The goal of *FDRsamplesize2* is to computer the average power and
determine the sample size needed to achieve desired FDR and desired
average power. For power calculation, the package covers various
statistical test settings,including:

- two-samples $t$-test
- one-sample $t$-test
- rank-sum test
- signed-rank test
- Fisher’s exact test
- the $t$-test for correlation
- comparison of two Poisson distributions
- comparison of two negative binomial distributions
- the two-proportions $z$-test
- one-way ANOVA
- Cox proportional hazards regression

You can install *FDRsamplesize2* from github:

```
# install.packages("devtools")
devtools::install_github("yonghui-ni/FDRsamplesize_2.0")
```

Or from CRAN:

```
install.packages("FDEsamplesize2")
```

load the package

```
library("FDRsamplesize2")
```

This is an example which shows you how to determine the sample size necessary to identify genes with microarray expression signals that are associated with progression-free survival. A single-predictor Cox regression model will be used to test the association of each gene’s expression with progression-free survival (PFS). We are interested in determining the number of events necessary to identify 80% of genes truly associate with PFS while controlling the FDR at 10% in a setting in which 1% of the genes have a hazard ratio of 2 and a variance of 1.

```
log.HR=log(rep(c(1,2),c(9900,100))) # log hazard ratio for each gene
v=rep(1,10000) # variance of each gene
res=n.fdr.coxph(fdr=0.1, pwr=0.8,logHR=log.HR, v=v, pi0.hat="BH")
res
#> $n
#> [1] 37
#>
#> $computed.avepow
#> [1] 0.8139159
#>
#> $desired.avepow
#> [1] 0.8
#>
#> $desired.fdr
#> [1] 0.1
#>
#> $input.pi0
#> [1] 0.99
#>
#> $alpha
#> [1] 0.0008879023
#>
#> $n0
#> [1] 36
#>
#> $n1
#> [1] 37
#>
#> $n.its
#> [1] 7
#>
#> $max.its
#> [1] 50
```

Step by step to calculate power and sample size. This procedure is more
flexible for user to plug in average power function of other statistical
tests that are not available in *FDRsamplesize2*.

```
pi0=9900/10000 # proportion of true null hypothesis
adj.p=alpha.power.fdr(fdr=0.1,
pwr=0.8,
pi0=pi0,
method="BH")
print(adj.p)
#> [1] 0.0008879023
find.sample.size(alpha=adj.p, # Fixed p-value threshold
pwr=0.8, # Power of single α-level test
avepow.func=average.power.coxph, # an R function to compute average power
n0=3, # Lower limit for initial sample size range
n1=6, # Upper limit for initial sample size range
logHR=log(rep(c(1,2),c(9900,100))),
v=rep(1,10000),
max.its=50 # Maximum number of iterations, default is 50
)
#> $n
#> [1] 37
#>
#> $computed.avepow
#> [1] 0.8139159
#>
#> $desired.avepow
#> [1] 0.8
#>
#> $alpha
#> [1] 0.0008879023
#>
#> $n.its
#> [1] 7
#>
#> $max.its
#> [1] 50
#>
#> $n0
#> [1] 36
#>
#> $n1
#> [1] 37
```

To get the fixed p-value threshold $\alpha$ in *alpha.power.fdr*
function for multiple testing procedure, approximation method options
include:

- Benjamini and Hochberg 1995 (BH)
- Jung 2005 (Jung)
- p-value histogram height (HH)
- p-value histogram mean (HM)

- 0.2.0 version:

add fdr.avepow() to compute FDR and average power for a given sample size and effect size vector;

add fdr.power.alpha() to compute FDR for given p-value threshold, average power and proportion of tests with a true null

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