arXiv subjects

Jelle J. Goeman

Publications and source records attributed to Jelle J. Goeman.

At least 19 recordsLinked to original sources

arXiv2026

eTFCE: Exact Threshold-Free Cluster Enhancement via Fast Cluster Retrieval

Threshold-free cluster enhancement (TFCE) is widely used for cluster-based inference in neuroimaging, but existing implementations typically rely on discretized approximations that may introduce numerical variability. We present eTFCE, an efficient framework that provides a numerically exact evaluation of the TFCE integral using an optimized cluster retrieval algorithm. Across multiple datasets, eTFCE and the standard implementation produce highly consistent inference results. Voxel-wise comparisons reveal a systematic asymmetry: the standard method yields smaller p-values for more voxels, while eTFCE concentrates stronger statistical evidence within a smaller subset. These differences are primarily confined to voxels near the inference boundary and have minimal impact on overall inference. This pattern is consistent with discretization effects in standard implementations, where the TFCE integral is approximated using a finite set of threshold levels, introducing subtle biases in statistical evidence accumulation across thresholds. Furthermore, eTFCE improves computational efficiency (71.3% of runtime on average) and enables unified computation of multiple cluster-based statistics within a single permutation framework. Overall, eTFCE provides an exact, efficient, and extensible approach to nonparametric neuroimaging inference.

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arXiv2025

Carefree multiple testing with e-processes

E-processes enable hypothesis testing with ongoing data collection while maintaining Type I error control. However, when testing multiple hypotheses simultaneously, current $e$-value based multiple testing methods such as e-BH are not invariant to the order in which data are gathered for the different $e$-processes. This can lead to undesirable situations, e.g., where a hypothesis rejected at time $t$ is no longer rejected at time $t+1$ after choosing to gather more data for one or more $e$-processes unrelated to that hypothesis. We argue that multiple testing methods should always work with suprema of $e$-processes. We provide an example to illustrate that e-BH does not control the FDR, at level $α$ when applied to suprema of $e$-processes. From the same example we see that the FWER is not controlled with averaging, and also closed e-BH does not control the FDR. We show that adjusters can be used to ensure FDR-sup control with e-BH under arbitrary dependence.

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arXiv2025

Bad estimation, good prediction: the Lasso in dense regimes

For high-dimensional omics data, sparsity-inducing regularization methods such as the Lasso are widely used and often yield strong predictive performance, even in settings when the assumption of sparsity is likely violated. We demonstrate that under a specific dense model, namely the high-dimensional joint latent variable model, the Lasso produces sparse prediction rules with favorable prediction error bounds, even when the underlying regression coefficient vector is not sparse at all. We further argue that this model better represents many types of omics data than sparse linear regression models. We prove that the prediction bound under this model in fact decreases with increasing number of predictors, and confirm this through simulation examples. These results highlight the need for caution when interpreting sparse prediction rules, as strong prediction accuracy of a sparse prediction rule may not imply underlying biological significance of the individual predictors.

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arXiv2025

A generalized distance covariance framework for genome-wide association studies

When testing for the association of a single SNP with a phenotypic response, one usually considers an additive genetic model, assuming that the mean of of the response for the heterozygous state is the average of the means for the two homozygous states. However, this simplification often does not hold. In this paper, we present a novel framework for testing the association of a single SNP and a phenotype. Different from the predominant standard approach, our methodology is guaranteed to detect all dependencies expressed by classical genetic association models. The asymptotic distribution under mild regularity assumptions is derived. Moreover, the finite sample distribution under Gaussianity is provided in which the exact p-value can be efficiently evaluated via the classical Appell hypergeometric series. Both results are extended to a regression-type setting with nuisance covariates, enabling hypotheses testing in a wide range of scenarios. A connection of our approach to score tests is explored, leading to intuitive interpretations as locally most powerful tests. A simulation study demonstrates the computational efficiency and excellent statistical performance of the proposed methodology. A real data example is provided.

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arXiv2024

Variable selection via fused sparse-group lasso penalized multi-state models incorporating molecular data

In multi-state models based on high-dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint variable selection. A useful technique to reduce model complexity is to address homogeneous covariate effects for distinct transitions. We integrate this approach to data-driven variable selection by extended regularization methods within multi-state model building. We propose the fused sparse-group lasso (FSGL) penalized Cox-type regression in the framework of multi-state models combining the penalization concepts of pairwise differences of covariate effects along with transition grouping. For optimization, we adapt the alternating direction method of multipliers (ADMM) algorithm to transition-specific hazards regression in the multi-state setting. In a simulation study and application to acute myeloid leukemia (AML) data, we evaluate the algorithm's ability to select a sparse model incorporating relevant transition-specific effects and similar cross-transition effects. We investigate settings in which the combined penalty is beneficial compared to global lasso regularization.

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arXiv2024

OCEAN: Flexible Feature Set Aggregation for Analysis of Multi-omics Data

Integrated analysis of multi-omics datasets holds great promise for uncovering complex biological processes. However, the large dimension of omics data poses significant interpretability and multiple testing challenges. Simultaneous Enrichment Analysis (SEA) was introduced to address these issues in single-omics analysis, providing an in-built multiple testing correction and enabling simultaneous feature set testing. In this paper, we introduce OCEAN, an extension of SEA to multi-omics data. OCEAN is a flexible approach to analyze potentially all possible two-way feature sets from any pair of genomics datasets. We also propose two new error rates which are in line with the two-way structure of the data and facilitate interpretation of the results. The power and utility of OCEAN is demonstrated by analyzing copy number and gene expression data for breast and colon cancer.

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arXiv2024

Permutation-based multiple testing when fitting many generalized linear models

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by combining a recently developed sign-flip test with permutation-based multiple-testing procedures. Our method builds upon the univariate standardized flip-scores test which offers robustness against misspecified variances in generalized linear models, a crucial feature in high-dimensional settings where comprehensive model validation is particularly challenging. We extend this approach to the multivariate setting, enabling adaptation to unknown response correlation structures. This approach yields relevant power improvements over conventional multiple testing methods when correlation is present.

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arXiv2024

Inference in generalized linear models with robustness to misspecified variances

Generalized linear models usually assume a common dispersion parameter, an assumption that is seldom true in practice. Consequently, standard parametric methods may suffer appreciable loss of type I error control. As an alternative, we present a semi-parametric group-invariance method based on sign flipping of score contributions. Our method requires only the correct specification of the mean model, but is robust against any misspecification of the variance. We present tests for single as well as multiple regression coefficients. The test is asymptotically valid but shows excellent performance in small samples. We illustrate the method using RNA sequencing count data, for which it is difficult to model the overdispersion correctly. The method is available in the R library flipscores.

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arXiv2024

Simultaneous false discovery proportion bounds via knockoffs and closed testing

We propose new methods to obtain simultaneous false discovery proportion bounds for knockoff-based approaches. We first investigate an approach based on Janson and Su's $k$-familywise error rate control method and interpolation. We then generalize it by considering a collection of $k$ values, and show that the bound of Katsevich and Ramdas is a special case of this method and can be uniformly improved. Next, we further generalize the method by using closed testing with a multi-weighted-sum local test statistic. This allows us to obtain a further uniform improvement and other generalizations over previous methods. We also develop an efficient shortcut for its implementation. We compare the performance of our proposed methods in simulations and apply them to a data set from the UK Biobank.

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arXiv2023

Adaptive Cluster Thresholding with Spatial Activation Guarantees Using All-resolutions Inference

Classical cluster inference is hampered by the spatial specificity paradox. Given the null-hypothesis of no active voxels, the alternative hypothesis states that there is at least one active voxel in a cluster. Hence, the larger the cluster the less we know about where activation in the cluster is. Rosenblatt et al. (2018) proposed a post-hoc inference method, All-resolutions Inference (ARI), that addresses this paradox by estimating the number of active voxels of any brain region. ARI allows users to choose arbitrary brain regions and returns a simultaneous lower confidence bound of the true discovery proportion (TDP) for each of them, retaining control of the family-wise error rate. ARI does not, however, guide users to regions with high enough TDP. In this paper, we propose an efficient algorithm that outputs all maximal supra-threshold clusters, for which ARI gives a TDP lower confidence bound that is at least a chosen threshold, for any number of thresholds that need not be chosen a priori nor all at once. After a preprocessing step in linearithmic time, the algorithm only takes linear time in the size of its output. We demonstrate the algorithm with an application to two fMRI datasets. For both datasets, we found several clusters whose TDP confidently meets or exceeds a given threshold in less than a second.

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arXiv2023

Permutation-Based True Discovery Guarantee by Sum Tests

Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the alpha-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity ensures control of the TDP even when the subset of interest is selected post hoc. It adapts to the unknown joint distribution of the data through permutation testing. Any sum test may be employed, depending on the desired power properties. We present an iterative shortcut for the closed testing procedure, based on the branch and bound algorithm, which converges to the full closed testing results, often after few iterations; even if it is stopped early, it controls the TDP. We compare the properties of different choices for the sum test through simulations, then we illustrate the feasibility of the method for high dimensional data on brain imaging and genomics data.

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arXiv2022

Cluster extent inference revisited: quantification and localization of brain activity

Cluster inference based on spatial extent thresholding is the most popular analysis method for finding activated brain areas in neuroimaging. However, the method has several well-known issues. While powerful for finding brain regions with some activation, the method as currently defined does not allow any further quantification or localization of signal. In this paper we repair this gap. We show that cluster-extent inference can be used (1.) to infer the presence of signal in anatomical regions of interest and (2.) to quantify the percentage of active voxels in any cluster or region of interest. These additional inferences come for free, i.e. they do not require any further adjustment of the alpha-level of tests, while retaining full familywise error control. We achieve this extension of the possibilities of cluster inference by an embedding of the method into a closed testing procedure, and solving the graph-theoretic k-separator problem that results from this embedding. The new method can be used in combination with random field theory or permutations. We demonstrate the usefulness of the method in a large-scale application to neuroimaging data from the Neurovault database.

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arXiv2022

Resampling-Based Multisplit Inference for High-Dimensional Regression

We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make confidence statements on relevant predictor variables. The method constructs permutation test statistics for any individual hypothesis by means of repeated splits of the data and a variable selection technique; then it defines a test for any subset by suitably aggregating its variables' test statistics. The resulting procedure is extremely flexible, as it allows different selection techniques and several combining functions. We present it in two ways: an exact method and an approximate one, that requires less memory usage and shorter computation time, and can be scaled up to higher dimensions. We illustrate the performance of the method with simulations and the analysis of real gene expression data.

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arXiv2020

Another look at the Lady Tasting Tea and differences between permutation tests and randomization tests

The statistical literature is known to be inconsistent in the use of the terms "permutation test" and "randomization test". Several authors succesfully argue that these terms should be used to refer to two distinct classes of tests and that there are major conceptual differences between these classes. The present paper explains an important difference in mathematical reasoning between these classes: a permutation test fundamentally requires that the set of permutations has a group structure, in the algebraic sense; the reasoning behind a randomization test is not based on such a group structure and it is possible to use an experimental design that does not correspond to a group. In particular, we can use a randomization scheme where the number of possible treatment patterns is larger than in standard experimental designs. This leads to exact \emph{p}-values of improved resolution, providing increased power for very small significance levels, at the cost of decreased power for larger significance levels. We discuss applications in randomized trials and elsewhere. Further, we explain that Fisher's famous Lady Tasting Tea experiment, which is commonly referred to as the first permutation test, is in fact a randomization test. This distinction is important to avoid confusion and invalid tests.

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arXiv2018

Simultaneous Confidence Intervals for Ranks With Application to Ranking Institutions

When a ranking of institutions such as medical centers or universities is based on an indicator provided with a standard error, confidence intervals should be calculated to assess the quality of these ranks. We consider the problem of constructing simultaneous confidence intervals for the ranks of means based on an observed sample. For this aim, the only available method from the literature uses Monte-Carlo simulations and is highly anticonservative especially when the means are close to each other or have ties. We present a novel method based on Tukey's honest significant difference test (HSD). Our new method is on the contrary conservative when there are no ties. By properly rescaling these two methods to the nominal confidence level, they surprisingly perform very similarly. The Monte-Carlo method is however unscalable when the number of institutions is large than 30 to 50 and stays thus anticonservative. We provide extensive simulations to support our claims and the two methods are compared in terms of their simultaneous coverage and their efficiency. We provide a data analysis for 64 hospitals in the Netherlands and compare both methods. Software for our new methods is available online in package ICRanks downloadable from CRAN. Supplementary materials include supplementary R code for the simulations and proofs of the propositions presented in this paper.

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arXiv2018

An improvement of Tukey's HSD with application to ranking institutions

When a ranking of institutions such as medical centers or universities is based on an indicator provided with a standard error, confidence intervals should be calculated to assess the quality of these ranks. We consider the problem of constructing simultaneous confidence intervals (CIs) for the ranks of centers based on an observed sample. We present a novel method based on Tukey's honest significant difference test (HSD) which is the first method to produce valid simultaneous CIs for ranks. Moreover, we introduce a new variant of Tukey's HSD based on the sequential rejection principle. The new algorithm ensures familywise error control, and produces simultaneous confidence intervals for the ranks uniformly shorter than those provided by Tukey's HSD for the same level of significance. We illustrate the method through both simulations and real data analysis from 64 hospitals in the Netherlands. Software for our new methods is available online in package \texttt{ICRanks} downloadable from CRAN. Supplementary materials include supplementary R code for the simulations and proofs of the propositions presented in this paper.

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arXiv2018

Permutation-based simultaneous confidence bounds for the false discovery proportion

When multiple hypotheses are tested, interest is often in ensuring that the proportion of false discoveries (FDP) is small with high confidence. In this paper, confidence upper bounds for the FDP are constructed, which are simultaneous over all rejection cut-offs. In particular this allows the user to select a set of hypotheses post hoc such that the FDP lies below some constant with high confidence. Our method uses permutations to account for the dependence structure in the data. So far only Meinshausen provided an exact, permutation-based and computationally feasible method for simultaneous FDP bounds. We provide an exact method, which uniformly improves this procedure. Further, we provide a generalization of this method. It lets the user select the shape of the simultaneous confidence bounds. This gives the user more freedom in determining the power properties of the method. Interestingly, several existing permutation methods, such as Significance Analysis of Microarrays (SAM) and Westfall and Young's maxT method, are obtained as special cases.

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arXiv2018

Adaptive Critical Value for Constrained Likelihood Ratio Testing

We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the quantile of one and only one chi-squared random variable with a data-dependent degrees of freedom instead of a mixture of chi-squares. Our new test is proved to have a valid finite-sample significance level $α$ and provides more power especially for sparse alternatives (those with a few or moderate number of null constraints violations) in comparison to the classical approach. Our method is also easier to use than the classical approach which requires to calculate or simulate a set of complicated weights. Two special cases are considered with more details, namely the case of testing orthants $μ_1<0, \cdots, μ_n<0$ and the isotonic case of testing $μ_1<μ_2<μ_3$ against all alternatives. Contours of the difference in power are shown for these examples showing the interest of our new approach.

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