Sterrett {binGroup2} R Documentation

## Summary measures for Sterrett algorithms

### Description

Summary measures for Sterrett algorithms.

### Usage

```Sterrett(
p,
Sp,
Se,
plot = TRUE,
plot.cut.dorf = TRUE,
cond.prob.plot = FALSE,
font.name = "sans"
)
```

### Arguments

 `p` a vector of individual risk probabilities. `Sp` the specificity of the diagnostic test. `Se` the sensitivity of the diagnostic test. `plot` logical; if TRUE, a plot of the informative Sterrett CDFs will be displayed. Further details are given under 'Details'. `plot.cut.dorf` logical; if TRUE, the cut-tree for Dorfman testing will be displayed. Further details are given under 'Details'. `cond.prob.plot` logical; if TRUE, a second axis for the conditional probability plot will be displayed on the right side of the plot. `font.name` the name of the font to be used in plots.

### Details

This function calculates summary measures for informative Sterrett algorithms. Informative algorithms include one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman (two-stage hierarchical testing).

The mean and standard deviation of the number of tests, probability mass function (PMF), and cumulative distribution function (CDF) are calculated for all informative Sterrett algorithms and Dorfman testing. Conditional PMFs and conditional moments are calculated for all informative Sterrett algorithms. Subtracting the mean number of tests for two procedures gives the area difference between their CDFs. This area difference is calculated for each pairwise comparison of 1SIS, 2SIS, FIS, and Dorfman testing. CDF plots provide a visualization of how probabilities are distributed over the number of tests. CDFs that increase more rapidly to 1 correspond to more efficient retesting procedures.

Non-informative Sterrett (NIS) decodes positive groups by retesting individuals at random, so there are I! different possible NIS implementations. CDFs are found by permuting the elements in the vector of individual risk probabilities and using the FIS CDF expression without reordering the individual probabilities. That is, the FIS procedure uses the most efficient NIS implementation, which is to retest individuals in order of descending probabilities. When implementing the informative Sterrett algorithms with a large number of individuals, an algorithm is used to compute the PMF for the number of tests under FIS. This is done automatically by Sterrett for I>12. The algorithm is described in detail in the Appendix of Bilder et al. (2010).

### Value

A list containing:

 `mean.sd` a data frame containing the mean and standard deviation of the expected number of tests for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing. `PMF` a data frame containing the probability mass function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing. `CDF` a data frame containing the cumulative distribution function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing. `cond.PMF` a data frame containing the conditional probability mass function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), and full informative Sterrett (FIS) testing. `cond.moments` a data frame containing the mean and standard deviation of the conditional moments for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), and full informative Sterrett (FIS) testing. `save.diff.CDF` a data frame containing the sum of the differences in the cumulative distribution function for each pairwise comparison of one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing.

### Author(s)

This function was originally written as info.gt by Christopher Bilder for Bilder et al. (2010). The function was obtained from http://chrisbilder.com/grouptesting/. Minor modifications were made for inclusion of the function in the `binGroup2` package.

### References

Bilder, C., Tebbs, J., Chen, P. (2010). “Informative retesting.” Journal of the American Statistical Association, 105, 942–955. doi: 10.1198/jasa.2010.ap09231, https://doi.org/10.1198/jasa.2010.ap09231.

`expectOrderBeta` for generating a vector of individual risk probabilities for informative group testing and `opChar1` for calculating operating characteristics with hierarchical and array-based group testing algorithms.

Other operating characteristic functions: `halving()`, `operatingCharacteristics1()`, `operatingCharacteristics2()`

### Examples

```# Example 1: FIS provides the smallest mean
#   number of tests and the smallest standard
#   deviation. 2SIS has slightly larger mean
#   and standard deviation than FIS, but
#   its performance is comparable, indicating
#   2SIS may be preferred because it is
#   easier to implement.
set.seed(1231)
p.vec1 <- rbeta(n = 8, shape1 = 1, shape2 = 10)
save.it1 <- Sterrett(p = p.vec1, Sp = 0.90, Se = 0.95)
save.it1\$mean.sd

# Example 2: One individual is "high risk" and
#   the others are "low risk". Since there is
#   only one high-risk individual, the three
#   informative Sterrett procedures perform
#   similarly. All three informative Sterrett
#   procedures offer large improvements over
#   Dorfman testing.
p.vec2 <- c(rep(x = 0.01, times = 9), 0.5)
save.it2 <- Sterrett(p = p.vec2, Sp = 0.99, Se = 0.99,
cond.prob.plot = TRUE)
save.it2\$mean.sd

# Example 3: Two individuals are at higher
#   risk than the others. All three informative
#   Sterrett procedures provide large
#   improvements over Dorfman testing.
# Due to the large initial group size, an
#   algorithm (described in the Appendix of
#   Bilder et al. (2010)) is used for FIS.
#   The Sterrett() function does this
#   automatically for I>12.
p.vec3 <- c(rep(x = 0.01, times = 98), 0.1, 0.1)
save.it3 <- Sterrett(p = p.vec3, Sp = 0.99, Se = 0.99)
save.it3\$mean.sd
```

[Package binGroup2 version 1.1.0 Index]