Synthesizing external aggregated information in the penalized Cox regression under population heterogeneity

Semiparametric estimation of the transformation model by leveraging external aggregate data in the presence of population heterogeneity

Leveraging information in aggregate data from external sources to improve estimation efficiency and prediction accuracy with smaller scale studies has drawn a great deal of attention in recent years. Yet, conventional methods often either ignore uncertainty in the external information or fail to account for the heterogeneity between internal and external studies. This article proposes an empirical likelihood-based framework to improve the estimation of the semiparametric transformation models by incorporating information about the t-year subgroup survival probability from external sources. The proposed estimation procedure incorporates an additional likelihood component to account for uncertainty in the external information and employs a density ratio model to characterize population heterogeneity. We establish the consistency and asymptotic normality of the proposed estimator and show that it is more efficient than the conventional pseudopartial likelihood estimator without combining information. Simulation studies show that the proposed estimator yields little bias and outperforms the conventional approach even in the presence of information uncertainty and heterogeneity. The proposed methodologies are illustrated with an analysis of a pancreatic cancer study.

Integrative analysis of individual-level data and high-dimensional summary statistics

MOTIVATION

Researchers usually conduct statistical analyses based on models built on raw data collected from individual participants (individual-level data). There is a growing interest in enhancing inference efficiency by incorporating aggregated summary information from other sources, such as summary statistics on genetic markers' marginal associations with a given trait generated from genome-wide association studies. However, combining high-dimensional summary data with individual-level data using existing integrative procedures can be challenging due to various numeric issues in optimizing an objective function over a large number of unknown parameters.

RESULTS

We develop a procedure to improve the fitting of a targeted statistical model by leveraging external summary data for more efficient statistical inference (both effect estimation and hypothesis testing). To make this procedure scalable to high-dimensional summary data, we propose a divide-and-conquer strategy by breaking the task into easier parallel jobs, each fitting the targeted model by integrating the individual-level data with a small proportion of summary data. We obtain the final estimates of model parameters by pooling results from multiple fitted models through the minimum distance estimation procedure. We improve the procedure for a general class of additive models commonly encountered in genetic studies. We further expand these two approaches to integrate individual-level and high-dimensional summary data from different study populations. We demonstrate the advantage of the proposed methods through simulations and an application to the study of the effect on pancreatic cancer risk by the polygenic risk score defined by BMI-associated genetic markers.

AVAILABILITY AND IMPLEMENTATION

R package is available at https://github.com/fushengstat/MetaGIM.