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Cauchy Combination Test for p-value aggregation

Description

Combines multiple p-values using the Cauchy distribution method, which providesanalytical p-value calculation under arbitrary dependency structures.

Usage

CCT(pvals, weights = NULL)

Arguments

Details

The Cauchy Combination Test (CCT) transforms p-values using the inverse Cauchydistribution and combines them with specified weights. This method is particularlypowerful because it:

• Works under arbitrary dependency structures

• Provides exact analytical p-values (no simulation needed)

• Maintains good power properties across different scenarios

Special Cases:

• If any p-value equals 0, returns 0 immediately

• P-values equal to 1 are adjusted to 0.999 with a warning

• Very small p-values (< 1e-16) receive special numerical treatment

Value

Single aggregated p-value combining all input p-values.

References

Liu, Y., & Xie, J. (2020). Cauchy combination test: a powerful testwith analytic p-value calculation under arbitrary dependency structures.Journal of the American Statistical Association, 115(529), 393-402.doi:10.1080/01621459.2018.1554485

Examples

# Basic usage with equal weightspvalues <- c(0.02, 0.0004, 0.2, 0.1, 0.8)CCT(pvals = pvalues)# Usage with custom weightsweights <- c(2, 3, 1, 1, 1)CCT(pvals = pvalues, weights = weights)

Perform single-marker association tests using a fitted null model

Description

Conducts single-marker association tests between genetic variants and phenotypes usingvarious statistical methods supported by GRAB.

Usage

GRAB.Marker(  objNull,  GenoFile,  OutputFile,  GenoFileIndex = NULL,  OutputFileIndex = NULL,  control = NULL)

Arguments

Value

The function returnsNULL invisibly. Results are written toOutputFile.For method-specific examples and output columns and format, see:

• POLMM method:GRAB.POLMM

• SPACox method:GRAB.SPACox

• SPAmix method:GRAB.SPAmix

• WtCoxG method:GRAB.WtCoxG

• SPAGRM method:GRAB.SPAGRM

• SAGELD method:GRAB.SAGELD

Top-level API for generating a null model object used by GRAB.Marker and GRAB.Region

Description

GRAB performs two-step genetic association testing. This functionimplements the first step: fitting a null model and preparing the dataset required fordownstream marker-level (GRAB.Marker) and region-level (GRAB.Region) analyses.

Usage

GRAB.NullModel(  formula,  data,  subjIDcol = NULL,  subjData = NULL,  method,  traitType,  GenoFile = NULL,  GenoFileIndex = NULL,  SparseGRMFile = NULL,  control = NULL,  ...)

Arguments

Value

An S3 object with class "{method}_NULL_Model". All returned objects contain the following elements:

N

Sample size (integer).

subjData

Character vector of subject IDs included in analysis.

Call

Original function call.

sessionInfo

R session and package information.

time

Analysis completion timestamp (character).

control

List of control parameters used in fitting.

This object serves as input forGRAB.Marker orGRAB.Region.

See method-specific documentation for additional elements included in the returned object.

Instruction of POLMM method

Description

POLMM inplements single-variant association tests for ordinal categorical phenotypes, whichaccounts for sample relatedness. It can control type I error rates at a stringent significancelevel regardless of the phenotypic distribution, and is more powerful than alternative methods.This instruction covers null model fitting and marker-level analysis using POLMM.For region-based analysis with POLMM-GENE, seeGRAB.POLMM.Region.

Usage

GRAB.POLMM()

Details

Genotype file:GenoFile is mandatory forGRAB.NullModel() when using POLMM.It is required for estimating the variance ratio parameter, which is essential for calibratingthe test statistics in subsequent association tests.

Genetic Relationship Matrix (GRM) Options:POLMM supports both sparse and dense GRM for modeling genetic relatedness:

• IfSparseGRMFile is provided toGRAB.NullModel(),the sparse GRM will be used in model fitting.

• IfSparseGRMFile is not provided,GRAB.NullModel()will calculate a dense GRM fromGenoFile.

Additional Control Parameters for GRAB.NullModel():

• memoryChunk (numeric, default: 2): Memory chunk size for computation.

• seed (integer, default: -1): Random seed (-1 means no seed is set).

• tracenrun (integer, default: 30): Number of runs for trace calculation.

• maxiter (integer, default: 100): Maximum number of iterations for model fitting.

• tolBeta (numeric, default: 0.001): Convergence tolerance for beta estimates.

• tolTau (numeric, default: 0.002): Convergence tolerance for tau estimates.

• tau (numeric, default: 0.2): Initial variance component value.

• maxiterPCG (integer, default: 100): Maximum iterations for preconditioned conjugate gradient.

• tolPCG (numeric, default: 1e-6): Tolerance for preconditioned conjugate gradient.

• showInfo (logical, default: FALSE): Whether to print PCG iteration information for debugging.

• maxiterEps (integer, default: 100): Maximum iterations for epsilon estimation.

• tolEps (numeric, default: 1e-10): Tolerance for epsilon estimation.

• minMafVarRatio (numeric, default: 0.1): Minimum MAF for variance ratio estimation.

• maxMissingVarRatio (numeric, default: 0.1): Maximum missing rate for variance ratio estimation.

• nSNPsVarRatio (integer, default: 20): Number of SNPs used for variance ratio estimation.

• CVcutoff (numeric, default: 0.0025): Coefficient of variation cutoff.

• grainSize (integer, default: 1): Grain size for parallel processing.

• minMafGRM (numeric, default: 0.01): Minimum MAF for GRM construction.

• maxMissingGRM (numeric, default: 0.1): Maximum missing rate for GRM construction.

Method-specific elements in thePOLMM_NULL_Model object returned byGRAB.NullModel()::

• M: Number of ordinal categories (integer).

• iter: Number of iterations to convergence (numeric).

• eta: Linear predictor (matrix).

• yVec: Phenotype matrix (matrix).

• Cova: Design matrix of covariates (matrix).

• muMat: Fitted probabilities for each category (matrix).

• YMat: Indicator matrix for ordinal categories (matrix).

• beta: Estimated covariate coefficients (matrix).

• bVec: Random effect estimates (matrix).

• tau: Variance component estimate (numeric).

• eps: Cutpoints for ordinal categories (matrix).

Additional Control Parameters for GRAB.Marker():

• ifOutGroup (logical, default: FALSE): Whether to output group-specific statistics(alternative allele frequency, counts, and sample size for each ordinal category).When TRUE, adds columns AltFreqInGroup., AltCountsInGroup., and nSamplesInGroup.* to the output file.

Marker-level results (OutputFile) columns:

Marker

Marker identifier (rsID or CHR:POS:REF:ALT).

Info

Marker information in format CHR:POS:REF:ALT.

AltFreq

Alternative allele frequency in the overall sample.

AltCounts

Total count of alternative alleles.

MissingRate

Proportion of missing genotypes.

Pvalue

P-value from the score test.

beta

Effect size estimate (log-odds scale).

seBeta

Standard error of beta.

zScore

Z-score from the score test.

AltFreqInGroup.1, AltFreqInGroup.2, ...

(Only ififOutGroup = TRUE)Alternative allele frequency in each ordinal category.

AltCountsInGroup.1, AltCountsInGroup.2, ...

(Only ififOutGroup = TRUE)Alternative allele counts in each ordinal category.

nSamplesInGroup.1, nSamplesInGroup.2, ...

(Only ififOutGroup = TRUE) Sample size in each ordinal category.

References

Bi et al. (2021). Efficient mixed model approach for large-scale genome-wide association studiesof ordinal categorical phenotypes.doi:10.1016/j.ajhg.2021.03.019

Examples

GenoFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")SparseGRMFile <- system.file("extdata", "SparseGRM.txt", package = "GRAB")OutputFile <- file.path(tempdir(), "resultPOLMMmarker.txt")PhenoFile <- system.file("extdata", "simuPHENO.txt", package = "GRAB")PhenoData <- data.table::fread(PhenoFile, header = TRUE)PhenoData$OrdinalPheno <- factor(PhenoData$OrdinalPheno, levels = c(0, 1, 2))# Step 1obj.POLMM <- GRAB.NullModel( OrdinalPheno ~ AGE + GENDER, data = PhenoData, subjIDcol = "IID", method = "POLMM", traitType = "ordinal", GenoFile = GenoFile, SparseGRMFile = SparseGRMFile)# Step 2GRAB.Marker(obj.POLMM, GenoFile, OutputFile,  control = list(ifOutGroup = TRUE))head(data.table::fread(OutputFile))

Instruction of POLMM-GENE method

Description

POLMM-GENE implements region-based association tests for ordinal categorical phenotypes,adjusting for sample relatedness. It is well-suited for analyzing rare variants in large-scale biobank data,and effectively controls type I error rates while maintaining statistical power.

Usage

GRAB.POLMM.Region()

Details

For single-variant tests, seeGRAB.POLMM.

SeeGRAB.POLMM for details on step 1.

Additional Control Parameters for GRAB.Region() with POLMM:

• showInfo (logical, default: FALSE): Whether to print PCG iteration information for debugging.

• tolPCG (numeric, default: 0.001): Tolerance for PCG in region testing.

• maxiterPCG (integer, default: 100): Maximum PCG iterations in region testing.

Results are saved to four files:

1. OutputFile: Region-based test results (SKAT-O, SKAT, Burden p-values).

2. paste0(OutputFile, ".markerInfo"): Marker-level results for rare variants(MAC >=min_mac_region) included in region tests.

3. paste0(OutputFile, ".otherMarkerInfo"): Information for excluded markers(ultra-rare variants or failed QC).

4. paste0(OutputFile, ".infoBurdenNoWeight"): Summary statistics for burdentests without weights.

Region-level results (OutputFile) columns:

Region

Region identifier fromGroupFile.

nMarkers

Number of rare variants with MAF < cutoff and MAC >=min_mac_region.

nMarkersURV

Number of ultra-rare variants with MAC <min_mac_region.

Anno.Type

Annotation type fromGroupFile.

MaxMAF.Cutoff

Maximum MAF cutoff used for variant selection.

pval.SKATO

SKAT-O test p-value.

pval.SKAT

SKAT test p-value.

pval.Burden

Burden test p-value.

Marker-level results (paste0(OutputFile, ".markerInfo")) columns:

Region

Region identifier.

ID

Marker identifier.

Info

Marker information in format CHR:POS:REF:ALT.

Anno

Annotation fromGroupFile.

AltFreq

Alternative allele frequency.

MAC

Minor allele count.

MAF

Minor allele frequency.

MissingRate

Proportion of missing genotypes.

IndicatorVec

Marker status indicator (1 = rare variant included, 3 = ultra-rare variant included).

StatVec

Score test statistic.

altBetaVec

Effect size estimate.

seBetaVec

Standard error of effect size estimate.

pval0Vec

Unadjusted p-value.

pval1Vec

SPA-adjusted p-value.

posRow

Position row index.

Other marker info (paste0(OutputFile, ".otherMarkerInfo")) columns:

ID

Marker identifier.

Annos

Annotation fromGroupFile.

Region

Region identifier.

Info

Marker information in format CHR:POS:REF:ALT.

Anno

Annotation category.

AltFreq

Alternative allele frequency.

MAC

Minor allele count.

MAF

Minor allele frequency.

MissingRate

Proportion of missing genotypes.

IndicatorVec

Status indicator (0 or 2 for excluded markers).

Burden test summary (paste0(OutputFile, ".infoBurdenNoWeight")) columns:

region

Region identifier.

anno

Annotation type.

max_maf

Maximum MAF cutoff.

sum

Sum of genotypes.

Stat

Score test statistic.

beta

Effect size estimate.

se.beta

Standard error of effect size estimate.

pvalue

P-value for burden test.

References

Bi et al. (2023). Scalable mixed model methods for set-based association studies on large-scalecategorical data analysis and its application to exome-sequencing data in UK Biobank.doi:10.1016/j.ajhg.2023.03.010

Examples

GenoFileStep1 <- system.file("extdata", "simuPLINK.bed", package = "GRAB")GenoFileStep2 <- system.file("extdata", "simuPLINK_RV.bed", package = "GRAB")SparseGRMFile <- system.file("extdata", "SparseGRM.txt", package = "GRAB")GroupFile <- system.file("extdata", "simuPLINK_RV.group", package = "GRAB")OutputFile <- file.path(tempdir(), "resultPOLMMregion.txt")PhenoFile <- system.file("extdata", "simuPHENO.txt", package = "GRAB")PhenoData <- data.table::fread(PhenoFile, header = TRUE)PhenoData$OrdinalPheno <- factor(PhenoData$OrdinalPheno, levels = c(0, 1, 2))# Step 1obj.POLMM <- GRAB.NullModel( OrdinalPheno ~ AGE + GENDER, data = PhenoData, subjIDcol = "IID", method = "POLMM", traitType = "ordinal", GenoFile = GenoFileStep1, SparseGRMFile = SparseGRMFile, control = list(tolTau = 0.2, tolBeta = 0.1))# Step 2GRAB.Region(obj.POLMM, GenoFileStep2, OutputFile,  GroupFile = GroupFile,  SparseGRMFile = SparseGRMFile,  MaxMAFVec = "0.01,0.005")head(data.table::fread(OutputFile))head(data.table::fread(paste0(OutputFile, ".markerInfo")))head(data.table::fread(paste0(OutputFile, ".otherMarkerInfo")))head(data.table::fread(paste0(OutputFile, ".infoBurdenNoWeight")))

Read genotype data from multiple file formats

Description

Reads genotype data from PLINK or BGEN format files with flexible filteringand processing options. Supports efficient memory usage and variousimputation methods for missing genotypes.

Usage

GRAB.ReadGeno(  GenoFile,  GenoFileIndex = NULL,  SampleIDs = NULL,  control = NULL,  sparse = FALSE)

Arguments

Details

File Format Support:

PLINK Format: Binary BED/BIM/FAM files. Seehttps://www.cog-genomics.org/plink/2.0/ for specifications.

BGEN Format: Version 1.2 with 8-bit compression. Seehttps://www.well.ox.ac.uk/~gav/bgen_format/spec/v1.2.html for details.Requires BGI index file created with bgenix tool.

Value

List containing:

GenoMat

Genotype matrix (samples × markers) with values 0, 1, 2, or NA.

markerInfo

Data frame with columns CHROM, POS, ID, REF, ALT.

Examples

## Raw genotype dataRawFile <- system.file("extdata", "simuRAW.raw.gz", package = "GRAB")GenoMat <- data.table::fread(RawFile)GenoMat[1:10, 1:10]## PLINK filesPLINKFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")# If include/exclude files are not specified, then control$AllMarker should be TRUEGenoList <- GRAB.ReadGeno(PLINKFile, control = list(AllMarkers = TRUE))GenoMat <- GenoList$GenoMatmarkerInfo <- GenoList$markerInfohead(GenoMat[, 1:6])head(markerInfo)## BGEN files (Note the different REF/ALT order for BGEN and PLINK formats)BGENFile <- system.file("extdata", "simuBGEN.bgen", package = "GRAB")GenoList <- GRAB.ReadGeno(BGENFile, control = list(AllMarkers = TRUE))GenoMat <- GenoList$GenoMatmarkerInfo <- GenoList$markerInfohead(GenoMat[, 1:6])head(markerInfo)## The below is to demonstrate parameters in controlPLINKFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")IDsToIncludeFile <- system.file("extdata", "simuGENO.IDsToInclude", package = "GRAB")RangesToIncludeFile <- system.file("extdata", "RangesToInclude.txt", package = "GRAB")GenoList <- GRAB.ReadGeno(PLINKFile,  control = list(    IDsToIncludeFile = IDsToIncludeFile,    RangesToIncludeFile = RangesToIncludeFile,    AlleleOrder = "ref-first"  ))GenoMat <- GenoList$GenoMathead(GenoMat)markerInfo <- GenoList$markerInfohead(markerInfo)## The below is for PLINK/BGEN files with missing dataPLINKFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")GenoList <- GRAB.ReadGeno(PLINKFile, control = list(AllMarkers = TRUE))head(GenoList$GenoMat)GenoList <- GRAB.ReadGeno(PLINKFile, control = list(AllMarkers = TRUE, imputeMethod = "mean"))head(GenoList$GenoMat)BGENFile <- system.file("extdata", "simuBGEN.bgen", package = "GRAB")GenoList <- GRAB.ReadGeno(BGENFile, control = list(AllMarkers = TRUE))head(GenoList$GenoMat)

Perform region-based association tests

Description

Tests for association between phenotypes and genomic regions containing multiplegenetic variants, primarily low-frequency and rare variants.

Usage

GRAB.Region(  objNull,  GenoFile,  OutputFile,  GenoFileIndex = NULL,  OutputFileIndex = NULL,  GroupFile,  SparseGRMFile = NULL,  MaxMAFVec = "0.01,0.001,0.0005",  annoVec = "lof,lof:missense,lof:missense:synonymous",  control = NULL)

Arguments

Value

The function returnsNULL invisibly. Results are saved to four files:

1. OutputFile: Region-based test results (SKAT-O, SKAT, Burden p-values).

2. paste0(OutputFile, ".markerInfo"): Marker-level results for rare variants(MAC >=min_mac_region) included in region tests.

3. paste0(OutputFile, ".otherMarkerInfo"): Information for excluded markers(ultra-rare variants or failed QC).

4. paste0(OutputFile, ".infoBurdenNoWeight"): Summary statistics for burdentests without weights.

For method-specific examples and output columns and format, see:

• POLMM method:GRAB.POLMM.Region

SAGELD method in GRAB package

Description

SAGELD method is Scalable and Accurate algorithm for Gene-Environmentinteraction analysis using Longitudinal Data for related samples in alarge-scale biobank. SAGELD extended SPA_GRM to supportgene-environment interaction analysis.

Usage

GRAB.SAGELD()

Details

Additional list ofcontrol inSAGELD.NullModel() function.

Additional list ofcontrol inGRAB.Marker() function.

Value

No return value, called for side effects (prints information about the SAGELD method to the console).

Instruction of SPACox method

Description

SPACox is primarily intended for time-to-event traits in unrelated samples from large-scalebiobanks. It uses the empirical cumulant generating function (CGF) to perform SPA-basedsingle-variant association tests, enabling analysis with residuals from any null model.

Usage

GRAB.SPACox()

Details

Additional Control Parameters for GRAB.NullModel():

• range (numeric vector, default: c(-100, 100)):Range for saddlepoint approximation grid. Must be symmetric (range[2] = -range[1]).

• length.out (integer, default: 10000): Number of grid points for saddlepoint approximation.

Method-specific elements in theSPACox_NULL_Model object returned byGRAB.NullModel()::

• mresid: Martingale residuals (numeric or "Residual" class).

• cumul: Cumulative sums for variance estimation (matrix).

• tX: Transpose of design matrix (matrix).

• yVec: Event indicator (numeric or "Residual" class).

• X.invXX: Matrix for variance calculations (matrix).

Additional Control Parameters for GRAB.Marker():

• pVal_covaAdj_Cutoff (numeric, default: 5e-05): P-value cutoff for covariate adjustment.

Output file columns:

Marker

Marker identifier (rsID or CHR:POS:REF:ALT).

Info

Marker information in format CHR:POS:REF:ALT.

AltFreq

Alternative allele frequency in the sample.

AltCounts

Total count of alternative alleles.

MissingRate

Proportion of missing genotypes.

Pvalue

P-value from the score test.

zScore

Z-score from the score test.

References

Bi et al. (2020). Fast and accurate method for genome-wide time-to-event data analysis and itsapplication to UK Biobank.doi:10.1016/j.ajhg.2020.06.003

Examples

PhenoFile <- system.file("extdata", "simuPHENO.txt", package = "GRAB")GenoFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")OutputFile <- file.path(tempdir(), "resultSPACox.txt")PhenoData <- data.table::fread(PhenoFile, header = TRUE)# Step 1 option 1obj.SPACox <- GRAB.NullModel(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER,  data = PhenoData,  subjIDcol = "IID",  method = "SPACox",  traitType = "time-to-event")# Step 1 option 2residuals <- survival::coxph(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER,  data = PhenoData,  x = TRUE)$residualsobj.SPACox <- GRAB.NullModel(  residuals ~ AGE + GENDER,  data = PhenoData,  subjIDcol = "IID",  method = "SPACox",  traitType = "Residual")# Step 2GRAB.Marker(obj.SPACox, GenoFile, OutputFile)head(data.table::fread(OutputFile))

Instruction of SPAGRM method

Description

SPAGRM is a scalable and accurate framework for retrospective association tests.It treats genetic loci as random vectors and uses a precise approximation of theirjoint distribution. This approach enables SPAGRM to handle any type of complex trait,including longitudinal and unbalanced phenotypes. SPAGRM extends SPACox to supportsample relatedness.

Usage

GRAB.SPAGRM()

Details

SeeSPAGRM.NullModel for detailed instructionson preparing a SPAGRM_NULL_Model object required for GRAB.Marker().

Additional Control Parameters for GRAB.Marker():

• zeta (numeric, default: 0): SPA moment approximation parameter.

• tol (numeric, default: 1e-5): Numerical tolerance for SPA convergence.

Marker-level results (OutputFile) columns:

Marker

Marker identifier (rsID or CHR:POS:REF:ALT).

Info

Marker information in format CHR:POS:REF:ALT.

AltFreq

Alternative allele frequency in the sample.

AltCounts

Total count of alternative alleles.

MissingRate

Proportion of missing genotypes.

zScore

Z-score from the score test.

Pvalue

P-value from the score test.

hwepval

Hardy-Weinberg equilibrium p-value.

References

Xu et al. (2025). SPAGRM: effectively controlling for sample relatedness in large-scalegenome-wide association studies of longitudinal traits.doi:10.1038/s41467-025-56669-1

Examples

ResidMatFile <- system.file("extdata", "ResidMat.txt", package = "GRAB")SparseGRMFile <- system.file("extdata", "SparseGRM.txt", package = "GRAB")PairwiseIBDFile <- system.file("extdata", "PairwiseIBD.txt", package = "GRAB")GenoFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")OutputFile <- file.path(tempdir(), "resultSPAGRM.txt")# Step 2a: pre-calculate genotype distributionsobj.SPAGRM <- SPAGRM.NullModel(  ResidMatFile = ResidMatFile,  SparseGRMFile = SparseGRMFile,  PairwiseIBDFile = PairwiseIBDFile,  control = list(ControlOutlier = FALSE))# Step 2b: perform association testsGRAB.Marker(obj.SPAGRM, GenoFile, OutputFile)head(data.table::fread(OutputFile))

Instruction of SPAmix method

Description

SPAmix performs retrospective single-variant association tests using genotypes andresiduals from null models of any complex trait in large-scale biobanks. It extendsSPACox to support complex population structures, such as admixed ancestry andmultiple populations, but does not account for sample relatedness.

Usage

GRAB.SPAmix()

Details

Additional Control Parameters for GRAB.NullModel():

• PC_columns (character, required): Comma-separated column namesof principal components (e.g., "PC1,PC2").

• OutlierRatio (numeric, default: 1.5): IQR multiplier for outlier detection.Outliers are defined as values outside [Q1 - rIQR, Q3 + rIQR].

Method-specific elements in theSPAmix_NULL_Model object returned byGRAB.NullModel()::

• resid: Residuals from mixed model (matrix or "Residual" class).

• yVec: Phenotype vector (numeric or "Residual" class).

• PCs: Principal components for dimension reduction (matrix).

• nPheno: Number of phenotypes analyzed (integer).

• outLierList: List identifying outlier subjects for SPA adjustment.

Additional Control Parameters for GRAB.Marker():

• dosage_option (character, default: "rounding_first"):Dosage handling option. Must be either "rounding_first" or "rounding_last".

Output file columns:

Pheno

Phenotype identifier (for multi-trait analysis).

Marker

Marker identifier (rsID or CHR:POS:REF:ALT).

Info

Marker information in format CHR:POS:REF:ALT.

AltFreq

Alternative allele frequency in the sample.

AltCounts

Total count of alternative alleles.

MissingRate

Proportion of missing genotypes.

Pvalue

P-value from the score test.

zScore

Z-score from the score test.

References

Ma et al. (2025). SPAmix: a scalable, accurate, and universal analysis framework for large‑scalegenetic association studies in admixed populations.doi:10.1186/s13059-025-03827-9

Examples

PhenoFile <- system.file("extdata", "simuPHENO.txt", package = "GRAB")GenoFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")OutputFile <- file.path(tempdir(), "resultSPAmix.txt")PhenoData <- data.table::fread(PhenoFile, header = TRUE)# Step 1 option 1obj.SPAmix <- GRAB.NullModel(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER + PC1 + PC2,  data = PhenoData,  subjIDcol = "IID",  method = "SPAmix",  traitType = "time-to-event",  control = list(PC_columns = "PC1,PC2"))# Step 1 option 2residuals <- survival::coxph(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER + PC1 + PC2,  data = PhenoData)$residualsobj.SPAmix <- GRAB.NullModel(  residuals ~ AGE + GENDER + PC1 + PC2,  data = PhenoData,  subjIDcol = "IID",  method = "SPAmix",  traitType = "Residual",  control = list(PC_columns = "PC1,PC2"))# Step 1 option 2: analyze multiple traits at onceres_cox <- survival::coxph(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER + PC1 + PC2,  data = PhenoData)$residualsres_lm <- lm(QuantPheno ~ AGE + GENDER + PC1 + PC2, data = PhenoData)$residualsobj.SPAmix <- GRAB.NullModel(  res_cox + res_lm ~ AGE + GENDER + PC1 + PC2,  data = PhenoData,  subjIDcol = "IID",  method = "SPAmix",  traitType = "Residual",  control = list(PC_columns = "PC1,PC2"))# Step 2GRAB.Marker(obj.SPAmix, GenoFile, OutputFile)head(data.table::fread(OutputFile))

Simulate genotype data matrix for related and unrelated subjects

Description

Generates genotype data for association studies, supporting both unrelated subjectsand family-based designs with various pedigree structures.

Usage

GRAB.SimuGMat(  nSub,  nFam,  FamMode,  nSNP,  MaxMAF = 0.5,  MinMAF = 0.05,  MAF = NULL)

Arguments

Details

Genotypes are simulated under Hardy-Weinberg equilibrium with MAF ~ Uniform(MinMAF, MaxMAF).

Family Structures:

• 4-members: 1+2→3+4 (parents 1,2 → offspring 3,4)

• 10-members: 1+2→5+6, 3+5→7+8, 4+6→9+10

• 20-members: Complex multi-generational pedigree with 20 members

Total subjects:nSub + nFam × family_size

Value

List containing:

GenoMat

Numeric genotype matrix (subjects × markers) with values 0, 1, 2.

markerInfo

Data frame with marker IDs and MAF values.

See Also

GRAB.makePlink for converting to PLINK format.

Examples

nSub <- 100nFam <- 10FamMode <- "10-members"nSNP <- 10000OutList <- GRAB.SimuGMat(nSub, nFam, FamMode, nSNP)GenoMat <- OutList$GenoMatmarkerInfo <- OutList$markerInfoGenoMat[1:10, 1:10]head(markerInfo)## The following is to calculate GRMMAF <- apply(GenoMat, 2, mean) / 2GenoMatSD <- t((t(GenoMat) - 2 * MAF) / sqrt(2 * MAF * (1 - MAF)))GRM <- GenoMatSD %*% t(GenoMatSD) / ncol(GenoMat)GRM1 <- GRM[1:10, 1:10]GRM2 <- GRM[100 + 1:10, 100 + 1:10]GRM1GRM2

Simulate genotype matrix from external genotype file

Description

Generates genotype matrices for families and unrelated subjects usinghaplotype data from existing genotype files. Primarily designed forrare variant analysis simulations.

Usage

GRAB.SimuGMatFromGenoFile(  nFam,  nSub,  FamMode,  GenoFile,  GenoFileIndex = NULL,  SampleIDs = NULL,  control = NULL)

Arguments

Details

This function supports both unrelated and related subjects. Founder genotypesare sampled from the input genotype file, and offspring genotypes are generatedthrough Mendelian inheritance.

Note: When simulating related subjects, alleles are randomly assigned tohaplotypes during the phasing process.

Family Structures:

• 4-members: Total subjects = nSub + 4×nFam. Structure: 1+2→3+4

• 10-members: Total subjects = nSub + 10×nFam.Structure: 1+2→5+6, 3+5→7+8, 4+6→9+10

• 20-members: Total subjects = nSub + 20×nFam.Structure: 1+2→9+10, 3+9→11+12, 4+10→13+14, 5+11→15+16,6+12→17, 7+13→18, 8+14→19+20

Value

List containing:

GenoMat

Simulated genotype matrix (subjects × variants).

SubjIDs

Subject identifiers for simulated samples.

markerInfo

Variant information from input file.

Examples

nFam <- 50nSub <- 500FamMode <- "10-members"# PLINK data format. Currently, this function does not support BGEN data format.PLINKFile <- system.file("extdata", "example_n1000_m236.bed", package = "GRAB")IDsToIncludeFile <- system.file("extdata", "example_n1000_m236.IDsToInclude", package = "GRAB")GenoList <- GRAB.SimuGMatFromGenoFile(nFam, nSub, FamMode, PLINKFile,  control = list(IDsToIncludeFile = IDsToIncludeFile))

Simulate phenotypes from linear predictors

Description

Generates various types of phenotypes (quantitative, binary, ordinal,time-to-event) from linear predictors using appropriate link functions.

Usage

GRAB.SimuPheno(  eta,  traitType = "binary",  control = list(pCase = 0.1, sdError = 1, pEachGroup = c(1, 1, 1), eventRate = 0.1),  seed = NULL)

Arguments

Details

Trait Type Details:

• Quantitative: Y = eta + error, where error ~ N(0, sdError²)

• Binary: Logistic model with specified case proportion

• Ordinal: Proportional odds model with specified group proportions

• Time-to-event: Weibull survival model with specified event rate

For more details, see: https://wenjianbi.github.io/grab.github.io/docs/simulation_phenotype.html

Value

Simulated phenotype vector or data frame:

quantitative

Numeric vector of continuous values.

binary

Numeric vector of 0/1 values.

ordinal

Numeric vector of categorical levels.

time-to-event

Data frame with SurvTime and SurvEvent columns.

Simulate random effects based on family structure

Description

Generates random effect vectors (bVec) that account for family relationshipsthrough kinship-based correlation structures.

Usage

GRAB.SimubVec(nSub, nFam, FamMode, tau)

Arguments

Details

For related subjects, random effects follow a multivariate normal distributionwith covariance proportional to kinship coefficients. For unrelated subjects,effects are independent normal random variables.

Value

Data frame with columns:

IID

Subject identifiers.

bVec

Random effect values following appropriate correlation structure.

Instruction of WtCoxG method

Description

WtCoxG is a Cox-based association test method for time-to-event traits. It effectivelyaddresses case ascertainment and rare variant analysis. By leveraging external minorallele frequencies from public resources, WtCoxG can further boost statistical power.

Usage

GRAB.WtCoxG()

Details

Additional Parameters forGRAB.NullModel():

• RefAfFile (character, required): Reference allele frequency file path.File must contain columns: CHROM, POS, ID, REF, ALT, AF_ref, AN_ref

• RefPrevalence (numeric, required): Population-level disease prevalencefor weighting. Must be in range (0, 0.5)

Additional Control Parameters for GRAB.NullModel():

• OutlierRatio (numeric, default: 1.5): IQR multiplier for outlier detection

Method-specific elements in theWtCoxG_NULL_Model object returned byGRAB.NullModel()::

• mresid: Martingale residuals from weighted Cox model (numeric).

• Cova: Design matrix of covariates (matrix).

• yVec: Event indicator (numeric).

• weight: Observation weights based on reference prevalence (numeric).

• RefPrevalence: Reference population prevalence used for weighting (numeric).

• outLierList: List identifying outlier subjects for SPA adjustment.

• mergeGenoInfo: Data frame with batch effect QC results and external reference data.

Additional Control Parameters for GRAB.Marker():

• cutoff (numeric, default: 0.1): Cutoff of batch effect test p-value forassociation testing. Variants with batch effect p-value below this cutoffwill be excluded from association testing.

Output file columns:

Pheno

Phenotype identifier (for multi-trait analysis).

Marker

Marker identifier (rsID or CHR:POS:REF:ALT).

Info

Marker information in format CHR:POS:REF:ALT.

AltFreq

Alternative allele frequency in the sample.

AltCounts

Total count of alternative alleles.

MissingRate

Proportion of missing genotypes.

Pvalue

P-value from the score test.

zScore

Z-score from the score test.

References

Li et al. (2025). Applying weighted Cox regression to genome-wide association studies oftime-to-event phenotypes.doi:10.1038/s43588-025-00864-z

Examples

# Step 1: fit null model and test batch effectPhenoFile <- system.file("extdata", "simuPHENO.txt", package = "GRAB")PhenoData <- data.table::fread(PhenoFile, header = TRUE)SparseGRMFile <- system.file("extdata", "SparseGRM.txt", package = "GRAB")GenoFile <- system.file("extdata", "simuPLINK.bed", package = "GRAB")RefAfFile <- system.file("extdata", "simuRefAf.txt", package = "GRAB")OutputFile <- file.path(tempdir(), "resultWtCoxG.txt")obj.WtCoxG <- GRAB.NullModel(  survival::Surv(SurvTime, SurvEvent) ~ AGE + GENDER,  data = PhenoData,  subjIDcol = "IID",  method = "WtCoxG",  traitType = "time-to-event",  GenoFile = GenoFile,  SparseGRMFile = SparseGRMFile,  RefAfFile = RefAfFile,  RefPrevalence = 0.1)# Step2GRAB.Marker(obj.WtCoxG, GenoFile, OutputFile)head(data.table::fread(OutputFile))

Get allele frequency and missing rate information from genotype data

Description

This function shares input as in functionGRAB.ReadGeno, pleasecheck?GRAB.ReadGeno for more details.

Usage

GRAB.getGenoInfo(  GenoFile,  GenoFileIndex = NULL,  SampleIDs = NULL,  control = NULL)

Arguments

Value

A data frame containing marker information with allele frequenciesand missing rates. The data frame includes columns from marker information(CHROM, POS, ID, REF, ALT, etc.) plus additional columns:

altFreq

Alternative allele frequency (before genotype imputation)

missingRate

Missing rate for each marker

Convert genotype matrix to PLINK format files

Description

Converts a numeric genotype matrix to PLINK text files (PED and MAP format)for use with PLINK software and other genetic analysis tools.

Usage

GRAB.makePlink(  GenoMat,  OutputPrefix,  A1 = "G",  A2 = "A",  CHR = NULL,  BP = NULL,  Pheno = NULL,  Sex = NULL)

Arguments

Details

Genotype Encoding:

• 0, 1, 2 → copies of minor allele

• -9 → missing genotype (coded as "00" in PED)

• A1="G", A2="A": 0→"GG", 1→"AG", 2→"AA", -9→"00"

Output Files:

• .ped: Pedigree file with genotype data

• .map: Marker map file with positions

Downstream Processing:

# Convert to binary formatplink --file prefix --make-bed --out prefix# Convert to raw formatplink --bfile prefix --recode A --out prefix_raw# Convert to BGEN formatplink2 --bfile prefix --export bgen-1.2 bits=8 ref-first --out prefix_bgen# Create BGEN indexbgenix -g prefix_bgen.bgen --index

Value

Character message confirming file creation location.

Examples

### Step 1: simulate a numeric genotype matrixn <- 1000m <- 20MAF <- 0.3set.seed(123)GenoMat <- matrix(rbinom(n * m, 2, MAF), n, m)rownames(GenoMat) <- paste0("Subj-", 1:n)colnames(GenoMat) <- paste0("SNP-", 1:m)OutputDir <- tempdir()outputPrefix <- file.path(OutputDir, "simuPLINK")### Step 2(a): make PLINK files without missing genotypeGRAB.makePlink(GenoMat, outputPrefix)### Step 2(b): make PLINK files with genotype missing rate of 0.1indexMissing <- sample(n * m, 0.1 * n * m)GenoMat[indexMissing] <- -9GRAB.makePlink(GenoMat, outputPrefix)## The following are in shell environment# plink --file simuPLINK --make-bed --out simuPLINK# plink --bfile simuPLINK --recode A --out simuRAW# plink2 --bfile simuPLINK --export bgen-1.2 bits=8 ref-first --out simuBGEN# UK Biobank use 'ref-first'# bgenix -g simuBGEN.bgen --index

Construct SAGELD/GALLOP null model from a mixed-effects fit

Description

Builds the SAGELD (or GALLOP) null model from a fitted mixed-effects modeland relatedness inputs. Extracts variance components, forms the penalizationmatrix, derives residual summaries, and (for SAGELD) integrates sparse GRMand pairwise IBD to prepare graph-based components for marker testing.

Usage

SAGELD.NullModel(  NullModel,  UsedMethod = "SAGELD",  PlinkFile,  SparseGRMFile,  PairwiseIBDFile,  PvalueCutoff = 0.001,  control = list())

Arguments

Value

A list of class"SAGELD_NULL_Model" with elements:

subjData

Character vector of subject IDs.

N

Number of subjects.

Method

Method label:"SAGELD" or"GALLOP".

XTs

Per-subject sums for crossprod(X, G) terms.

SS

Per-subject Rot %*% Si matrices for random effects.

AtS

Per-subject cross-products used in variance assembly.

Q

Fixed-effect precision matrix (p x p).

A21

Block matrix linking random and fixed effects.

TTs

Per-subject sums for crossprod(G).

Tys

Per-subject sums for crossprod(G, y).

sol

Fixed-effects solution vector.

blups

Random-effects BLUPs per subject.

sig

Scale parameter extracted from VarCorr.

Resid

Residuals used in SAGELD testing.

Resid_G

Genetic component residuals.

Resid_GxE

GxE component residuals.

Resid_E

Environmental component residuals.

Resid.unrelated.outliers

Residuals for unrelated outlier subjects.

Resid.unrelated.outliers_G

G residuals for unrelated outliers.

Resid.unrelated.outliers_GxE

GxE residuals for unrelated outliers.

R_GRM_R

Quadratic form Resid' * GRM * Resid (all subjects).

R_GRM_R_G

Quadratic form for G residuals.

R_GRM_R_GxE

Quadratic form for GxE residuals.

R_GRM_R_G_GxE

Cross-term quadratic form between G and GxE.

R_GRM_R_E

Quadratic form for E residuals.

R_GRM_R_TwoSubjOutlier

Contribution from two-subject outlier families.

R_GRM_R_TwoSubjOutlier_G

Two-subject outlier contribution (G).

R_GRM_R_TwoSubjOutlier_GxE

Two-subject outlier contribution (GxE).

R_GRM_R_TwoSubjOutlier_G_GxE

Two-subject outlier cross-term (G,GxE).

sum_R_nonOutlier

Sum of residuals for non-outlier unrelated subjects.

sum_R_nonOutlier_G

Sum of G residuals for non-outlier unrelated subjects.

sum_R_nonOutlier_GxE

Sum of GxE residuals for non-outlier unrelated subjects.

R_GRM_R_nonOutlier

Quadratic form for non-outlier unrelated subjects.

R_GRM_R_nonOutlier_G

Quadratic form for G (non-outlier unrelated).

R_GRM_R_nonOutlier_GxE

Quadratic form for GxE (non-outlier unrelated).

R_GRM_R_nonOutlier_G_GxE

Cross-term for G/GxE (non-outlier unrelated).

TwoSubj_list

Per-family lists for N=2 outlier families.

ThreeSubj_list

CLT and standardized scores for larger families.

MAF_interval

MAF breakpoints used in CLT construction.

zScoreE_cutoff

Z-score threshold for E used in screening.

Fit SPAGRM null model from residuals and relatedness inputs

Description

Builds the SPAGRM null model object using subject residuals, sparse GRM,and pairwise IBD estimates, detecting residual outliers and constructingfamily-level graph structures for downstream saddlepoint marker tests.

Usage

SPAGRM.NullModel(  ResidMatFile,  SparseGRMFile,  PairwiseIBDFile,  control = list(MaxQuantile = 0.75, MinQuantile = 0.25, OutlierRatio = 1.5,    ControlOutlier = TRUE, MaxNuminFam = 5, MAF_interval = c(1e-04, 5e-04, 0.001, 0.005,    0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5)))

Arguments

Value

A list of class"SPAGRM_NULL_Model" with elements:

Resid

Numeric vector of residuals used in analysis.

subjData

Character vector of subject IDs (length = N).

N

Number of subjects.

Resid.unrelated.outliers

Residuals of unrelated outlier subjects.

R_GRM_R

Sum of quadratic form Resid' * GRM * Resid for all subjects.

R_GRM_R_TwoSubjOutlier

Aggregate contribution from two-subject outlier families.

sum_R_nonOutlier

Sum of residuals for non-outlier unrelated subjects.

R_GRM_R_nonOutlier

Quadratic form contribution for non-outlier unrelated subjects.

TwoSubj_list

List with per two-member family residual/Rho info.

ThreeSubj_list

List with Chow–Liu tree structures and standardized scores for larger families.

MAF_interval

Vector of MAF breakpoints used in tree construction.

Quality control to check batch effect between study cohort and reference population.

Description

This function performs quality control to test for the batch effect between a studycohort and a reference population. And fit a weighted null model.

Usage

TestforBatchEffect(  objNull,  data,  GenoFile = NULL,  GenoFileIndex = NULL,  Geno.mtx = NULL,  SparseGRMFile = NULL,  RefAfFile,  IndicatorColumn,  SurvTimeColumn,  RefPrevalence)

Arguments

Value

A dataframe of marker info and reference MAF.

Fit POLMM null model for ordinal outcomes

Description

Initializes the POLMM null model from an ordered categorical response andcovariate matrix, preparing C++ state for subsequent marker/region tests.

Usage

fitNullModel.POLMM(  response,  designMat,  subjData,  control,  optionGRM,  GenoFile,  GenoFileIndex,  SparseGRMFile)

Arguments

Value

An object of class"POLMM_NULL_Model" representing theinitialized null model; state is stored in C++ and not intended for directelement-wise access from R.

Fit SPACox null model from survival outcomes or residuals

Description

Computes martingale residuals (or uses provided residuals) and an empiricalcumulant generating function (CGF) for SPA-based single-variant tests.

Usage

fitNullModel.SPACox(response, designMat, subjData, control, ...)

Arguments

Value

A list of class"SPACox_NULL_Model" with elements:

N

Number of subjects.

mresid

Martingale residuals (numeric vector).

cumul

CGF grid as a matrix with columns t, K0, K1, K2.

tX

Transpose of design matrix with intercept (p+1 x n).

yVec

Status/event indicator or residual-based response.

X.invXX

Projection helper: X %% solve(t(X) %% X).

subjData

Character vector of subject IDs.

Fit a SPAmix null model from a survival response (Surv) withcovariates or from precomputed residuals. Principal components (PCs) namedincontrol$PC_columns are extracted; residual outliers are detectedusing an IQR rule with adjustable multiplier and stored for SPA testing.

Description

Fit a SPAmix null model from a survival response (Surv) withcovariates or from precomputed residuals. Principal components (PCs) namedincontrol$PC_columns are extracted; residual outliers are detectedusing an IQR rule with adjustable multiplier and stored for SPA testing.

Usage

fitNullModel.SPAmix(response, designMat, subjData, control, ...)

Arguments

Details

Ifresponse isSurv, a Cox model is fit and martingaleresiduals are used. Ifresponse isResidual, its values areused directly. Outliers per phenotype are defined by[Q1 - r*IQR, Q3 + r*IQR] withr = OutlierRatio; if none arefound,r is iteratively reduced by 20% until at least one appears.

Value

A list of class"SPAmix_NULL_Model" containing:

resid

Residual matrix (n x k)

N

Number of subjects

yVec

Response vector (event indicator for survival models)

PCs

Selected principal component columns

nPheno

Number of phenotypes (columns of residuals)

outLierList

List of per-phenotype indices (0-based) and residualsubsets for outlier/non-outlier strata

Fit weighted Cox null model with outlier handling and batch-effect QC

Description

Fits a weighted Cox model using case/control weighting based on referenceprevalence and identifies residual outliers for SPA testing. Optionallyperforms batch-effect QC by cross-referencing external allele frequencies.

Usage

fitNullModel.WtCoxG(  response,  designMat,  subjData,  control,  data,  GenoFile,  GenoFileIndex,  SparseGRMFile,  SurvTimeColumn,  IndicatorColumn,  ...)

Arguments

Value

A list of class"WtCoxG_NULL_Model" with elements:

mresid

Martingale residuals from weighted Cox model.

Cova

Design matrix used in the null model (n x p).

yVec

Event indicator extracted fromSurv.

weight

Observation weights derived from reference prevalence.

RefPrevalence

Reference prevalence used to define weights.

N

Number of subjects.

outLierList

Lists indices (0-based) and residual subsets for SPA.

control

Copy of control options used.

mergeGenoInfo

QC-derived marker metadata for batch-effect testing (if run).

subjData

Character vector of subject IDs.

Calculate Pairwise IBD (Identity By Descent)

Description

This function calculates pairwise IBD probabilities for related samples usingPLINK genotype data and sparse GRM. It follows the getSparseGRM() function workflow.

Usage

getPairwiseIBD(  PlinkPrefix,  SparseGRMFile,  PairwiseIBDOutput,  frqFile = NULL,  tempDir = NULL,  maxSampleNums = 2500,  minMafIBD = 0.01,  rm.tempFile = FALSE)

Arguments

Value

Character. Message indicating where the pairwise IBD results have been stored.

Examples

PlinkPrefix <- file.path(system.file(package = "GRAB"), "extdata", "simuPLINK")SparseGRMFile <- system.file("extdata", "SparseGRM.txt", package = "GRAB")PairwiseIBDOutput <- file.path(tempdir(), "PairwiseIBD.txt")getPairwiseIBD(PlinkPrefix, SparseGRMFile, PairwiseIBDOutput)

Make aSparseGRMFile forGRAB.NullModel.

Description

If the sample size in analysis is greater than 100,000, we recommend using sparse GRM(instead of dense GRM) to adjust for sample relatedness.This function is to useGCTA (link)to make aSparseGRMFile to be passed to functionGRAB.NullModel.This function can only supportLinux andPLINK files as required byGCTA software. To make aSparseGRMFile, two steps are needed.Please checkDetails section for more details.

Usage

getSparseGRM(  PlinkPrefix,  nPartsGRM,  SparseGRMFile,  tempDir = NULL,  relatednessCutoff = 0.05,  minMafGRM = 0.01,  maxMissingGRM = 0.1,  rm.tempFiles = FALSE)

Arguments

Details

• Step 1: RungetTempFilesFullGRM to save temporary filestotempDir.

• Step 2: RungetSparseGRM to combine the temporary files to makeaSparseGRMFile to be passed to functionGRAB.NullModel.

Users can customize parameters including(minMafGRM, maxMissingGRM, nPartsGRM),but functionsgetTempFilesFullGRM andgetSparseGRM should use the same ones.Otherwise, packageGRAB cannot accurately identify temporary files.

Value

A character string containing a message with the path to the output filewhere the sparse Genetic Relationship Matrix (SparseGRM) has been stored.

The following shows a typical workflow for creating a sparse GRM:

# Input data (We recommend setting nPartsGRM=250 for UKBB with N=500K):

GenoFile = system.file("extdata", "simuPLINK.bed", package = "GRAB")

PlinkPrefix = tools::file_path_sans_ext(GenoFile)

nPartsGRM = 2

Step 1: We strongly recommend parallel computing in high performance clusters (HPC).

# For Linux, get the file path of gcta64 by which command:

gcta64File <- system("which gcta64", intern = TRUE)

# For Windows, set the file path directly:

gcta64File <- "C:\\path\\to\\gcta64.exe"

# The temp outputs (may be large) will be in tempdir() by default:

for(partParallel in 1:nPartsGRM) getTempFilesFullGRM(PlinkPrefix, nPartsGRM,partParallel, gcta64File)

Step 2: Combine files in Step 1 to make a SparseGRMFile

tempDir = tempdir()

SparseGRMFile = file.path(tempDir, "SparseGRM.txt")

getSparseGRM(PlinkPrefix, nPartsGRM, SparseGRMFile)

Make temporary files to be passed to functiongetSparseGRM.

Description

Make temporary files to be passed to functiongetSparseGRM.We strongly suggest using parallel computing for differentpartParallel.

Usage

getTempFilesFullGRM(  PlinkPrefix,  nPartsGRM,  partParallel,  gcta64File,  tempDir = NULL,  subjData = NULL,  minMafGRM = 0.01,  maxMissingGRM = 0.1,  threadNum = 8)

Arguments

Details

• Step 1: RungetTempFilesFullGRM to get temporary files.

• Step 2: RungetSparseGRM to combine the temporary filesto make aSparseGRMFile to be passed toGRAB.NullModel.

Value

A character string message indicating the completion status and locationof the temporary files.

Examples

## Please check help(getSparseGRM) for an example.