely on internal data, in terms of the mean squared error of the target CATE vectors, even under departures of the compatibility assumption. We apply our data integration method to a post hoc intersectional CATE analysis by sex and race in a tirzepatide weight-loss trial (SURMOUNT-1), incorporating sex-specific and race-specific effect estimates from two prior semaglutide trials (STEP 1 and STEP 2). 

Meta-analysis typically combines measures of association across multiple studies. Outside of carefully-controlled lab experiments, these are not plausibly identical and the underlying effects will differ. Methods for describing this heterogeneity are limited: the default choices are either purely statistical measures of the differences between the estimates (I-squared or Cochran's Q) or - making particular modeling assumptions - the variance of an assumed random effects distribution, typically denoted tau-squared. We present a simple alternative measure of heterogeneity of the underlying parameters, measured on the same scale as them, and straightforward plug-in estimates of it. As well as providing inference on this measure of spread, we show how interpretably-penalized versions of it lead to simple sparse descriptions of the set of heterogeneous parameters. Several examples will be given. 

The simultaneous estimation of many parameters based on data collected from corresponding studies is a key research problem that has received renewed attention in the high-dimensional setting. Many practical situations involve heterogeneous data where heterogeneity is captured by a nuisance parameter. Effectively pooling information across samples while correctly accounting for heterogeneity presents a significant challenge in large-scale estimation problems. We address this issue by introducing the "Nonparametric Empirical Bayes Structural Tweedie" (NEST) estimator, which efficiently estimates the unknown effect sizes and properly adjusts for heterogeneity via a generalized version of Tweedie's formula. For the normal means problem, NEST simultaneously handles the two main selection biases introduced by heterogeneity: one, the selection bias in the mean, which cannot be effectively corrected without also correcting for, two, selection bias in the variance. We develop theory to show that NEST is asymptotically as good as the optimal Bayes rule that uniquely minimizes a weighted squared error loss. In our simulation studies NEST outperforms competing methods, with much efficiency gains in many settings. The proposed method is demonstrated on estimating the batting averages of baseball players and Sharpe ratios of mutual fund returns. Extensions to other members of the two-parameter exponential family are discussed. 

Integrative analysis of multiple heterogeneous datasets has arisen in many research fields. Existing approaches oftentimes suffer from limited power in capturing nonlinear structures, insufficient account of noisiness and effects of high-dimensionality, lack of adaptivity to signals and sample sizes imbalance, and their results are sometimes difficult to interpret. To address these limitations, we propose a kernel spectral method that achieves joint embeddings of two independently observed high-dimensional noisy datasets. The proposed method automatically captures and leverages shared low-dimensional structures across datasets to enhance embedding quality. The obtained low-dimensional embeddings can be used for downstream tasks such as simultaneous clustering, data visualization, and denoising. The proposed method is justified by rigorous theoretical analysis, which guarantees its consistency in capturing the signal structures, and provides a geometric interpretation of the embeddings. Under a joint manifold model framework, we establish the convergence of the embeddings to the eigenfunctions of some natural integral operators. These operators, referred to as duo-landmark integral operators, are defined by the convolutional kernel maps of some reproducing kernel Hilbert spaces (RKHSs). These RKHSs capture the underlying, shared low-dimensional nonlinear signal structures between the two datasets. Our numerical experiments and analyses of two pairs of single-cell omics datasets demonstrate the empirical advantages of the proposed method over existing methods in both embeddings and several downstream tasks.