CLfdr: Conditional local FDR (CLfdr)
In calm: Covariate Assisted Large-scale Multiple testing

Description Usage Arguments Details Value Author(s) References Examples

View source: R/CLfdr.R

CLfdr returns the local false discovery rate (FDR) conditional on auxiliary covariate information

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CLfdr(x, y, pval = NULL, pi0.method = "RB", bw.init = NULL,
    bw = NULL, reltol = 1e-04, n.subsample = NULL, check.gam = FALSE,
    k.gam = NULL, info = TRUE)

`x`	covariates, could be a vector of length m or a matrix with m rows.
`y`	a vector of z-values of length m.
`pval`	a vector of p-values of length m. The p-values are only used to computed the overall true null proportion when `pi0.method`="RB".
`pi0.method`	method to estimate the overall true null proportion (pi0). "RB" for the right-boundary procedure (Liang and Nettleton, 2012, JRSSB) or "JC" (Jin and Cai, 2007, JASA).
`bw.init`	initial values for bandwidth, optional. If not specified, normal-reference rule will be used.
`bw`	bandwidth values.
`reltol`	relative tolerance in optim function.
`n.subsample`	size of the subsample when esitmating bandwidth.
`check.gam`	indicator to perform gam.check function on the nonparametric fit.
`k.gam`	tuning parameter for mgcv::gam.
`info`	indicator to print out fitting information.

In many multiple testing applications, the auxiliary information is widely available and can be useful. Such information can be summary statistics from a similar experiment or disease, the lengths of gene coding regions, and minor allele frequencies of SNPs.

y is a vector of m z-values, one of each hypothesis under test. The z-values follow N(0,1) if their corresponding null hypotheses are true. Other types of test statistics, such as t-statistics and p-values can be transformed to z-values. In practice, if the distribution of z-values is far from N(0,1), recentering and rescaling of the z-values may be necessary.

x contains auxiliary covariate information. For a single covariate, x should be a vector of length m. For multiple covariates, x should be a matrix with m rows. The covariates can be either continuous or ordered.

pi0.method specifies the method used to estimate the overall true null proportion. If the z-values are generated from the normal means model, the "JC" method from Jin and Cai (2007) JASA can be a good candidate. Otherwise, the right-boundary procedure ("RB", Liang and Nettleton, 2012, JRSSB) is used.

bw are bandwidth values for estimating local alternative density. Suppose there are p covariates, then bw should be a vector of p+1 positive numerical values. By default, these bandwidth values are chosen by cross-validation to minimize a certain error measure. However, finding the optimal bandwidth values by cross-validation can be computationally intensive, especially when p is not small. If good estimates of bandwidth values are available, for example, from the analysis of a similar dataset, the bandwidth values can be specified explicitly to save time.

reltol specifies the relative convergence tolerance when choosing the bandwidth values (bw). It will be passed on to stats::optim(). For most analyses, the default value of 1e-4 provides reasonably good results. A smaller value such as 1e-5 or 1e-6 could be used for further improvement at the cost of more computation time.

`fdr`	a vector of local FDR estimates. fdr[i] is the posteiror probability of the ith null hypothesis is true given all the data. 1-fdr[i] is the posterior probability of being a signal (the corresponding null hypothesis is false).
`FDR`	a vector of FDR values (q-values), which can be used to control FDR at a certain level by thresholding the FDR values.
`pi0`	a vector of true null probability estimates. This contains the prior probabilities of being null.
`bw`	a vector of bandwidths for conditional alternative density estimation
`fit.gam`	an object of mgcv::gam

Kun Liang, kun.liang@uwaterloo.ca

Liang (2019), Empirical Bayes analysis of RNA sequencing experiments with auxiliary information, to appear in Annals of Applied Statistics

data(pso)
ind.nm <- is.na(pso$tval_mic)
x <- pso$len_gene[ind.nm]
# normalize covariate
x <- rank(x)/length(x)
y <- pso$zval[ind.nm]
# assign names to the z-values helps to give names to the output variables
names(y) <- row.names(pso)[ind.nm]

fit.nm <- CLfdr(x=x, y=y)
fit.nm$fdr[1:5]