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When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, ? 2-consistency and Neuroscience Applications.

ABSTRACT: Many studies in biomedical and health sciences involve small sample sizes due to logistic or financial constraints. Often, identifying weak (but scientifically interesting) associations between a set of predictors and a response necessitates pooling datasets from multiple diverse labs or groups. While there is a rich literature in statistical machine learning to address distributional shifts and inference in multi-site datasets, it is less clear when such pooling is guaranteed to help (and when it does not) - independent of the inference algorithms we use. In this paper, we present a hypothesis test to answer this question, both for classical and high dimensional linear regression. We precisely identify regimes where pooling datasets across multiple sites is sensible, and how such policy decisions can be made via simple checks executable on each site before any data transfer ever happens. With a focus on Alzheimer's disease studies, we present empirical results showing that in regimes suggested by our analysis, pooling a local dataset with data from an international study improves power.

SUBMITTER: Zhou HH

PROVIDER: S-EPMC6859896 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

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When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, ℓ 2-consistency and Neuroscience Applications.

Zhou Hao Henry HH Zhang Yilin Y Ithapu Vamsi K VK Johnson Sterling C SC Wahba Grace G Singh Vikas V

Proceedings of machine learning research 20170801

Many studies in biomedical and health sciences involve small sample sizes due to logistic or financial constraints. Often, identifying weak (but scientifically interesting) associations between a set of predictors and a response necessitates pooling datasets from multiple diverse labs or groups. While there is a rich literature in statistical machine learning to address distributional shifts and inference in multi-site datasets, it is less clear when such pooling is guaranteed to help (an ...[more]

PMID: 31742253

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Project description:BackgroundFor many practical hypothesis testing (H-T) applications, the data are correlated and/or with heterogeneous variance structure. The regression t-test for weighted linear mixed-effects regression (LMER) is a legitimate choice because it accounts for complex covariance structure; however, high computational costs and occasional convergence issues make it impractical for analyzing high-throughput data. In this paper, we propose computationally efficient parametric and semiparametric tests based on a set of specialized matrix techniques dubbed as the PB-transformation. The PB-transformation has two advantages: 1. The PB-transformed data will have a scalar variance-covariance matrix. 2. The original H-T problem will be reduced to an equivalent one-sample H-T problem. The transformed problem can then be approached by either the one-sample Student's t-test or Wilcoxon signed rank test.ResultsIn simulation studies, the proposed methods outperform commonly used alternative methods under both normal and double exponential distributions. In particular, the PB-transformed t-test produces notably better results than the weighted LMER test, especially in the high correlation case, using only a small fraction of computational cost (3 versus 933 s). We apply these two methods to a set of RNA-seq gene expression data collected in a breast cancer study. Pathway analyses show that the PB-transformed t-test reveals more biologically relevant findings in relation to breast cancer than the weighted LMER test.ConclusionsAs fast and numerically stable replacements for the weighted LMER test, the PB-transformed tests are especially suitable for "messy" high-throughput data that include both independent and matched/repeated samples. By using our method, the practitioners no longer have to choose between using partial data (applying paired tests to only the matched samples) or ignoring the correlation in the data (applying two sample tests to data with some correlated samples). Our method is implemented as an R package 'PBtest' and is available at https://github.com/yunzhang813/PBtest-R-Package .

Project description:BackgroundTime series analysis is critical for understanding brain signals and their relationship to behavior and cognition. Cluster-based permutation tests (CBPT) are commonly used to analyze a variety of electrophysiological signals including EEG, MEG, ECoG, and sEEG data without a priori assumptions about specific temporal effects. However, two major limitations of CBPT include the inability to directly analyze experiments with multiple fixed effects and the inability to account for random effects (e.g. variability across subjects). Here, we propose a flexible multi-step hypothesis testing strategy using CBPT with Linear Mixed Effects Models (LMEs) and Generalized Linear Mixed Effects Models (GLMEs) that can be applied to a wide range of experimental designs and data types.MethodsWe first evaluate the statistical robustness of LMEs and GLMEs using simulated data distributions. Second, we apply a multi-step hypothesis testing strategy to analyze ERPs and broadband power signals extracted from human ECoG recordings collected during a simple image viewing experiment with image category and novelty as fixed effects. Third, we assess the statistical power differences between analyzing signals with CBPT using LMEs compared to CBPT using separate t-tests run on each fixed effect through simulations that emulate broadband power signals. Finally, we apply CBPT using GLMEs to high-gamma burst data to demonstrate the extension of the proposed method to the analysis of nonlinear data.ResultsFirst, we found that LMEs and GLMEs are robust statistical models. In simple simulations LMEs produced highly congruent results with other appropriately applied linear statistical models, but LMEs outperformed many linear statistical models in the analysis of "suboptimal" data and maintained power better than analyzing individual fixed effects with separate t-tests. GLMEs also performed similarly to other nonlinear statistical models. Second, in real world human ECoG data, LMEs performed at least as well as separate t-tests when applied to predefined time windows or when used in conjunction with CBPT. Additionally, fixed effects time courses extracted with CBPT using LMEs from group-level models of pseudo-populations replicated latency effects found in individual category-selective channels. Third, analysis of simulated broadband power signals demonstrated that CBPT using LMEs was superior to CBPT using separate t-tests in identifying time windows with significant fixed effects especially for small effect sizes. Lastly, the analysis of high-gamma burst data using CBPT with GLMEs produced results consistent with CBPT using LMEs applied to broadband power data.ConclusionsWe propose a general approach for statistical analysis of electrophysiological data using CBPT in conjunction with LMEs and GLMEs. We demonstrate that this method is robust for experiments with multiple fixed effects and applicable to the analysis of linear and nonlinear data. Our methodology maximizes the statistical power available in a dataset across multiple experimental variables while accounting for hierarchical random effects and controlling FWER across fixed effects. This approach substantially improves power and accuracy leading to better reproducibility. Additionally, CBPT using LMEs and GLMEs can be used to analyze individual channels or pseudo-population data for the comparison of functional or anatomical groups of data.

Dataset Information

When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, ? 2-consistency and Neuroscience Applications.

Publications

When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, <i>ℓ</i> <sub>2</sub>-consistency and Neuroscience Applications.

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