simulate.data: Simulate p-values and covariates under various scenarios.
In jchen1981/CAMT: Covariate Adaptive Multiple Testing

Description Usage Arguments Value Author(s) References Examples

The function simulates p-values and covariates under different signal structures (density and strength) and covariate models. It also allows special correlation structures among the p-values.

## S3 method for class 'data'
simulate(
  paras.mapping = paras.mapping.func(),
  covariate.strength = c("None", "Moderate", "Strong"),
  covariate.model = c("pi0", "f1", "both"),
  covariate.dist = c("Normal", "Uniform", "T"),
  null.model = c("Unif", "Left", "Right"),
  skewness = 0.15,
  f1.sd = 1,
  feature.no = 10000,
  sig.dist = c("Normal", "Gamma"),
  sig.density = c("Low", "Medium", "High"),
  sig.strength = c("L1", "L2", "L3", "L4", "L5", "L6", "L7", "L8"),
  cor.struct = c("None", "Block", "AR1"),
  cor.rho = 0,
  cor.sign = c("PosCor", "PosNegCor"),
  cor.nblock = 500
)

`paras.mapping`	a list with slots `'sig.strengths', 'sig.densities', 'pi.strengths', 'f1.strengths'`, which define the actual numeric values used for different levels of `'sig.strength', 'sig.density', 'covariate.strength'`. `'covariate.strength'` consists of both `'pi.strengths'` and `'f1.strengths'`. The mapping can be generated by using the `paras.mapping.func` function.
`covariate.strength`	a character string from `'None', 'Moderate', 'Strong'` indicating the covariate strength.
`covariate.model`	a character string from `'pi0', 'f1', 'both'` indicating whether the prior null proability, the alterantive distribution or both are affected by the covariate.
`covariate.dist`	a character string from `'Normal', 'Uniform', 'T'` indicating the distribution of the covariate. For t-distribution, a degree of freedom of five is used.
`null.model`	a character string from `'Unif', 'Left', 'Right'` indicating whether the null distribution of the p-value is uniform, left skewed or right skewed.
`skewness`	a numeric value indicating the skewness of the p-value distribution under the null (mean of the z-value)
`f1.sd`	a numeric value indicating the variance of the z-score under the alternative. Default is 1.
`feature.no`	an integar, the number of features to be simulated.
`sig.dist`	a character string from `'Normal', 'Gamma'` indicating the distribution of the z-value under alternative.
`sig.density`	a character string from `'Low', 'Medium', 'High'` indicating the level of signal density.
`sig.strength`	a character string from `'L1', 'L2', 'L3', 'L4', 'L5', 'L6', 'L7', 'L8'` indicating the level of signal strength.
`cor.struct`	a character string from `'None', 'Block', 'AR1'` indicating the correlation structure to be simulated including no correlation, block correlation and AR(1) correlation.
`cor.rho`	a numeric value giving the correlation coefficient for `'Block', 'AR1'`.
`cor.sign`	a character string from `'PosCor', 'PosNegCor'` indicating whether to simulate only positive or both postive and negative correlations.
`cor.nblock`	an integar, the number of blocks to be simulated for block correlation structure

A list with the elements

`pvals`	a numeric vector of p-values.
`pi0.var`	a vector of covariate values for the prior null probability.
`f1.var`	a vector of covariate values for the alternative distribution.
`pi0`	a vector of the simulated null probabilities.
`truth`	a vector simulated truth for H0 (=0) or H1 (=1).
`lfdr`	a vector of oracle LFDR based on the simulated pi0, f1.
`fdr`	a vector of oracle FDR based on LFDR.

Jun Chen

Xianyang Zhang, Jun Chen. Covariate Adaptive False Discovery Rate Control with Applications to Omics-Wide Multiple Testing. JASA. To appear.

data <- simulate.data(feature.no = 10000, covariate.strength = 'Moderate', covariate.model = 'pi0',
	sig.density = 'Medium', sig.strength = 'L3', cor.struct = 'None')
camt.fdr.obj <- camt.fdr(pvals = data$pvals, pi0.var = data$pi0.var, f1.var = data$f1.var, 
	alg.type = 'EM', control.method = 'knockoff+')
plot.camt.fdr(camt.fdr.obj, covariate = as.vector(rank(data$pi0.var)), covariate.name = 'Covariate rank',
	log = TRUE, file.name = 'CovariateModerate.pdf')