Inf.Dorf {binGroup}  R Documentation 
Find the optimal testing configuration for informative twostage hierarchical (Dorfman) testing
Description
Find the optimal testing configuration (OTC) for informative twostage hierarchical (Dorfman) testing and calculate the associated operating characteristics.
Usage
Inf.Dorf(p, Se, Sp, group.sz, obj.fn, weights = NULL, alpha = 2)
Arguments
p 
the probability of disease, which can be specified as an overall probability of disease, from which a heterogeneous vector of individual probabilities will be generated, or a heterogeneous vector of individual probabilities specified by the user. 
Se 
the sensitivity of the diagnostic test. 
Sp 
the specificity of the diagnostic test. 
group.sz 
a single block size for which to find the OTC out of all possible configurations, or a range of block 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. 
alpha 
a scale parameter for the beta distribution that specifies the degree of heterogeneity for the generated probability vector. If a heterogeneous vector of individual probabilities is specified by the user, alpha can be specified as NA or will be ignored. 
Details
This function finds the OTC and computes the associated operating characteristics for informative twostage hierarchical (Dorfman) testing, implemented via the poolspecific optimal Dorfman (PSOD) method described in McMahan et al. (2012). This function finds the optimal testing configuration by considering all possible testing configurations instead of using the greedy algorithm proposed for PSOD testing. 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) or McMahan et al. (2012) at http://chrisbilder.com/grouptesting for additional details on the implementation of informative twostage hierarchical (Dorfman) testing.
The value(s) specified by group.sz represent the overall block size used in the poolspecific optimal Dorfman (PSOD) method, where the overall group size is not tested. Instead, multiple initial pool sizes within this block are found and tested in the first stage of testing. The second stage of testing consists of individual retesting. For more details on informative twostage hierarchical testing implemented via the PSOD method, see Hitt et al. (2018) and McMahan et al. (2012).
If a single value is provided for group.sz, the OTC will be found over all possible testing 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 
the level of heterogeneity used to generate the vector of individual probabilities. 
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.
Dorfman, R. (1943). “The Detection of Defective Members of Large Populations.” The Annals of Mathematical Statistics, 14(4), 436–440. ISSN 00034851, doi: 10.1214/aoms/1177731363, https://www.jstor.org/stable/2235930.
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.
See Also
NI.Dorf
for noninformative twostage hierarchical (Dorfman)
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
, NI.A2M
,
NI.Array
, NI.D3
,
NI.Dorf
, OTC
Examples
# Find the OTC for informative twostage hierarchical
# (Dorfman) testing.
# 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 = 2. 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 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:
set.seed(9245)
Inf.Dorf(p=0.01, Se=0.95, Sp=0.95, group.sz=3:30,
obj.fn=c("ET", "MAR"), alpha=2)
## 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 i76500U processor.
set.seed(9245)
Inf.Dorf(p=0.01, Se=0.95, Sp=0.95, group.sz=5:10,
obj.fn=c("ET", "MAR"), alpha=2)
# Find the OTC for informative twostage hierarchical
# (Dorfman) testing, for a specified block size.
# This example uses rbeta() to generate random probabilities
# 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(8791)
Inf.Dorf(p=p.vec.func(p=0.03, alpha=0.5, grp.sz=50),
Se=0.90, Sp=0.90, group.sz=50, obj.fn=c("ET", "MAR", "GR"),
weights=matrix(data=c(1,1,10,10), nrow=2, ncol=2, byrow=TRUE),
alpha=NA)
## End(Not run)