Simulate p-values for two indipendent experiments

Description

The function simulate two vectors of p-values using the procedure described in Hwang et al. for independent experiments

Usage

1
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simulation.indep(n, GammaA = 2, GammaB = 2, epsilonM = 0,
epsilonSD = 1, r1, r2, DEfirst, DEsecond)

Arguments

n

Number of features to be simulated

GammaA

Parameter of the Gamma distribution

GammaB

Parameter of the Gamma distribution

epsilonM

Parameter of the Gaussian noise

epsilonSD

Parameter of the Gaussian noise

r1

Additional experiment-specific noise

r2

Additional experiment-specific noise

DEfirst

Number of DE features in the first experiment

DEsecond

Number of DE features in in the second experiment

Details

Considering two experiments (k=1,2), each of them with two classes, and n genes, for each gene we simulate a true difference between the classes delta(g), drawn from a Gamma distribution with random sign. The true difference delta(g) is 0 if the gene is not differentially expressed. We then add two normal random noise components, r[k] that act as experiment specific components and epsilon(gk), that is the gene-experiment components. The former is assigned deterministically, whilst the latter is drawn from a standard Gaussian distribution. So the log fold change (FC(gk)) is the sum of all these components for each gene and experiment. We divide the n genes in three groups: genes differentially expressed only in the first experiment, genes differentially expressed only in the second experiment and genes differentially expressed in neither experiment. There are not true positive genes (i.e. truly DE in both experiments), so we should find no genes in common using our method.

Then, as described in Hwang et al., a two tails T-test is performed for each FC(gk) and a p-value is generated as: P(gk) = 2 Normal cdf(-absolute value (FC(gk)/r(k))) where FC(gk) is the t statistic that evaluates the differential expression between the two classes for the g gene and k experiment.

Value

names

Which group each simulated gene expression value belongs to

FC1

T statistic for the first experiment

FC2

T statistic for the second experiment

Pval

p-values for the experiment to be compared

Author(s)

Alberto Cassese, Marta Blangiardo

References

Hwang D, Rust A, Ramsey S, Smith J, Leslie D, Weston A, de Atauri P, Aitchison J, Hood L, Siegel A, Bolouri H (2005): A data integration methodology for system biology. PNAS 2005.

M.Blangiardo and S.Richardson (2007) Statistical tools for synthesizing lists of differentially expressed features in related experiments, Genome Biology, 8, R54.

Examples

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data.indep = simulation.indep(n=500,GammaA=1,
GammaB=1,r1=0.5,r2=0.8,DEfirst=300,DEsecond=200)