OTC {binGroup}  R Documentation 
Find the optimal testing configuration
Description
Find the optimal testing configuration (OTC) for standard group testing algorithms and calculate the associated operating characteristics.
Usage
OTC(algorithm, p = NULL, probabilities = NULL, Se = 0.99, Sp = 0.99,
group.sz, obj.fn = c("ET", "MAR"), weights = NULL, alpha = 2)
Arguments
algorithm 
character string defining the group testing algorithm to be used. Noninformative testing options include twostage hierarchical ("D2"), threestage hierarchical ("D3"), square array testing without master pooling ("A2"), and square array testing without master pooling ("A2M"). Informative testing options include twostage hierarchical ("ID2"), threestage hierarchical ("ID3"), and square array testing without master pooling ("IA2"). 
p 
overall probability of disease that will be used to generate a
vector/matrix of individual probabilities. For noninformative algorithms, a
homogeneous set of probabilities will be used. For informative algorithms, the

probabilities 
a vector of individual probabilities, which is homogeneous for noninformative testing algorithms and heterogeneous for informative testing algorithms. Either p or probabilities should be specified, but not both. 
Se 
the sensitivity of the diagnostic test. 
Sp 
the specificity of the diagnostic test. 
group.sz 
a single group size or range of group sizes for which to calculate operating characteristics and/or find the OTC. The details of group size specification are given under 'Details'. 
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. 
alpha 
a shape parameter for the beta distribution that specifies the degree of heterogeneity for the generated probability vector (for informative testing only). 
Details
This function finds the OTC and computes the associated operating characteristics for standard group testing algorithms, as described in Hitt et al. (2018) at http://chrisbilder.com/grouptesting.
Available algorithms include two and threestage hierarchical testing and array testing with and without master pooling. Both noninformative and informative group testing settings are allowed for each algorithm, except informative array testing with master pooling is unavailable because this method has not appeared in the group testing literature. Operating characteristics calculated are expected number of tests, pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value for each individual.
The value(s) specified by group.sz represent the initial (stage 1) group size for threestage hierarchical testing and noninformative twostage hierarchical testing. For informative twostage hierarchical testing, the group.sz specified represents the block size used in the poolspecific optimal Dorfman (PSOD) method, where the initial group (block) is not tested. For more details on informative twostage hierarchical testing implemented via the PSOD method, see Hitt et al. (2018) and McMahan et al. (2012a). For array testing without master pooling, the group.sz specified represents the row/column size for initial (stage 1) testing. For array testing with master pooling, the group.sz specified represents the row/column size for stage 2 testing. The group size for initial testing is overall array size, given by the square of the row/column size.
If a single value is provided for group.sz with array testing or noninformative twostage hierarchical testing, operating characteristics will be calculated and no optimization will be performed. If a single value is provided for group.sz with threestage hierarchical or informative twostage hierarchical, the OTC will be found over all possible configurations. 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, or within the entire array for an arraybased 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).
Value
A list containing:
prob 
the probability of disease, as specified by the user. 
alpha 
level of heterogeneity for the generated probability vector (for informative testing only). 
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:

Author(s)
Brianna D. Hitt
References
Altman, D., Bland, J. (1994). “Diagnostic tests 1: sensitivity and specificity.” BMJ, 308, 1552.
Altman, D., Bland, J. (1994). “Diagnostic tests 2: predictive values.” BMJ, 309, 102.
Graff, L., Roeloffs, R. (1972). “Group testing in the presence of test error; an extension of the Dorfman procedure.” Technometrics, 14(1), 113–122. ISSN 15372723, doi: 10.1080/00401706.1972.10488888, https://www.tandfonline.com/doi/abs/10.1080/00401706.1972.10488888.
Hitt, B., Bilder, C., Tebbs, J., McMahan, C. (2018). “The Optimal Group Size Controversy for Infectious Disease Testing: Much Ado About Nothing?!” Manuscript submitted for publication.
Malinovsky, Y., Albert, P., Roy, A. (2016). “Reader reaction: A note on the evaluation of group testing algorithms in the presence of misclassification.” Biometrics, 72(1), 299–302. ISSN 15410420, doi: 10.1111/biom.12385.
McMahan, C., Tebbs, J., Bilder, C. (2012). “Informative Dorfman Screening.” Biometrics, 68(1), 287–296. ISSN 0006341X, doi: 10.1111/j.15410420.2011.01644.x.
McMahan, C., Tebbs, J., Bilder, C. (2012). “TwoDimensional Informative Array Testing.” Biometrics, 68(3), 793–804. ISSN 0006341X, doi: 10.1111/j.15410420.2011.01726.x.
See Also
NI.Dorf
for noninformative twostage (Dorfman) testing, Inf.Dorf
for
informative twostage (Dorfman) testing, NI.D3
for noninformative threestage
hierarchical testing, Inf.D3
for informative threestage hierarchical testing,
NI.Array
for noninformative array testing, Inf.Array
for informative
array testing, and NI.A2M
for noninformative array testing with master pooling.
http://chrisbilder.com/grouptesting
Other OTC functions: Inf.Array
,
Inf.D3
, Inf.Dorf
,
NI.A2M
, NI.Array
,
NI.D3
, NI.Dorf
Examples
# Find the OTC for noninformative
# twostage hierarchical (Dorfman) 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 i76500U processor.
OTC(algorithm="D2", p=0.05, Se=0.99, Sp=0.99, group.sz=2:100,
obj.fn=c("ET", "MAR"))
# Find the OTC for informative
# twostage hierarchical (Dorfman) testing, implemented
# via the poolspecific optimal Dorfman (PSOD) method
# described in McMahan et al. (2012a), where the greedy
# algorithm proposed for PSOD is replaced by considering
# all possible testing configurations.
# A vector of individual probabilities is generated using
# the expected value of order statistics from a beta
# distribution with p = 0.01 and a heterogeneity level
# of alpha = 0.5. Depending on the specified probability,
# alpha level, and overall group size, simulation may
# be necessary in order to generate the vector of individual
# probabilities. This is done using p.vec.func() and
# requires the user to set a seed in order to reproduce
# results.
# This example takes approximately 2.5 minutes to run.
# Estimated running time was calculated using a
# computer with 16 GB of RAM and one core of an
# Intel i76500U processor.
## Not run:
set.seed(52613)
OTC(algorithm="ID2", p=0.01, Se=0.95, Sp=0.95, group.sz=50,
obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1, 1, 10, 10, 0.5, 0.5),
nrow=3, ncol=2, byrow=TRUE), alpha=0.5)
## End(Not run)
# Find the OTC over all possible
# testing configurations for a specified group size for
# noninformative threestage hierarchical testing
# This example takes approximately 1 second to run.
# Estimated running time was calculated using a
# computer with 16 GB of RAM and one core of an
# Intel i76500U processor.
OTC(algorithm="D3", p=0.001, Se=0.95, Sp=0.95, group.sz=18,
obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1, 1), nrow=1, ncol=2, byrow=TRUE))
# Find the OTC for noninformative
# threestage hierarchical testing
# 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 i76500U processor.
## Not run:
OTC(algorithm="D3", p=0.06, Se=0.90, Sp=0.90,
group.sz=3:30, obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1, 1, 10, 10, 100, 100),
nrow=3, ncol=2, byrow=TRUE))
## End(Not run)
# Find the OTC over all possible configurations
# for a specified group size, given a
# heterogeneous vector of probabilities.
# 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 i76500U processor.
OTC(algorithm="ID3", probabilities=c(0.012, 0.014, 0.011,
0.012, 0.010, 0.015), Se=0.99, Sp=0.99, group.sz=6,
obj.fn=c("ET","MAR","GR"), weights=matrix(data=c(1, 1),
nrow=1, ncol=2, byrow=TRUE), alpha=0.5)
# Calculate the operating characteristics for a specified array size
# for noninformative array testing without master pooling
# 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 i76500U processor.
OTC(algorithm="A2", p=0.005, Se=0.95, Sp=0.95, group.sz=8,
obj.fn=c("ET", "MAR"))
# Find the OTC for informative array testing without
# master pooling
# A vector of individual probabilities is generated using
# the expected value of order statistics from a beta
# distribution with p = 0.03 and a heterogeneity level
# of alpha = 2. The probabilities are then arranged in
# a matrix using the gradient method described in
# McMahan et al. (2012b). Depending on the specified
# probability, alpha level, and overall group size,
# simulation may be necessary in order to generate the
# vector of individual probabilities. This is done using
# p.vec.func() and requires the user to set a
# seed in order to reproduce results.
# This example takes approximately 30 seconds to run.
# Estimated running time was calculated using a
# computer with 16 GB of RAM and one core of an
# Intel i76500U processor.
## Not run:
set.seed(1002)
OTC(algorithm="IA2", p=0.03, Se=0.95, Sp=0.95,
group.sz=3:20, obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1, 1, 10, 10, 100, 100),
nrow=3, ncol=2, byrow=TRUE), alpha=2)
## End(Not run)
# Find the OTC for noninformative array testing
# with master pooling
# 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 i76500U processor.
## Not run:
OTC(algorithm="A2M", p=0.02, Se=0.90, Sp=0.90,
group.sz=3:20, obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1, 1, 10, 10, 0.5, 0.5, 2, 2,
100, 100, 10, 100), nrow=6, ncol=2, byrow=TRUE))
## End(Not run)