Peisong Han

In the era of big data, secondary outcomes have become increasingly important alongside primary outcomes. These secondary outcomes, which can be derived from traditional endpoints in clinical trials, compound measures, or risk prediction scores, hold the potential to enhance the analysis of primary outcomes. Our method is motivated by the challenge of utilizing multiple secondary outcomes, such as blood biochemistry markers and urine assays, to improve the analysis of the primary outcome related to liver health. Current integration methods often fall short, as they impose strong model assumptions or require prior knowledge to construct over-identified working functions. This article addresses these challenges and opens a new avenue in data integration by introducing a novel integrative learning framework applicable in a general setting. The proposed framework allows for the robust, data-driven integration of information from multiple secondary outcomes, promotes the development of efficient learning algorithms, and ensures optimal use of available data. Extensive simulation studies demonstrate that the proposed method significantly reduces variance in primary outcome analysis, outperforming existing integration approaches. Additionally, applying this method to UK Biobank reveals that cigarette smoking is associated with increased fatty liver measures, with these effects being particularly pronounced in the older adult cohort.

With the advent of innovative data collection methods and the exponential growth of data availability in the ‘Big Data’ era, statistical analyses have increasingly relied on the integration of data from multiple sources. A single data source frequently fails to meet the rising demand for high-quality statistical products. Probability sample surveys provide ideal data sources to achieve population representation but are faced with challenges of increasing costs and nonresponse rates. Randomized clinical trials are typically considered the gold standard for investigating treatment effects in medical research, but their findings are often not easily transportable to the target population. Meanwhile, electronic health records and large administrative databases can supplement rich information to survey or clinical trial data, but their quality needs careful assessment since they are not collected for specific research purposes.

Recent years have witnessed a rise in the popularity of information integration without sharing of raw data. By leveraging and incorporating summary information from external sources, internal studies can achieve enhanced estimation efficiency and prediction accuracy. However, a noteworthy challenge in utilizing summary-level information is accommodating the inherent heterogeneity across diverse data sources. In this study, we delve into the issue of prior probability shift between two cohorts, wherein the difference of two data distributions depends on the outcome. We introduce a novel semi-parametric constrained optimization-based approach to integrate information within this framework, which has not been extensively explored in existing literature. Our proposed method tackles the prior probability shift by introducing the outcome-dependent selection function and effectively addresses the estimation uncertainty associated with summary information from the external source. Our approach facilitates valid inference even in the absence of a known variance-covariance estimate from the external source. Through extensive simulation studies, we observe the superiority of our method over existing ones, showcasing minimal estimation bias and reduced variance for both binary and continuous outcomes. We further demonstrate the utility of our method through its application in investigating risk factors related to essential hypertension, where the reduced estimation variability is observed after integrating summary information from an external data.

We consider the setting where (1) an internal study builds a linear regression model for prediction based on individual-level data, (2) some external studies have fitted similar linear regression models that use only subsets of the covariates and provide coefficient estimates for the reduced models without individual-level data, and (3) there is heterogeneity across these study populations. The goal is to integrate the external model summary information into fitting the internal model to improve prediction accuracy. We adapt the James–Stein shrinkage method to propose estimators that are no worse and are oftentimes better in the prediction mean squared error after information integration, regardless of the degree of study population heterogeneity. We conduct comprehensive simulation studies to investigate the numerical performance of the proposed estimators. We also apply the method to enhance a prediction model for patella bone lead level in terms of blood lead level and other covariates by integrating summary information from published literature.

We aim to estimate parameters in a generalized linear model (GLM) for a binary outcome when, in addition to the raw data from the internal study, more than 1 external study provides summary information in the form of parameter estimates from fitting GLMs with varying subsets of the internal study covariates. We propose an adaptive penalization method that exploits the external summary information and gains efficiency for estimation, and that is both robust and computationally efficient. The robust property comes from exploiting the relationship between parameters of a GLM and parameters of a GLM with omitted covariates and from downweighting external summary information that is less compatible with the internal data through a penalization. The computational burden associated with searching for the optimal tuning parameter for the penalization is reduced by using adaptive weights and by using an information criterion when searching for the optimal tuning parameter. Simulation studies show that the proposed estimator is robust against various types of population distribution heterogeneity and also gains efficiency compared to direct maximum likelihood estimation. The method is applied to improve a logistic regression model that predicts high-grade prostate cancer making use of parameter estimates from 2 external models.

Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive because it can handle zero Phase 2 selection probabilities and avoids modeling the covariate distribution. However, most existing CML-based methods use only the Phase 2 sample and thus may be less efficient than other methods. We propose a general empirical likelihood method that uses CML augmented with additional information in the whole Phase 1 sample to improve estimation efficiency. The proposed method maintains the ability to handle zero selection probabilities and avoids modeling the covariate distribution, but can lead to substantial efficiency gains over CML in the inexpensive covariates, or in the influential covariate when a surrogate is available, because of an effective use of the Phase 1 data. Simulations and a real data illustration using NHANES data are presented.

We congratulate Qin, Liu and Li (QLL) on a thoughtful and much needed review of many interesting methods for combining information from similar studies. We appreciate being given the opportunity to...

Summary: We provide a critical review on calibration methods developed in three different areas: survey sampling, missing data analysis and causal inference. We highlight the connections and variations of calibration techniques used in missing data analysis and causal inference to conventional calibration weighting and estimation in survey sampling and provide a common framework through model‐calibration and empirical likelihood to unify different calibration methods proposed in recent literature. The goal is to demonstrate the success and effectiveness of calibration methods in achieving some highly desired properties for missing data analysis and causal inference.

Consider the setting where (i) individual‐level data are collected to build a regression model for the association between an event of interest and certain covariates, and (ii) some risk calculators predicting the risk of the event using less detailed covariates are available, possibly as algorithmic black boxes with little information available about how they were built. We propose a general empirical‐likelihood‐based framework to integrate the rich auxiliary information contained in the calculators into fitting the regression model, to make the estimation of regression parameters more efficient. Two methods are developed: one using working models to extract the calculator information and the other making a direct use of calculator predictions without working models. Theoretical and numerical investigations show that the calculator information can substantially reduce the variance of regression parameter estimation. As an application, we study the dependence of the risk of high‐grade prostate cancer on both conventional risk factors and newly identified molecular biomarkers by integrating information from the Prostate Biopsy Collaborative Group (PBCG) risk calculator, which was built based on conventional risk factors alone.

It is common to have access to summary information from external studies. Such information can be useful for an internal study of interest to improve parameter estimation efficiency when incorporated. However, external studies may target populations different from the internal study, in which case an incorporation of the corresponding information may introduce estimation bias. We develop a penalized constrained maximum likelihood (PCML) method that simultaneously (i) selects the external studies whose information is useful for internal model fitting and (ii) incorporates the corresponding information into internal estimation. The PCML estimator has the same efficiency as an oracle estimator that fully incorporates the useful external information alone. We establish estimation consistency, parametric rate of convergence, external information selection consistency, asymptotic normality, and oracle efficiency. An algorithm for implementation is provided, together with a data-adaptive tuning parameter selection. Supplemental materials are available online containing some details referred to throughout the article.