NI.Dorf {binGroup}  R Documentation 
Find the optimal testing configuration for noninformative twostage hierarchical testing
Description
Find the optimal testing configuration (OTC) for noninformative twostage hierarchical (Dorfman) testing and calculate the associated operating characteristics.
Usage
NI.Dorf(p, Se, Sp, group.sz, obj.fn, weights = NULL)
Arguments
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 for which to calculate operating characteristics, or a range of group sizes over which to 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. 
Details
This function finds the OTC and computes the associated operating characteristics for noninformative twostage hierarchical (Dorfman) 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) at http://chrisbilder.com/grouptesting, Dorfman (1943), or Kim et al. (2007) for additional details on the implementation of noninformative twostage 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, operating characteristics will be calculated and no optimization will be performed. 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).
Value
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:

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.
Kim, H., Hudgens, M., Dreyfuss, J., Westreich, D., Pilcher, C. (2007). “Comparison of group testing algorithms for case identification in the presence of test error.” Biometrics, 63(4), 1152–1163. ISSN 0006341X, doi: 10.1111/j.15410420.2007.00817.x.
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.
See Also
Inf.Dorf
for informative twostage hierarchical (Dorfman) testing,
NI.D3
for noninformative threestage hierarchical testing,
Inf.D3
for informative threestage 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.D3
, OTC
Examples
# Find the OTC for noninformative twostage
# hierarchical (Dorfman) testing over a range
# of group sizes.
# 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.
NI.Dorf(p=0.01, Se=0.95, Sp=0.95, group.sz=2:100,
obj.fn=c("ET", "MAR"))
# Calculate the operating characteristics for a specified
# initial group size 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.
NI.Dorf(p=rep(0.025, 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))