simData: Simulation of microarray data

In optBiomarker: Estimation of Optimal Number of Biomarkers for Two-Group Microarray Based Classifications at a Given Error Tolerance Level for Various Classification Rules

Description

The function simulates microarray data for two-group comparison with user supplied parameters such as number of biomarkers (genes or proteins), sample size, biological and experimental (technical) variation, replication, differential expression, and correlation between biomarkers.

Usage

simData(nTrain=100,
        nGr1=floor(nTrain/2),
        nBiom=50,nRep=3,
        sdW=1.0,
        sdB=1.0,
        rhoMax=NULL, rhoMin=NULL, nBlock=NULL,bsMin=3, bSizes=NULL, gamma=NULL,
        sigma=0.1,diffExpr=TRUE,
        foldMin=2,
        orderBiom=TRUE,
        baseExpr=NULL)

Arguments

nTrain	Training set size,.i.e., the total number of biological samples in group 1 (nGr1) and group 2.
nGr1	Size of group 1. Defaults to floor(nTrain/2).
nBiom	Number of biomarkers (genes, probes or proteins).
nRep	Number of technical replications.
sdW	Experimental (technical) variation (σ_e) of data in log (base 2) scale.
sdB	Biological variation (σ_b) of data in log (base 2) scale.
rhoMax	Maximum Pearson's correlation coefficient between biomarkers. To ensure positive definiteness, allowed values are restricted between 0 and 0.95 inclusive. If NULL, set to runif(1,min=0.6,max=0.8).
rhoMin	Minimum Pearson's correlation coefficient between biomarkers. To ensure positive definiteness, allowed values are restricted between 0 and 0.95 inclusive. If NULL, set to runif(1,min=0.2,max=0.4).
nBlock	Number of blocks in the block diagonal (Hub-Toeplitz) correlation matrix. If NULL, set to 1 for nBiom<5 and randomly selected from c(1:floor(nBiom/bsMin)) for nBiom>=5.
bsMin	Minimum block size. bsMin=3 by default.
bSizes	A vector of length nBlock representing the block sizes (should sum to nBlock). If NULL, set to c(bs+mod,rep(bs,nBlock-1), where bs is the integer part of nBiom/nBlock and mod is the remainder after integer division.
gamma	Specifies a correlation structure. If NULL, assumes independence.gamma=0 indicates a single block exchangeable correlation marix with constant correlation rho=0.5*(rhoMin+rhoMax). A value greater than zero indicates block diagonal (Hub-Toeplitz) correlation matrix with decline rate determined by the value of gamma. Decline rate is linear for gamma=1.
sigma	Standard deviation of the normal distribution (before truncation) where fold changes are generated from. See details.
diffExpr	Logical. Should systematic difference be introduced between the data of the two groups?
foldMin	Minimum value of fold changes. See details.
orderBiom	Logical. Should columns (biomarkers) be arranged in order of differential expression?
baseExpr	A vector of length nBiom to be used as base expressions μ. See realBiomarker for details.

Details

Differential expressions are introduced by adding zδ to the data of group 2 where δ values are generated from a truncated normal distribution and z is randomly selected from (-1,1) to characterise up- or down-regulation.

Assuming that Y ~is~ N(μ, σ^2), and A=[a_1,a_2], a subset of -Inf <y < Inf, the conditional distribution of Y given A is called truncated normal distribution:

f(y, μ, σ)= (1/σ) φ((y-μ)/σ) / (Φ((a2-μ)/σ) - Φ((a_1-μ)/σ))

for a_1 <= y <= a_2, and 0 otherwise,

where μ is the mean of the original Normal distribution before truncation, σ is the corresponding standard deviation,a_2 is the upper truncation point, a_1 is the lower truncation point, φ(x) is the density of the standard normal distribution, and Φ(x) is the distribution function of the standard normal distribution. For simData function, we consider a_1=log_2(\code{foldMin}) and a_2=Inf. This ensures that the biomarkers are differentially expressed by a fold change of foldMin or more.

Value

A dataframe of dimension nTrain by nBiom+1. The first column is a factor (class) representing the group memberships of the samples.

Author(s)

Mizanur Khondoker, Till Bachmann, Peter Ghazal
Maintainer: Mizanur Khondoker [e-mail].

References

Khondoker, M. R., Till T. Bachmann, T. T., Mewissen, M., Dickinson, P. et al.(2010). Multi-factorial analysis of class prediction error: estimating optimal number of biomarkers for various classification rules. Journal of Bioinformatics and Computational Biology, 8, 945-965.

See Also

classificationError

Examples

simData(nTrain=10,nBiom=3)

optBiomarker documentation built on Jan. 19, 2021, 1:06 a.m.