simulation: Simulate p-values for two related experiments

In sdef: Synthesizing List of Differentially Expressed Features

Description

The function simulates two vectors of p-values using the procedure described in Hwang et al.

Usage

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

Arguments

n	Number of features to simulate
GammaA	Parameter of the Gamma distribution
GammaB	Parameter of the Gamma distribution
epsilonM	Parameter of the Gaussian noise specific to the genes and experiment
epsilonSD	Parameter of the Gaussian noise specific to the genes and experiment
r1	Additional experiment-specific noise
r2	Additional experiment-specific noise
DEfirst	Number of DE features in each experiment
DEsecond	Number of DE features in each experiment
DEcommon	Number of DE features in common between the two experiments

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 are the gene-experiment components. The former is assigned deterministically, whilst the latter is drawn from a standard Gaussian distribution. The log fold change (FC(gk)) is the sum of all these components for each gene and experiment. We assign the n genes to four groups: genes differentially expressed (DE) in both experiments, genes differentially expressed only in the first experiment, genes differentially expressed only in the second experiment and genes differentially expressed in neither experiment. When the genes are differentially expressed in both experiments, they share the same delta(g) and the only difference between them is given by the random components: FC(g1) = delta(g) + r(1) times epsilon(g1) FC(g2) = delta(g) + r(2) times epsilon(g2) This group represents the true positive genes (i.e. truly DE in both experiments) that we are interested in finding using our method. The two groups of genes differentially expressed only in one of the two experiments act like additional noise and make the simulation more realistic.

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))).

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-value for the experiments 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

data = simulation(n=500,GammaA=1,GammaB=1,
r1=0.5,r2=0.8,DEfirst=300,DEsecond=200,
DEcommon=100)

sdef documentation built on May 2, 2019, 8:55 a.m.