farm.FDR: Control FDR given a list of pvalues
In kbose28/farmtest: Factor Adjusted Robust Multiple Testing

Description Usage Arguments Details Value References Examples

Given a list of p-values, this function conducts multiple testing and outputs the indices of the rejected hypothesis. Uses an adaptive Benjamini-Hochberg (BH) procedure where the proportion of true nulls π_0 is estimated. This estimation is done based on the pi0est function in the qvalue package. See Storey(2015).

1
2
3

farm.FDR(pvalue, alpha = NULL, type = c("mBH", "BH"), lambda = seq(0.05,
  0.95, 0.05), pi0.method = c("smoother", "bootstrap"), smooth.df = 3,
  smooth.log.pi0 = FALSE)

`pvalue`	a vector of p-values obtained from multiple testing
`alpha`	an optional significance level for testing (in decimals). Default is 0.05. Must be in (0,1).
`type`	an optional character string specifying the type of test. The default is the modified BH procedure (type = "mBH"). The usual BH procedure is also available (type = "BH"). See Benjamini and Hochberg (1995).
`lambda`	an optional threshold for estimating the proportion of true null hypotheses π_0. Must be in [0,1).
`pi0.method`	optional, either "smoother" or "bootstrap"; the method for automatically choosing tuning parameter in the estimation of π_0, the proportion of true null hypotheses.
`smooth.df`	an optional number of degrees-of-freedom to use when estimating π_0 with a smoother.
`smooth.log.pi0`	an optional TRUE/FALSE. If TRUE and pi0.method = "smoother", π_0 will be estimated by applying a smoother to a scatterplot of \log(π_0) estimates against the tuning parameter lambda. Default is FALSE.

The "mBH" procedure is simply the regular Benjamini-Hochberg pocedure, but in the rejection threshold the denominator p is replaced by π_0 * p. This is a less conservative approach. See Storey (2002).

`rejected`	the indices of rejected hypotheses, along with their corresponding p values, and adjusted p values, ordered from most significant to least significant
`alldata`	all the indices of the tested hypotheses, along with their corresponding p values, adjusted p values, and a column with 1 if declared siginificant and 0 if not
`significant`	The number of hypotheses rejected

Benjamini, Y. and Hochberg, Y. (1995). "Controlling the False Discovery Rate: A Practical and PowerfulApproach to Multiple Testing." Journal of the Royal Statistical Society B, 51, 289–300.

Storey, J.D. (2015). "qvalue: Q-value estimation for false discovery rate control. R package version 2.8.0, https://github.com/jdstorey/qvalue.

Storey, J.D. (2002). " Direct Approach to False Discovery Rates." Journal of the Royal Statistical Society B, 64(3), 479–498.

set.seed(100)
Y = matrix(rnorm(1000, 0, 1),10)
pval = apply(Y, 1, function(x) t.test(x)$p.value)
farm.FDR(pval, 0.05)
farm.FDR(pval, 0.01, type = "BH")