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Nonlinear kernel-based high-dimensional inference for set-based genetic association studies.

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  1. [1] § Results › Results from real data analyses ↔ lasso_model_omnibus.R, lines 1–24 · score 0.52 · de sparsified LASSO, MinP, omnibus, ART

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The authors' code

R · 246 lines · 6.5 KB · MIT · 1 match

  1. ## lasso_model_omnibus.R
  2. ##
  3. ## For a given design matrix X_design and response Y, this function:
  4. ## 1) runs de-sparsified lasso (lasso.proj),
  5. ## 2) computes group-wise MinP (Westfall–Young) and iART-A statistics,
  6. ## 3) combines them via ACATO to obtain omnibus p-values for Group 1 and Group 2.
  7. ##
  8. ## Additional safeguards:
  9. ## - If ncol(X_design) < 3, it skips lasso.proj() to avoid glmnet errors
  10. ## (glmnet requires at least 2 predictors in nodewise regressions).
  11. ## - Parallel settings are automatically adjusted depending on the OS
  12. ## (Windows is forced to run serially).
  13. get_repo_root <- function() {
  14. # 1) If using RStudio project, assume working dir is project root
  15. if (file.exists("hdi_lasso")) return(".")
  16. # 2) Otherwise, try location of this file (when sourced)
  17. this_file <- tryCatch(normalizePath(sys.frames()[[1]]$ofile), error = function(e) NA)
  18. if (!is.na(this_file)) {
  19. cand <- dirname(this_file)
  20. if (file.exists(file.path(cand, "hdi_lasso"))) return(cand)
  21. }
  22. # 3) fallback: current dir
  23. return(".")
  24. }
  26. repo_root <- get_repo_root()
  27. hdi_dir <- file.path(repo_root, "hdi_lasso")
  29. hdi_files <- c(
  30. "ART.A.R",
  31. "lasso.proj.R",
  32. "prepare.data.R",
  33. "calculate.Z.R",
  34. "score.nodewiselasso.R",
  35. "nodewise.getlambdasequence.R",
  36. "cv.nodewise.bestlambda.R",
  37. "cv.nodewise.err.unitfunction.R",
  38. "cv.nodewise.totalerr.R",
  39. "score.getZforlambda.R",
  40. "score.getZforlambda.unitfunction.R",
  41. "score.rescale.R",
  42. "initial.estimator.R",
  43. "do.initial.fit.R",
  44. "despars.lasso.est.R",
  45. "est.stderr.despars.lasso.R",
  46. "preprocess.group.testing.R",
  47. "get.clusterGroupTest.function.R",
  48. "sandwich.var.est.stderr.R",
  49. "improve.lambda.pick.R",
  50. "calcM.R",
  51. "calcMforcolumn.R",
  52. "p.adjust.wy.R",
  53. "ridge.proj.R"
  54. )
  56. for (f in hdi_files) {
  57. fp <- file.path(hdi_dir, f)
  58. if (!file.exists(fp)) stop("Missing HDI-Lasso file: ", fp)
  59. source(fp)
  60. }
  63. lasso_model_omnibus <- function(
  64. X_design,
  65. Y,
  66. n_pc_g1,
  67. use_parallel = TRUE, # allow parallelization on non-Windows systems
  68. ncores = getOption("mc.cores", 2L)
  69. ) {
  70. p_one <- 1.0
  72. ## Case 1: empty design matrix
  73. if (is.null(X_design) || ncol(X_design) == 0L) {
  74. return(list(
  75. fit = NULL,
  76. PG1 = p_one,
  77. PG2 = p_one,
  78. P_ART1 = p_one,
  79. P_ART2 = p_one,
  80. Omnibus1 = p_one,
  81. Omnibus2 = p_one
  82. ))
  83. }
  85. ## Case 2: too few columns (< 3), safeguard against glmnet errors
  86. if (ncol(X_design) < 3L) {
  87. warning("X_design has less than 3 columns; skipping lasso.proj and returning p=1.")
  88. return(list(
  89. fit = NULL,
  90. PG1 = p_one,
  91. PG2 = p_one,
  92. P_ART1 = p_one,
  93. P_ART2 = p_one,
  94. Omnibus1 = p_one,
  95. Omnibus2 = p_one
  96. ))
  97. }
  99. ## Adjust parallel settings based on OS and available cores
  100. os_type <- .Platform$OS.type
  102. if (!use_parallel || os_type == "windows") {
  103. # On Windows or when parallelization is disabled, force serial execution
  104. use_parallel <- FALSE
  105. ncores <- 1L
  106. } else {
  107. # On non-Windows systems (Linux/macOS), check the actual number of cores
  108. if (!requireNamespace("parallel", quietly = TRUE)) {
  109. use_parallel <- FALSE
  110. ncores <- 1L
  111. } else {
  112. max_cores <- parallel::detectCores(logical = TRUE)
  113. if (is.na(max_cores) || max_cores < 2L) {
  114. use_parallel <- FALSE
  115. ncores <- 1L
  116. } else {
  117. ncores <- min(as.integer(ncores), max_cores)
  118. if (ncores <= 1L) {
  119. use_parallel <- FALSE
  120. ncores <- 1L
  121. }
  122. }
  123. }
  124. }
  126. ## Run de-sparsified lasso
  127. X_design <- scale(X_design)
  129. fit <- lasso.proj(
  130. x = as.matrix(X_design),
  131. y = Y,
  132. multiplecorr.method = "WY",
  133. parallel = use_parallel,
  134. ncores = ncores,
  135. robust = TRUE
  136. )
  138. pvals <- fit$pval
  139. cov <- fit$beta.cov
  140. L_tot <- length(pvals)
  142. if (L_tot == 0L) {
  143. return(list(
  144. fit = fit,
  145. PG1 = p_one,
  146. PG2 = p_one,
  147. P_ART1 = p_one,
  148. P_ART2 = p_one,
  149. Omnibus1 = p_one,
  150. Omnibus2 = p_one
  151. ))
  152. }
  154. ## Split into Group 1 and Group 2
  155. L1 <- as.integer(n_pc_g1)
  156. if (is.na(L1) || L1 < 0L) {
  157. L1 <- 0L
  158. }
  159. if (L1 > L_tot) {
  160. L1 <- L_tot
  161. }
  162. L2 <- L_tot - L1
  164. ## ===================== MinP (Westfall–Young) =====================
  165. ## group 1
  166. if (L1 == 0L) {
  167. PG1 <- p_one
  168. } else {
  169. idx1 <- seq_len(L1)
  170. cov1 <- cov[idx1, idx1, drop = FALSE]
  171. PG1 <- min(p.adjust.wy(cov = cov1, pval = pvals[idx1]))
  172. }
  174. ## group 2
  175. if (L2 == 0L) {
  176. PG2 <- p_one
  177. } else {
  178. if (L1 == 0L) {
  179. idx2 <- seq_len(L_tot)
  180. } else {
  181. idx2 <- seq.int(L1 + 1L, L_tot)
  182. }
  183. cov2 <- cov[idx2, idx2, drop = FALSE]
  184. P2 <- pvals[idx2]
  185. PG2 <- min(p.adjust.wy(cov = cov2, pval = P2))
  186. }
  188. ## ===================== iART-A (within-group) + ACATO =====================
  189. ## group 1
  190. if (L1 == 0L) {
  191. P_ART1 <- p_one
  192. } else if (L1 == 1L) {
  193. P_ART1 <- pvals[1L]
  194. } else {
  195. P1 <- sort(pvals[seq_len(L1)])
  196. k1 <- 2L
  197. k2 <- L1
  198. P_arta_1 <- numeric(length = k2 - k1 + 1L)
  199. for (k in k1:k2) {
  200. P_arta_1[k - k1 + 1L] <- ART.A(P1, k = k, L = L1)[1L]
  201. }
  202. P_ART1 <- ACATO(P_arta_1)
  203. P_ART1 <- ifelse(P_ART1 == 1, 1 - 1 / (L1 - 1L), P_ART1)
  204. }
  206. ## group 2
  207. if (L2 == 0L) {
  208. P_ART2 <- p_one
  209. } else if (L2 == 1L) {
  210. if (L1 == 0L) {
  211. P_ART2 <- pvals[1L]
  212. } else {
  213. P_ART2 <- pvals[L1 + 1L]
  214. }
  215. } else {
  216. if (L1 == 0L) {
  217. idx2 <- seq_len(L_tot)
  218. } else {
  219. idx2 <- seq.int(L1 + 1L, L_tot)
  220. }
  221. P2 <- sort(pvals[idx2])
  222. L2_eff <- length(P2)
  223. k1 <- 2L
  224. k2 <- L2_eff
  225. P_arta_2 <- numeric(length = k2 - k1 + 1L)
  226. for (k in k1:k2) {
  227. P_arta_2[k - k1 + 1L] <- ART.A(P2, k = k, L = L2_eff)[1L]
  228. }
  229. P_ART2 <- ACATO(P_arta_2)
  230. P_ART2 <- ifelse(P_ART2 == 1, 1 - 1 / (L2_eff - 1L), P_ART2)
  231. }
  233. ## ===================== Omnibus = ACATO(MinP, iART-A) =====================
  234. Omnibus1 <- ACATO(c(PG1, P_ART1))
  235. Omnibus2 <- ACATO(c(PG2, P_ART2))
  237. list(
  238. fit = fit,
  239. PG1 = PG1,
  240. PG2 = PG2,
  241. P_ART1 = P_ART1,
  242. P_ART2 = P_ART2,
  243. Omnibus1 = Omnibus1,
  244. Omnibus2 = Omnibus2
  245. )
  246. }

lasso_model_omnibus.R at commit efe6272, under MIT · at the source

Overview

Authors: Zechen Zhang1,2,3, Hui Yang1,2,3, Meilin Zhu1, Ran Guo1, Fuzhao Chen1, Hui Dong4, Yuehua Cui5, Haitao Yang1,2,3
ORCID iDs: Yuehua Cui, Haitao Yang
  1. Division of Health Statistics, School of Public Health, Hebei Medical University, 361 East Zhongshan Road, Shijiazhuang, Hebei 050017, P.R. China
  2. Hebei Key Laboratory of Environment and Human Health, School of Public Health, Hebei Medical University, 361 East Zhongshan Road, Shijiazhuang, Hebei 050017, P.R. China
  3. Hebei Key Laboratory of Forensic Medicine, School of Forensic Medicine, Hebei Medical University, 361 East Zhongshan Road, Shijiazhuang, Hebei 050017, P.R. China
  4. Department of Neurology, Second Hospital of Hebei Medical University, 215 West Heping Road, Shijiazhuang, Hebei 050000, P.R. China
  5. Department of Statistics and Probability, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, United States
Institutions: Hebei Medical University (China); Second Hospital of Hebei Medical University (China); Michigan State University (United States)
Journal: Briefings in bioinformatics, volume 27, issue 3, article bbag275
Dates: received 13 January 2026; accepted 4 May 2026; published online 27 May 2026; in print May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1093/bib/bbag275 · PMID 42202283 · PMCID PMC13215594 · OpenAlex W7162493287
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: genetics / omics (modality), human (organism), Alzheimer's / dementia (population), methods / tools (subfield)
Keywords: kernel method, nonlinear high-dimensional inference, P-value combination, omnibus test, SNP–set association
MeSH: Alzheimer Disease*, Genetic Association Studies*, Genome-Wide Association Study*, Models, Genetic*, Algorithms, Computer Simulation, Humans, Nonlinear Dynamics, Polymorphism, Single Nucleotide, Principal Component Analysis (* major topic)
Topic: Genetic Associations and Epidemiology (Genetics, Biochemistry, Genetics and Molecular Biology), according to OpenAlex
Funding: Medical Science Research Projects of Hebei (20200856, 20260608); the Science and Technology Program of Hebei Province (246W7703D, 252W7713D); National Natural Science Foundation of China (81872717); Hebei Key Laboratory of Forensic Medicine (JYFY 23ZR013); Education Department of Hebei Province (ZD2018022); Natural Science Foundation of Hebei Province (H2019206558)
Citations: not cited yet (Europe PMC); 63 references in the paper

Abstract

Nonlinear genetic architectures, including epistasis and threshold effects, are increasingly recognized as contributors to complex disease risk, yet most existing SNP-set association tests rely on linear modeling assumptions, resulting in reduced power and unstable inference when genetic effects are nonlinear or heterogeneously distributed across variants. To address this limitation, we propose a nonlinear high-dimensional inference framework for set-based genetic association analysis that integrates scalable kernel representations with valid statistical inference. The framework combines distance correlation-based sure independence screening to reduce ultra-high dimensional predictors, kernel principal component analysis with Nyström approximation for nonlinear feature extraction, and de-sparsified LASSO to enable asymptotically valid hypothesis testing in high dimensions, together with a two-stage omnibus testing strategy that adaptively aggregates evidence across complementary signal models. Extensive simulation studies demonstrate that the proposed method maintains well-calibrated Type I error and consistently achieves higher power than established set-based approaches, including Sequence Kernel Association Test and adaptive Sum of Powered Score test, particularly under nonlinear and heterogeneous genetic effect scenarios, while remaining competitive in linear settings. Application to Alzheimer’s Disease Neuroimaging Initiative data identifies gene-level associations with brain regional volumes that converge on neuronal excitability, calcium signaling, and cytoskeletal regulation, biological processes centrally implicated in neurodegeneration. Together, this work provides a robust and scalable framework for nonlinear set-based inference in genome-wide studies, expanding the analytical toolbox for dissecting complex genetic contributions to disease.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

zhangzechen123/NL-HSIM

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: efe6272c8aae181be0ee1870aaf715c1822c426c, 27 April 2026
Languages: R (38), Shell (1)
Size: 48 files, 39 scripts
Software Heritage: not archived
Found in: “Software availability”
Holds: README, license file, continuous integration
Not found: CITATION.cff, environment file, tests, documentation
Tools: caret (1 file), pheatmap (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
41 files
At the source: github.com/zhangzechen123/NL-HSIM

Software availability

The software implementation of the proposed NL-HSIM(O) method, including all scripts required to reproduce the analyses, is publicly available at https://github.com/zhangzechen123/NL-HSIM.

Reproduced under the paper's license (CC BY), from the paper cited above.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 39 scripts, each with its path and the digest of its content;
  • 1 match between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

The clinical data used in this study were obtained from the ADNI database (https://adni.loni.usc.edu/). Access to ADNI data is available to qualified researchers upon application and approval by the ADNI Data Sharing and Publications Committee. The simulation data analyzed in this study can be generated using the procedures and code provided by the authors.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 8 authors, 5 keywords, 10 MeSH terms, 6 funders, 63 references.

Cite

This paper

Zhang, Z., Yang, H., Zhu, M., Guo, R., Chen, F., Dong, H., Cui, Y., & Yang, H. (2026). Nonlinear kernel-based high-dimensional inference for set-based genetic association studies. Briefings in bioinformatics, 27(3), bbag275. https://doi.org/10.1093/bib/bbag275

BibTeX

@article{zhang2026nonlinear,
author = {Zhang, Zechen and Yang, Hui and Zhu, Meilin and Guo, Ran and Chen, Fuzhao and Dong, Hui and Cui, Yuehua and Yang, Haitao},
title = {{Nonlinear kernel-based high-dimensional inference for set-based genetic association studies}},
journal = {Briefings in bioinformatics},
year = {2026},
month = may,
volume = {27},
number = {3},
pages = {bbag275},
publisher = {Oxford University Press},
issn = {1467-5463},
doi = {10.1093/bib/bbag275},
url = {https://doi.org/10.1093/bib/bbag275},
pmid = {42202283},
pmcid = {PMC13215594}
}

RIS

TY - JOUR
AU - Zhang, Zechen
AU - Yang, Hui
AU - Zhu, Meilin
AU - Guo, Ran
AU - Chen, Fuzhao
AU - Dong, Hui
AU - Cui, Yuehua
AU - Yang, Haitao
TI - Nonlinear kernel-based high-dimensional inference for set-based genetic association studies
T2 - Briefings in bioinformatics
J2 - Brief Bioinform
PY - 2026
DA - 2026/05/01
VL - 27
IS - 3
SP - bbag275
SN - 1467-5463
PB - Oxford University Press
DO - 10.1093/bib/bbag275
UR - https://doi.org/10.1093/bib/bbag275
LA - en
ER -

CSL-JSON

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"type": "article-journal",
"title": "Nonlinear kernel-based high-dimensional inference for set-based genetic association studies",
"container-title": "Briefings in bioinformatics",
"author": [
{
"family": "Zhang",
"given": "Zechen"
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{
"family": "Zhu",
"given": "Meilin"
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"PMCID": "PMC13215594",
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"publisher": "Oxford University Press",
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"issued": {
"date-parts": [
[
2026,
5,
1
]
]
}
}

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