## Introduction

This illustrates the RJafroc implementation of sample-size estimation. Default $$\alpha$$ is 0.05 and default power (1-$$\beta$$) is 0.8. Three functions are provided. Each of these functions can be used with method "DBM" (illustrated here, the default) or method = "OR" (next vignette). Illustrated below, for the most part, is the random-reader random-case (RRRC) option, i.e., analysisOption = "RRRC". The last two examples illustrate fixed-reader random-case (FRRC) analysisOption = "FRRC" and random-reader fixed-case (RRFC) analysisOption = "RRFC" options.

• SsPowerGivenJK() Statistical power for specified numbers of readers and cases in an ROC study.
• SsPowerTable() Generate a power table, i.e., combinations of numbers of readers and cases yielding the desired power.
• SsSampleSizeKGivenJ Number of cases, for specified number of readers, to achieve desired power.

## Illustration of SsPowerGivenJK() using method = "DBM"

The selected dataset corresponds to the Van Dyke data.

power <- SsPowerGivenJK(dataset02, FOM = "Wilcoxon", J = 6, K = 112, analysisOption = "RRRC")

The returned value is a list containing the expected power power, the non-centrality parameter ncp, the denominator degrees of freedom ddf and the F-statistic f. The numerator degrees of freedom ndf is always I - 1, i.e., unity for this dataset.

str(power)
#> 'data.frame':    1 obs. of  4 variables:
#>  $powerRRRC: num 0.556 #>$ ncpRRRC  : num 4.8
#>  $df2RRRC : num 23.1 #>$ fRRRC    : num 4.28

Expected power is 0.55557885.

## Illustration of SsPowerTable() using method = "DBM"

powTab <- SsPowerTable(dataset02, FOM = "Wilcoxon", analysisOption = "RRRC")

Now show the power table powTab. Note that the last column is always close to 0.8, the desired power. The 2nd and 3rd columns show the number of readers and number of cases to achieve the desired power.

powTab
#>  $powerFRRC: num 0.801 The required number of cases is 131 and expected power is 0.80091813. Compare the number of cases to the FRRC value used in vignette 2. ### RRFC ncases <- SsSampleSizeKGivenJ(dataset02, FOM = "Wilcoxon", J = 10, method = "DBM", analysisOption = "RRFC") str(ncases) #> 'data.frame': 1 obs. of 2 variables: #>$ KRRFC    : num 53
#>  \$ powerRRFC: num 0.805

The required number of cases is 53 and expected power is 0.80496663. Compare the number of cases to the RRFC value used in vignette 2.