Package {iGasso}

Statistical Tests and utilities for Genetic Association

Description

iGasso is a collection of statistical tests developed by our group for genetic association studies. So far it contains functions for rare variants association, for association with multiple phenotypes, for linear mixed model analysis, and for model-free association analysis. There is also a function for genome plot. It will keep growing as more tests are developed. Use ?iGasso to see an introduction.

Details

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Anscombe F.J. (1948) The transformation of Poisson, binomial and negative-binomial data. Biometrika 35(3/4), 246–254.

Chanter, D. O. (1975). Modifications of the angular transformation. Journal of the Royal Statistical Society. Series B (Applied Statistics), 24 (3), 354–359.

Freeman, M. F., Tukey, J. W. (1950) Transformations related to the angular and the square root. The Annals of Mathematical Statistics 21(4), 607–611.

Wang, K. (2012) An application of the proportional odds model to genetic association studies. Submitted.

Wang K. (2012) Statistical tests of genetic association for case-control study designs. Biostatistics. Accepted. PMID: 22389176

Wang, K., Fingert, J. (2012) Statistical tests for detecting rare variants using variance-stabilizing transformations. Annals of Human Genetics. Accepted.

Zar, J. H. (1999) Biostatistical Analysis, 4th ed., New Jersey:Prentice-Hall, Inc.

Examples

y = rnorm(100)
chr = c(rep(1, 20), rep(3, 20), rep(10, 20), rep(19, 30), rep("X", 10))
pos = c(1:20, 1:20, 1:20, 1:30, 1:10)
mydata = data.frame(y=y, chr=chr, pos=pos)
genome.plot(mydata, sig.line=c(1, -1), ylab="T Statistic")

G = rbind(c(14, 999), c(3, 1081))
VSTF.test(G)

G = rbind(c(161, 474, 489), c(231, 444, 380))
MFree.test(G)

G = matrix(sample(c(0,1,2), 200, replace=TRUE), ncol=10)
y = rnorm(10)
X = matrix(rnorm(10), ncol=1)

Conditional Inference for the Kernel Association Test (KAT)

Description

Computes the asymptotic and the approximate conditional p-values for the kernel association test

Usage

KAT_coin(y, G, X = NULL, out_type = "D", distribution = "asymptotic", B = 1000)

Arguments

Details

The asymptotic conditional null distribution is obtained using results in Strasser and Weber (1999). The p-value based on this distribution is computed using Davies' method.

Value

A list with class "htest" containing the following components:

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Strasser, H. and Weber, C. (1999) On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics. 8(2):220-250.

Wang, K. (2017) Conditional Inference for the Kernel Association Test. Bioinformatics 33 (23), 3733-3739.

Examples

n=1000
y = c(rep(1, n/2), rep(0, n/2))
maf = seq(0.05, 0.5, 0.05)
g = NULL
for (j in 1:10){
   geno.freq = c(maf[j]^2, 2*maf[j]*(1-maf[j]), (1-maf[j])^2)
   g = cbind(g, sample(c(0,1,2), n, replace=TRUE, prob=geno.freq))
   }
KAT_coin(y, g, X=NULL, out_type="D", B=1000)

Model-free Association Tests

Description

MFree.test performs tests on association between an SNP and case-control status. It tests whether the frequencies of an allele are the same between cases and controls. It does not require specification of an inheritance model.

Usage

MFree.test(G, method = "score")

Arguments

Details

Each test is named after the author(s) of the corresponding publication.

Value

A list with class "test" containing the following components:

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang K. (2012) Statistical tests of genetic association for case-control study designs. Biostatistics. 13(4):724-33. PMID: 22389176

Examples

G = rbind(c(161, 474, 489), c(231, 444, 380))
MFree.test(G)
MFree.test(G, method = "Wald")
MFree.test(G, method = "LRT")

Test of Heterogeneity in MR using Principal Components

Description

MR_het_test performs tests of heterogeneity in MR.

Usage

MR_het_test(x.b, y.b, x.se, y.se, b0, k = NULL, cum.prop = 0.8)

Arguments

Value

A list containing the following components:

* P_\text{min}(b_0) statistic and its P-value.

* \tilde Q_\text{min}(b_0) statistic, its degrees of freedom, and its P-value.

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K, Alberding, Steven Y. (2024) Powerful test of heterogeneity in two-sample summary-data Mendelian randomization. Statistics in Medicine, 2024; 43:5791–5802.

Examples

p = 10
b = 0.5
gamma.true = runif(p, 0.34, 1.1)
x.se = runif(p, 0.06, 0.1)
y.se = runif(p, 0.015, 0.11)
x.b = rnorm(p, gamma.true, x.se)
y.b = rnorm(p, b*gamma.true, y.se)
b0 = 0.4

MR_het_test(x.b, y.b, x.se, y.se, b0)

A Gene- or Pathway-Based Test of Association SKATlus provides enhanced power over SKAT by properly estimating the null distribution of SKAT.

Description

This version uses only subjects with lower phenotypic values for estimating the null distribution. That is, the "controls" are those of lower phenotypic values. When "controls" are of higher phenotypic values, change the sign of the phenotypic values in order to use this function.

Usage

SKATplus(
  y,
  G,
  X = NULL,
  out_type = "D",
  tau = NULL,
  permutation = FALSE,
  B = 1000
)

Arguments

Value

A list with class "htest" containing the following components:

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K. (2016) Boosting the power of the sequence kernel association test (SKAT) almost surely by properly estimating its null distribution. A J Hum Genet. 99 (1), 104-114.

Examples

    n=1000
    y = c(rep(1, n/2), rep(0, n/2))
    maf = seq(0.05, 0.5, 0.05)
    g = NULL
    for (j in 1:10){
       geno.freq = c(maf[j]^2, 2*maf[j]*(1-maf[j]), (1-maf[j])^2)
       g = cbind(g, sample(c(0,1,2), n, replace=TRUE, prob=geno.freq))
       }
       SKATplus(y, g, X=NULL, out_type="D", tau=NULL, permutation=FALSE, B=1000)

Interval Estimates for Summary Data Mendelian Randomization Analysis in the Presence of Winner's Curse

Description

SMR_interval calculates conservative box method interval, k-unit support interval, and Wald confidence interval for the causal effect.

Usage

SMR_interval(
  summary.data,
  sig.level = 5e-08,
  k = 2,
  alpha = 0.05,
  method = "box"
)

Arguments

Value

The returned value is method-dependent.

For method == "box": A list containing the following components:

* an interval estimate.

* type of the interval: completely bounded, exclusive bounded, or bounded.

For method == "support": A list containing the following components:

* Estimate The likelihood estimate of b.

* an interval estimate.

For method == "wald": an interval estimate.

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K. (2023) Support interval for two-sample summary data-based mendelia randomization. Genes, 14(1):211.

Wang, K. (2023) Interval estimate of causal effect in summary data based Mendelian randomization in the presence of winner’s curse. Genetic Epidemiology, 14(1):211.

Zhu, Z. et al. (2016) Integration of summary data from GWAS and eQTL studies predicts complex trait gene targets. Nature Genetics, 48(5):481.

Examples

summary.data = c(0.13707, 0.0235162, -0.0637257, 0.013774)
SMR_interval(summary.data)
SMR_interval(summary.data, method = "support")
SMR_interval(summary.data, method = "wald")

Association Tests for Rare Variants Based on Variance-Stabilizing Transformation

Description

VSTF.test performs tests on association between a rare variant and case-control status using a variance-stabilizing transformation.

Usage

VSTF.test(G, method = "Anscombe")

Arguments

Details

Each test is named after the author(s) of the corresponding publication.

Value

A list with class "test" containing the following components:

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Anscombe, F. J. (1948) The transformation of Poisson, binomial and negative-binomial data. Biometrika 35(3/4), 246–254.

Chanter, D. O. (1975). Modifications of the angular transformation. Journal of the Royal Statistical Society. Series B (Applied Statistics) 24(3), 354–359.

Freeman, M. F., Tukey, J. W. (1950) Transformations related to the angular and the square root. The Annals of Mathematical Statistics 21(4), 607–611.

Wang, K., Fingert, J. (2012) Statistical tests for detecting rare variants using variance-stabilizing transformations. Annals of Human Genetics. 76(5):402-409.

Zar, J.H. (1999) Biostatistical Analysis, 4th ed., New Jersey:Prentice-Hall, Inc.

Examples

## Example 1 of Li et al. (2010)
G = rbind(c(14, 999), c(3, 1081))
VSTF.test(G)
VSTF.test(G, method = "arcsine")
VSTF.test(G, method = "Freeman-Tukey")

Effect of Body Mass Index (BMI) on Coronary Artery Disease (CAD)

Description

It contains independent datasets from three genome-wide association studies (GWASs):

1. Exposure dataset: A GWAS for BMI in round 2 of the UK BioBank (sample size: 336,107), http://www.nealelab.is/uk-biobank.

2. Outcome dataset: A GWAS A GWAS for CAD from the CARDIoGRAMplusC4D consortium (sample size: ~185,000), with genotype imputation using the 1000 Genome Project, (PubMed 26343387).

3. Selection dataset: A GWAS for BMI in the Japanese population (sample size: 173,430), (PubMed 28892062).

Usage

data(bmi.cad)

Format

A data.frame with 1119 rows and 42 variables.

Source

https://github.com/qingyuanzhao/mr.raps, https://github.com/tye27/mr.divw

Genome-wide Plot of a Variable

Description

genome.plot plots the value of a variable across the genome.

Usage

genome.plot(
  mydata,
  style = 1,
  type = "h",
  sig.line = c(4, -4),
  sig.color = c("red", "red"),
  ...
)

Arguments

Details

This function makes use of the function xyplot from package lattice.

Author(s)

Kai Wang <kai-wang@uiowa.edu>

Examples

  y = rnorm(100)
  chr = c(rep(1, 20), rep(3, 20), rep(10, 20), rep(19, 30), rep("X", 10))
  pos = c(1:20, 1:20, 1:20, 1:30, 1:10)
  mydata = data.frame(y=y, chr=chr, pos=pos)
  mydata2 = data.frame(y=y^2, chr=chr, pos=pos)
  
  genome.plot(mydata, sig.line=c(1, -1), ylab="T Statistic")
  genome.plot(mydata, sig.line=c(1, -1), ylab="T Statistic", type="b")
  genome.plot(mydata2, sig.line=c(2), ylab="y squared")
  genome.plot(mydata, style=2, sig.line=c(1, -1), ylab="T Statistic")
  genome.plot(mydata, style=2, sig.line=c(1, -1), ylab="T Statistic", type="b")

An exact method for SNP-heritability estimation using GWAS summary statistics

Description

h2_snp calculates heritability explained by a set of SNPs

Usage

h2_snp(beta, SE, N, R, alpha)

Arguments

Value

A list containing the following components:

* MLE of the heritability.

* umvu (uniformly minimum variance unbiased) estimator of the heritability.

* interval estimate for the heritability.

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K. (2023) An exact method for SNP-heritability estimation using GWAS summary statistics without heritability modeling. submitted

Examples

beta = c(0.225269, 0.221270, 0.162635, 0.261669, 0.150887, 
         0.214515, 0.170296, 0.204454, 0.254811, 0.213803)
SE = c(0.033244, 0.032551, 0.032171, 0.031042, 0.032815, 
       0.031908, 0.031717, 0.032023, 0.031907, 0.032291)
N = 10000
R = diag(1, 10)
alpha = 0.05
h2_snp(beta, SE, N, R, alpha)

Modified Bland-Altman plot for checking genetic homogeneity between two samples

Description

mBAplot checks genetic homogeneity between two samples using summary statistics.

Usage

mBAplot(
  b.x,
  se.x,
  n.x,
  b.y,
  se.y,
  n.y,
  k.x = 0,
  k.y = 0,
  main = "Modified Bland-Altman Plot"
)

Arguments

Value

A modified Bland-Altman plot

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K, Wang, Grace Z. (2026) Checking genetic homogeneity using summary statistics for valid Mendelian randomization analysis. Statistics in Medicine. https://doi.org/10.1002/sim.70663

Examples

attach(bmi.cad)
mBAplot(beta.selection, se.selection, 173430, beta.outcome, se.outcome, 185000, 
          main = "BMI-Japanese vs CAD-Consortium")
detach(bmi.cad)         

An Accurate Normalization Method for High Throughput Sequencing Data

Description

Estimates scaling factors using the trimmed average of ratios of quantiles (TARQ) method

Usage

tarq(X, tau = 0.3)

Arguments

Details

Estimation of scaling factors for NGS read counts data is challenging. TARQ provides a quantile-based method for estimating scaling factors. It starts by ordering the raw counts sample by sample and constructs a reference sample from these ordered counts. To compute the scaling factor for a sample, ratios of its quantiles to those of the reference sample are formed. Zero ratios are removed. Then extreme ratios (too large or too small) are trimmed before taking average over the remaining ratios.

Value

a vector of scaling factors. Normalized counts can be obtained by sweep(X, 2, scale.factors, FUN="/")

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K. (2018) An Accurate Normalization Method for Next-Generation Sequencing Data. Submitted.

Examples

#data(throat.otu.tab)
#data(throat.meta)
#otu.tab = t(throat.otu.tab)
#tarq(otu.tab, 0.3)

##### Use TARQ with DESeq2 
#dds <- DESeqDataSetFromMatrix(countData = otu.tab,
 #                             colData = throat.meta,
 #                             design= ~ SmokingStatus)
#sizeFactors(dds) <- tarq(otu.tab, 0.3)
#dds <- DESeq(dds)                 
#results(dds)
#
###### Use TARQ with edgeR
#cs <- colSums(otu.tab)
#scale.factors <- tarq(otu.tab, 0.3)
#tmp <- scale.factors/cs
#norm.factors <- tmp/exp(mean(log(tmp)))
#dgList <- DGEList(counts = otu.tab, genes=rownames(otu.tab), norm.factors = norm.factors)
#designMat <- model.matrix(~ throat.meta$SmokingStatus)
#dgList <- estimateGLMCommonDisp(dgList, design=designMat)
#fit <- glmFit(dgList, designMat)
#glmLRT(fit, coef=2)

Two-stage least squares estimator for two-sample summary statistics MR

Description

MR causal effect estimation using summary statistics from two independent GWASs

Usage

tssmr(b.x, se.x, n.x, b.y, se.y, n.y, k.x = 0, k.y = 0)

Arguments

Value

A list with the following components:

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K, Wang, Grace Z. (2026) Valid inference for two sample summary data Mendelian randomization. Submitted.
Wang, K, Wang, Grace Z. (2026) Valid two-sample summary-statistics Mendelian randomization with many invalid instruments. Submitted.

Examples

attach(bmi.cad)
tssmr(beta.selection, se.selection, 173430, beta.outcome, se.outcome, 185000)
detach(bmi.cad)         

V-V plot for checking genetic homogeneity between two samples

Description

vvplot checks genetic homogeneity between two samples using summary statistics.

Usage

vvplot(
  b.x,
  se.x,
  n.x,
  b.y,
  se.y,
  n.y,
  k.x = 0,
  k.y = 0,
  xlab = "Exposure",
  ylab = "Outcome",
  main = "V-V Plot"
)

Arguments

Value

A V-V plot

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang, K, Wang, Grace Z. (2026) Checking genetic homogeneity using summary statistics for valid Mendelian randomization analysis. Statistics in Medicine. https://doi.org/10.1002/sim.70663

Examples

attach(bmi.cad)
vvplot(beta.selection, se.selection, 173430, beta.outcome, se.outcome, 185000, 
          main = "BMI-Japanese vs CAD-Consortium")
detach(bmi.cad)