OTC2 {binGroup2}  R Documentation 
Find the optimal testing configuration (OTC) using noninformative and informative hierarchical and arraybased group testing algorithms. Multiplex assays for two diseases are used at each stage of the algorithms.
OTC2( algorithm, p.vec = NULL, probabilities = NULL, alpha = NULL, Se, Sp, ordering = matrix(data = c(0, 1, 0, 1, 0, 0, 1, 1), nrow = 4, ncol = 2), group.sz, trace = TRUE, print.time = TRUE, ... )
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 with master pooling ("A2M"). Informative testing options include twostage hierarchical ("ID2") and threestage hierarchical ("ID3") testing. 
p.vec 
vector of overall joint probabilities. The joint probabilities are assumed to be equal for all individuals in the algorithm (noninformative testing only). There are four joint probabilities to consider: p_00, the probability that an individual tests negative for both diseases; p_10, the probability that an individual tests positive only for the first disease; p_01, the probability that an individual tests positive only for the second disease; and p_11, the probability that an individual tests positive for both diseases. The joint probabilities must sum to 1. Only one of p.vec, probabilities, or alpha should be specified. 
probabilities 
matrix of joint probabilities for each individual, where rows correspond to the four joint probabilities and columns correspond to each individual in the algorithm. Only one of p.vec, probabilities, or alpha should be specified. 
alpha 
vector containing positive shape parameters of the Dirichlet distribution (for informative testing only). The vector will be used to generate a heterogeneous matrix of joint probabilities for each individual. The vector must have length 4. Further details are given under 'Details'. Only one of p.vec, probabilities, or alpha should be specified. 
Se 
matrix of sensitivity values, where one value is given for each disease (or infection) at each stage of testing. The rows of the matrix correspond to each disease k=1,...,K, and the columns of the matrix correspond to each stage of testing s=1,...,S. If a vector of K values is provided, the sensitivity values associated with disease k are assumed to be equal to the kth value in the vector for all stages of testing. Further details are given under 'Details'. 
Sp 
matrix of specificity values, where one value is given for each disease (or infection) at each stage of testing. The rows of the matrix correspond to each disease k=1,...,K, and the columns of the matrix correspond to each stage of testing s=1,...,S. If a vector of K values is provided, the specificity values associated with disease k are assumed to be equal to the kth value in the vector for all stages of testing. Further details are given under 'Details'. 
ordering 
matrix detailing the ordering for the binary responses of the diseases. The columns of the matrix correspond to each disease and the rows of the matrix correspond to each of the 4 sets of binary responses for two diseases. This ordering is used with the joint probabilities. The default ordering is (p_00, p_10, p_01, p_11). 
group.sz 
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'. 
trace 
a logical value indicating whether the progress of calculations should be printed for each initial group size provided by the user. The default is TRUE. 
print.time 
a logical value indicating whether the length of time for calculations should be printed. The default is TRUE. 
... 
additional arguments to be passed to functions for hierarchical testing with multiplex assays for two diseases. 
This function finds the OTC for standard group testing algorithms with a multiplex assay that tests for two diseases and computes the associated operating characteristics. Calculations for hierarchical group testing algorithms are performed as described in Bilder et al. (2019) and calculations for arraybased group testing algorithms are performed as described in Hou et al. (2019).
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 hierarchical algorithms. Only noninformative group testing settings are allowed for array testing algorithms. Operating characteristics calculated are expected number of tests, pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value for each individual.
For informative algorithms where the alpha argument is specified, a
heterogeneous matrix of joint probabilities for each individual is generated
using the Dirichlet distribution. This is done using
rBeta2009::rdirichlet
and requires the user to set a seed to
reproduce results. See Bilder et al. (2019) for additional details on the
use of the Dirichlet distribution for this purpose.
The sensitivity/specificity values are allowed to vary across stages of testing. For hierarchical testing, a different sensitivity/specificity value may be used for each stage of testing. For array testing, a different sensitivity/specificity value may be used for master pool testing (if included), row/column testing, and individual testing. The values must be specified in the order of the testing performed. For example, values are specified as (stage 1, stage 2, stage 3) for threestage hierarchical testing or (master pool testing, row/column testing, individual testing) for array testing with master pooling. A vector of K sensitivity/specificity values may be specified, and sensitivity/specificity values for all stages of testing are assumed to be equal. The first value in the vector will be used at each stage of testing for the first disease, and the second value in the vector will be used at each stage of testing for the second disease.
The value(s) specified by group.sz represent the initial (stage 1) group size for hierarchical testing and the row/column size for array testing. If a single value is provided for group.sz with twostage hierarchical or array testing, operating characteristics will be calculated and no optimization will be performed. If a single value is provided for group.sz with threestage hierarchical, the OTC will be found over all possible configurations with this initial group size. If a range of group sizes is specified, the OTC will be found over all group sizes.
In addition to the OTC, operating characteristics for some of the other configurations corresponding to each initial group size provided by the user are displayed. For algorithms where there is only one configuration for each initial group size (noninformative twostage hierarchical and all array testing algorithms), results for each initial group size are provided. For algorithms where there is more than one possible configuration for each initial group size (informative twostage hierarchical and all threestage hierarchical algorithms), two sets of configurations are provided: 1) the best configuration for each initial group size, and 2) the top 10 configurations for each initial group size provided by the user. If a single value is provided for group.sz with array testing or noninformative twostage hierarchical testing, operating characteristics will not be provided for configurations other than that specified by the user. Results are sorted by the value of the objective function per individual, value.
The displayed overall 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 (or block) 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. (2019). These expressions are based on accuracy definitions
given by Altman and Bland (1994a, 1994b). Individual accuracy measures can
be calculated using the operatingCharacteristics2
(opChar2
) function.
A list containing:
algorithm 
the group testing algorithm used for calculations. 
prob.vec 
the vector of joint probabilities provided by the user, if applicable (for noninformative algorithms only). 
joint.p 
the matrix of joint probabilities for each individual provided by the user, if applicable. 
alpha.vec 
the alpha vector provided by the user, if applicable (for informative algorithms only). 
Se 
the matrix of sensitivity values for each disease at each stage of testing. 
Sp 
the matrix of specificity values for each disease at each stage of testing. 
opt.ET 
a list containing:

Configs 
a data frame containing results for the best configuration for each initial group size provided by the user. The columns correspond to the initial group size, configuration (if applicable), overall array size (if applicable), expected number of tests, value of the objective function per individual, and accuracy measures for each disease. Accuracy measures include the pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value. No results are displayed if a single group.sz is provided. Further details are given under 'Details'. 
Top.Configs 
a data frame containing results for some of the top configurations for each initial group size provided by the user. The columns correspond to the initial group size, configuration, expected number of tests, value of the objective function per individual, and accuracy measures for each disease. Accuracy measures include the pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value. No results are displayed for noninformative twostage hierarchical testing or for array testing algorithms. Further details are given under 'Details'. 
This function returns the pooling positive and negative predictive values for all individuals even though these measures are diagnostic specific; e.g., the pooling positive predictive value should only be considered for those individuals who have tested positive.
Additionally, only stage dependent sensitivity and specificity values are allowed within the program (no group within stage dependent values are allowed). See Bilder et al. (2019) for additional information.
This function was written by Brianna D. Hitt. It calls ET.all.stages.new and PSePSpAllStages, which were originally written by Christopher Bilder for Bilder et al. (2019), and ARRAY, which was originally written by Peijie Hou for Hou et al. (2020). The functions ET.all.stages.new, PSePSpAllStages, and ARRAY were obtained from http://chrisbilder.com/grouptesting/. Minor modifications were made to the functions for inclusion in the binGroup2 package.
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.
Bilder, C., Tebbs, J., McMahan, C. (2019). “Informative group testing for multiplex assays.” Biometrics, 75, 278–288. doi: 10.1111/biom.12988, https://doi.org/10.1111/biom.12988.
Hitt, B., Bilder, C., Tebbs, J., McMahan, C. (2019). “The objective function controversy for group testing: Much ado about nothing?” Statistics in Medicine, 38, 4912–4923. doi: 10.1002/sim.8341, https://doi.org/10.1002/sim.8341.
Hou, P., Tebbs, J., Wang, D., McMahan, C., Bilder, C. (2020). “Array testing with multiplex assays.” To appear in Biostatistics.
McMahan, C., Tebbs, J., Bilder, C. (2012a). “Informative Dorfman Screening.” Biometrics, 68, 287–296. doi: 10.1111/j.15410420.2011.01644.x, https://doi.org/10.1111/j.15410420.2011.01644.x.
Other OTC functions:
OTC1()
Other multiplex testing functions:
operatingCharacteristics2()
# Estimated running time for all examples was calculated # using a computer with 16 GB of RAM and one core of # an Intel i76500U processor. Please take this into # account when interpreting the run times given. # Find the OTC for noninformative twostage # hierarchical (Dorfman) testing Se < matrix(data = c(0.95, 0.95, 0.99, 0.99), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) Sp < matrix(data = c(0.96, 0.96, 0.98, 0.98), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) OTC2(algorithm = "D2", p.vec = c(0.90, 0.04, 0.04, 0.02), Se = Se, Sp = Sp, group.sz = 2:30) # Find the OTC over all possible testing configurations # for informative twostage hierarchical (Dorfman) # testing with a specified group size. # A matrix of joint probabilities for each individual is # generated using the Dirichlet distribution. # This examples takes approximately 25 seconds to run. Se < matrix(data = rep(0.95, 4), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) Sp < matrix(data = rep(0.99, 4), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) set.seed(1002) OTC2(algorithm = "ID2", alpha = c(18.25, 0.75, 0.75, 0.25), Se = Se, Sp = Sp, group.sz = 10:20) # Find the OTC for noninformative threestage # hierarchical testing. # This example takes approximately 1 minute to run. Se < matrix(data = rep(0.95, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) Sp < matrix(data = rep(0.99, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) OTC2(algorithm = "D3", p.vec = c(0.95, 0.02, 0.02, 0.01), Se = Se, Sp = Sp, group.sz = 3:20) # Find the OTC over all possible configurations # for informative threestage hierarchical # testing with a specified group size # and a heterogeneous matrix of joint # probabilities for each individual. set.seed(8791) Se < matrix(data = rep(0.95, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) Sp < matrix(data = rep(0.99, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) p.unordered < t(rBeta2009::rdirichlet(n = 12, shape = c(18.25, 0.75, 0.75, 0.25))) p.ordered < p.unordered[, order(1  p.unordered[1,])] OTC2(algorithm = "ID3", probabilities = p.ordered, Se = Se, Sp = Sp, group.sz = 12, trace = FALSE, print.time = FALSE) # Find the OTC for noninformative array testing # without master pooling. Se < matrix(data = rep(0.95, 4), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) Sp < matrix(data = rep(0.99, 4), nrow = 2, ncol = 2, dimnames = list(Infection = 1:2, Stage = 1:2)) OTC2(algorithm = "A2", p.vec = c(0.90, 0.04, 0.04, 0.02), Se = Se, Sp = Sp, group.sz = 2:12) # Find the OTC for noninformative array testing # with master pooling. Se < matrix(data = rep(0.95, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) Sp < matrix(data = rep(0.99, 6), nrow = 2, ncol = 3, dimnames = list(Infection = 1:2, Stage = 1:3)) OTC2(algorithm = "A2M", p.vec = c(0.90, 0.04, 0.04, 0.02), Se = Se, Sp = Sp, group.sz = 10, trace = FALSE, print.time = FALSE)