NI.D3: Find the optimal testing configuration for non-informative...
In binGroup: Evaluation and Experimental Design for Binomial Group Testing

Description Usage Arguments Details Value Author(s) References See Also Examples

Find the optimal testing configuration (OTC) for non-informative three-stage hierarchical testing and calculate the associated operating characteristics.

1	NI.D3(p, Se, Sp, group.sz, obj.fn, weights = NULL)

`p`	the probability of disease, which can be specified as an overall probability of disease or a homogeneous vector of individual probabilities.
`Se`	the sensitivity of the diagnostic test.
`Sp`	the specificity of the diagnostic test.
`group.sz`	a single group size over which to find the OTC out of all possible testing configurations, or a range of group sizes over which to find the OTC.
`obj.fn`	a list of objective functions which are minimized to find the OTC. The expected number of tests per individual, "`ET`", will always be calculated. Additional options include "`MAR`" (the expected number of tests divided by the expected number of correct classifications, described in Malinovsky et al. (2016)), and "`GR`" (a linear combination of the expected number of tests, the number of misclassified negatives, and the number of misclassified positives, described in Graff & Roeloffs (1972)). See Hitt et al. (2018) at http://chrisbilder.com/grouptesting for additional details.
`weights`	a matrix of up to six sets of weights for the GR function. Each set of weights is specified by a row of the matrix.

This function finds the OTC and computes the associated operating characteristics for non-informative three-stage hierarchical testing, by considering all possible testing configurations. Operating characteristics calculated are expected number of tests, pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value for the algorithm. See Hitt et al. (2018) at http://chrisbilder.com/grouptesting or Kim et al. (2007) for additional details on the implementation of non-informative three-stage hierarchical testing.

The value(s) specified by group.sz represent the initial (stage 1) group size. If a single value is provided for group.sz, the OTC will be found over all possible testing configurations for that initial group size. If a range of group sizes is specified, the OTC will be found over all group sizes.

The displayed pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value are weighted averages of the corresponding individual accuracy measures for all individuals within the initial group for a hierarchical algorithm. Expressions for these averages are provided in the Supplementary Material for Hitt et al. (2018). These expressions are based on accuracy definitions given by Altman and Bland (1994a, 1994b).

A list containing:

`prob`	the probability of disease, as specified by the user.
`Se`	the sensitivity of the diagnostic test.
`Sp`	the specificity of the diagnostic test.
`opt.ET, opt.MAR, opt.GR`	a list for each objective function specified by the user, containing: OTC a list specifying elements of the optimal testing configuration, which include: Stage1 pool size for the first stage of testing, i.e. the initial group size. Stage2 pool sizes for the second stage of testing. p.vec the vector of individual probabilities ET the expected testing expenditure for the OTC. value the value of the objective function per individual. PSe the overall pooling sensitivity for the algorithm. Further details are given under 'Details'. PSp the overall pooling specificity for the algorithm. Further details are given under 'Details'. PPPV the overall pooling positive predictive value for the algorithm. Further details are given under 'Details'. PNPV the overall pooling negative predictive value for the algorithm. Further details are given under 'Details'.

Brianna D. Hitt

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Altman1994abinGroup

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Altman1994bbinGroup

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Graff1972binGroup

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Hitt2018binGroup

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Kim2007binGroup

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Malinovsky2016binGroup

Inf.D3 for informative three-stage hierarchical testing, NI.Dorf for non-informative two-stage hierarchical (Dorfman) testing, Inf.Dorf for informative two-stage hierarchical testing, and OTC for finding the optimal testing configuration for a number of standard group testing algorithms.

http://chrisbilder.com/grouptesting

Other OTC functions: Inf.Array, Inf.D3, Inf.Dorf, NI.A2M, NI.Array, NI.Dorf, OTC

# Find the OTC for non-informative three-stage 
#   hierarchical testing over a range of group sizes.
# This example takes approximately 20 seconds to run.
# Estimated running time was calculated using a 
#   computer with 16 GB of RAM and one core of an 
#   Intel i7-6500U processor.
## Not run: 
NI.D3(p=0.02, Se=0.90, Sp=0.90, group.sz=3:30, 
obj.fn=c("ET", "MAR"))
## End(Not run)

# This example takes less than 1 second to run.
# Estimated running time was calculated using a 
#   computer with 16 GB of RAM and one core of an 
#   Intel i7-6500U processor.
NI.D3(p=0.02, Se=0.90, Sp=0.90, group.sz=3:12, 
obj.fn=c("ET", "MAR"))

# Find the OTC out of all possible configurations for 
#   a specified group size for non-informative
#   three-stage hierarchical testing.
# This example takes less than 1 second to run.
# Estimated running time was calculated using a 
#   computer with 16 GB of RAM and one core of an 
#   Intel i7-6500U processor.
NI.D3(p=rep(0.005, 15), Se=0.99, Sp=0.99, group.sz=15,
obj.fn=c("ET", "MAR", "GR"), weights=matrix(data=c(1,1,10,10), 
nrow=2, ncol=2, byrow=TRUE))