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Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics.

ABSTRACT: Statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model. In many applications, the researcher assumes a model of the form Y=?+X?+Z?+?, where Y is the observed brain signal, and X and Z contain explanatory variables that are thought to be related to the brain signal. The goal is to test the null hypothesis H0:?=0 with the nuisance parameters ? included in the model. Several nonparametric (permutation) methods have been proposed for this problem, and each method uses some variant of the F ratio as the test statistic. However, recent research suggests that the F ratio can produce invalid permutation tests of H0:?=0 when the ? terms are heteroscedastic (i.e., have non-constant variance), which can occur for a variety of reasons. This study compares the classic F test statistic to the robust W (Wald) test statistic using eight different permutation methods. The results reveal that permutation tests using the F ratio can produce accurate results when the errors are homoscedastic, but high false positive rates when the errors are heteroscedastic. In contrast, permutation tests using the W test statistic produced valid results when the errors were homoscedastic, and asymptotically valid results when the errors were heteroscedastic. In the situation with homoscedastic errors, permutation tests using the W statistic showed slightly reduced power compared to the F statistic, but the difference disappeared as the sample size n increased. Consequently, the W test statistic is recommended for robust nonparametric hypothesis tests of regression coefficients in neuroimaging research.

SUBMITTER: Helwig NE

PROVIDER: S-EPMC6765412 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature

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Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics.

Helwig Nathaniel E NE

NeuroImage 20190719

Statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model. In many applications, the researcher assumes a model of the form Y=α+Xβ+Zγ+ε, where Y is the observed brain signal, and X and Z contain explanatory variables that are thought to be related to the brain signal. The goal is to test the null hypothesis H<sub>0</sub>:β=0 with the nuisance parameters γ included in the model. Several nonparametric (permutation) m ...[more]

PMID: 31330243

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Project description:Association tests that pool minor alleles into a measure of burden at a locus have been proposed for case-control studies using sequence data containing rare variants. However, such pooling tests are not robust to the inclusion of neutral and protective variants, which can mask the association signal from risk variants. Early studies proposing pooling tests dismissed methods for locus-wide inference using nonnegative single-variant test statistics based on unrealistic comparisons. However, such methods are robust to the inclusion of neutral and protective variants and therefore may be more useful than previously appreciated. In fact, some recently proposed methods derived within different frameworks are equivalent to performing inference on weighted sums of squared single-variant score statistics. In this study, we compared two existing methods for locus-wide inference using nonnegative single-variant test statistics to two widely cited pooling tests under more realistic conditions. We established analytic results for a simple model with one rare risk and one rare neutral variant, which demonstrated that pooling tests were less powerful than even Bonferroni-corrected single-variant tests in most realistic situations. We also performed simulations using variants with realistic minor allele frequency and linkage disequilibrium spectra, disease models with multiple rare risk variants and extensive neutral variation, and varying rates of missing genotypes. In all scenarios considered, existing methods using nonnegative single-variant test statistics had power comparable to or greater than two widely cited pooling tests. Moreover, in disease models with only rare risk variants, an existing method based on the maximum single-variant Cochran-Armitage trend chi-square statistic in the locus had power comparable to or greater than another existing method closely related to some recently proposed methods. We conclude that efficient locus-wide inference using single-variant test statistics should be reconsidered as a useful framework for devising powerful association tests in sequence data with rare variants.

Dataset Information

Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics.

Publications

Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics.

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