Package 'interep'

k-folds cross-validation for interep

Description

This function does k-fold cross-validation for interep and returns the optimal value of lambda.

Usage

cv.interep(e, g, y, beta0, lambda1, lambda2, nfolds, corre, pmethod, maxits)

Arguments

e	matrix of environment factors.
g	matrix of omics factors. In the case study, the omics measurements are lipidomics data.
y	the longitudinal response.
beta0	the intial value for the coefficient vector.
lambda1	a user-supplied sequence of $\lambda_{1}$ values, which serves as a tuning parameter for individual predictors.
lambda2	a user-supplied sequence of $\lambda_{2}$ values, which serves as a tuning parameter for interactions.
nfolds	the number of folds for cross-validation.
corre	the working correlation structure that is used in the estimation algorithm. interep provides three choices for the working correlation structure: "a" as AR-1", "i" as "independence" and "e" as "exchangeable".
pmethod	the penalization method. "mixed" refers to MCP penalty to individual main effects and group MCP penalty to interactions; "individual" means MCP penalty to all effects.
maxits	the maximum number of iterations that is used in the estimation algorithm.

Details

When dealing with predictors with both main effects and interactions, this function returns two optimal tuning parameters, $\lambda_{1}$ and $\lambda_{2}$; when there are only main effects in the predictors, this function returns $\lambda_{1}$, which is the optimal tuning parameter for individual predictors containing main effects.

Value

an object of class "cv.interep" is returned, which is a list with components:

lam1	the optimal $\lambda_{1}$.
lam2	the optimal $\lambda_{2}$.

References

Zhou, F., Ren, J., Li, G., Jiang, Y., Li, X., Wang, W.and Wu, C. (2019). Penalized variable selection for Lipid–environment interactions in a longitudinal lipidomics study. Genes, 10(12), 1002

Zhou, F., Ren, J., Liu, Y., Li, X., Wang, W.and Wu, C. (2022). Interep: An r package for high-dimensional interaction analysis of the repeated measurement data. Genes, 13(3): 554 doi:10.3390/genes13030544

Zhou, F., Ren, J., Lu, X., Ma, S. and Wu, C. (2021) Gene–Environment Interaction: a Variable Selection Perspective. Epistasis: Methods and Protocols, 191-223

Ren, J., Zhou, F., Li, X., Chen, Q., Zhang, H., Ma, S., Jiang,Y. and Wu, C. (2020). Semi-parametric Bayesian variable selection for Gene-Environment interactions. Statistics in Medicine, 39(5): 617-638 doi:10.1002/sim.8434

Wu, C., Zhou, F., Ren, J., Li, X., Jiang, Y., Ma, S. (2019). A Selective Review of Multi-Level Omics Data Integration Using Variable Selection. High-Throughput, 8(1) doi:10.3390/ht8010004

Ren, J., Du, Y., Li, S., Ma, S., Jiang, Y. and Wu, C. (2019). Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis. Genetic epidemiology, 43(3), 276-291 doi:10.1002/gepi.22194

Ren, J., Jung, L., Du, Y., Wu, C., Jiang, Y. and Liu, J. (2019). regnet: Network-Based Regularization for Generalized Linear Models. R package, version 0.4.0

Wu, C., Zhang, Q., Jiang, Y. and Ma, S. (2018). Robust network-based analysis of the associations between (epi) genetic measurements. Journal of multivariate analysis, 168, 119-130 doi:10.1016/j.jmva.2018.06.009

Wu, C., Zhong, P.-S., and Cui, Y. (2018). Additive varying-coefficient model for nonlinear gene-environment interactions. Statistical Applications in Genetics and Molecular Biology, 17(2) doi:10.1515/sagmb-2017-0008

Wu, C., Jiang, Y., Ren, J., Cui, Y., Ma, S. (2018). Dissecting gene-environment interactions: A penalized robust approach accounting for hierarchical structures. Statistics in Medicine, 37: 437–456 doi:10.1002/sim.7518

Ren, J., He, T., Li, Y., Liu, S., Du, Y., Jiang, Y. and Wu, C. (2017). Network-based regularization for high dimensional SNP data in the case–control study of Type 2 diabetes. BMC genetics, 18(1), 44 doi:10.1186/s12863-017-0495-5

Jiang, Y., Huang, Y., Du, Y., Zhao, Y., Ren, J., Ma, S., & Wu, C. (2017). Identification of prognostic genes and pathways in lung adenocarcinoma using a Bayesian approach. Cancer Inform, 1(7) doi:10.1177/1176935116684825

Wu, C., and Ma, S. (2015). A selective review of robust variable selection with applications in bioinformatics. Briefings in Bioinformatics, 16(5), 873–883 doi:10.1093/bib/bbu046

Wu, C., Shi, X., Cui, Y. and Ma, S. (2015). A penalized robust semiparametric approach for gene-environment interactions. Statistics in Medicine, 34 (30): 4016–4030 doi:10.1002/sim.6609

Wu, C., Cui, Y., and Ma, S. (2014). Integrative analysis of gene–environment interactions under a multi–response partially linear varying coefficient model. Statistics in Medicine, 33(28), 4988–4998 doi:10.1002/sim.6287

Wu, C. and Cui, Y. (2013). A novel method for identifying nonlinear gene–environment interactions in case–control association studies. Human Genetics, 132(12):1413–1425 doi:10.1007/s00439-013-1350-z

Wu, C. and Cui, Y. (2013). Boosting signals in gene–based association studies via efficient SNP selection. Briefings in Bioinformatics, 15(2):279–291 doi:10.1093/bib/bbs087

Wu, C., Zhong, P.S. and Cui, Y. (2013). High dimensional variable selection for gene-environment interactions. Technical Report, Michigan State University.

Wu, C., Li, S., and Cui, Y. (2012). Genetic Association Studies: An Information Content Perspective. Current Genomics, 13(7), 566–573 doi:10.2174/138920212803251382

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simulated data for demonstrating the features of interep

Description

Simulated data for demonstrating the features of interep.

Usage

data("dat")

Format

Each data consists of six components: e, z, x, y, coef and index; index shows the location of the true coefficients used to generate y.

Examples

data("dat")

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This function obtains the first derivative function of MCP (Minimax Concave Penalty)

Description

This function obtains the first derivative function of MCP (Minimax Concave Penalty)

Usage

dmcp(theta, lambda, gamma = 3)

Arguments

theta	a coefficient vector.
lambda	the tuning parameter.
gamma	the regularization parameter in MCP (Minimax Concave Penalty). It balances between the unbiasedness and concavity of MCP.

Details

Rigorously speaking, the regularization parametre $\gamma$ needs to be obtained via a data-driven approach. Published studies suggest experimenting with a few values, such as 1.8, 3, 4.5, 6, and 10, then fixing its value. In our numerical study, we have examined this sequence and found that the results are not sensitive to the choice of value of $\gamma$, and set the value at 3. In practice, to be prudent, values other than 3 should also be investigated. Similar discussions can be found in the references below.

Value

the first derivative of MCP function.

References

Ren, J., Du, Y., Li, S., Ma, S., Jiang, Y. and Wu, C. (2019). Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis. Genetic epidemiology, 43(3), 276-291 doi:10.1002/gepi.22194

Ren, J., Jung, L., Du, Y., Wu, C., Jiang, Y. and Liu, J. (2019). regnet: Network-Based Regularization for Generalized Linear Models. R package, version 0.4.0

Wu, C., Zhang, Q., Jiang, Y. and Ma, S. (2018). Robust network-based analysis of the associations between (epi) genetic measurements. Journal of multivariate analysis, 168, 119-130 doi:10.1016/j.jmva.2018.06.009

Ren, J., He, T., Li, Y., Liu, S., Du, Y., Jiang, Y. and Wu, C. (2017). Network-based regularization for high dimensional SNP data in the case–control study of Type 2 diabetes. BMC genetics, 18(1), 44 doi:10.1186/s12863-017-0495-5

Examples

theta=runif(20,-5,5)
lambda=1
dmcp(theta,lambda,gamma=3)

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fit generalized estimaitng equations with given tuning parameters

Description

This function makes predictions for generalized estimating equation with a given value of lambda. Typical usage is to have the cv.interep function compute the optimal lambda, then provide it to the interep function.

Usage

interep(e, g, y, beta0, corre, pmethod, lam1, lam2, maxits)

Arguments

e	matrix of environment factors.
g	matrix of omics factors. In the case study, the omics measurements are lipidomics data.
y	the longitudinal response.
beta0	the inital coefficient vector.
corre	the working correlation structure that is used in the estimation algorithm. interep provides three choices for the working correlation structure: "a" as AR-1", "i" as "independence" and "e" as "exchangeable".
pmethod	the penalization method. "mixed" refers to MCP penalty to individual main effects and group MCP penalty to interactions; "individual" means MCP penalty to all effects.
lam1	the tuning parameter lambda1 for individual predictors.
lam2	the tuning parameter lambda2 for interactions.
maxits	the maximum number of iterations that is used in the estimation algorithm. The default value is 30

Value

coef	the coefficient vector.

References

Zhou, F., Ren, J., Li, G., Jiang, Y., Li, X., Wang, W.and Wu, C. (2019). Penalized variable selection for Lipid–environment interactions in a longitudinal lipidomics study. Genes, 10(12), 1002

Zhou, F., Ren, J., Liu, Y., Li, X., Wang, W.and Wu, C. (2022). Interep: An r package for high-dimensional interaction analysis of the repeated measurement data. Genes, 13(3): 554 doi:10.3390/genes13030544

Zhou, F., Ren, J., Lu, X., Ma, S. and Wu, C. (2021) Gene–Environment Interaction: a Variable Selection Perspective. Epistasis: Methods and Protocols, 191-223

Examples

data("dat")
e=dat$e
g=dat$z
y=dat$y
beta0=dat$coef
index=dat$index
b = interep(e, g, y,beta0,corre="e",pmethod="mixed",lam1=dat$lam1, lam2=dat$lam2,maxits=30)
b[abs(b)<0.05]=0
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

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This function gives the penalty functions

Description

This function gives the penalty functions

Usage

penalty(x, n, p, q, beta, lam1, pmethod, p1, lam2)

Arguments

x	matrix of covariates.
n	the sample size.
p	the number of predictors.
q	the number of environment factors.
beta	the coefficient vector.
lam1	the tuning parameter lambda1 for individual penalty.
pmethod	the penalization method. "mixed" refers to MCP penalty to individual main effects and group MCP penalty to interactions; "individual" means MCP penalty to all effects.
p1	the number of gene factors.
lam2	the tuning parameter lambda2 for group penalty.

Value

E	the penalty function.

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This function changes the format of the longitudinal data from wide format to long format

Description

This function changes the format of the longitudinal data from wide format to long format

Usage

reformat(k, y, x)

Arguments

k	the number of repeated measurement.
y	the longitudinal response.
x	a matrix of predictors, consisting of omics and environment factors, as well as their interactions. In the case study, the omics measurements are lipidomics data.

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