Summary measures for Sterrett algorithms.
Sterrett(
p,
Sp,
Se,
plot = FALSE,
plot.cut.dorf = FALSE,
cond.prob.plot = FALSE,
font.name = "sans"
)a vector of individual risk probabilities.
the specificity of the diagnostic test.
the sensitivity of the diagnostic test.
logical; if TRUE, a plot of the informative Sterrett CDFs will be displayed. Further details are given under 'Details'.
logical; if TRUE, the cut-tree for Dorfman testing will be displayed. Further details are given under 'Details'.
logical; if TRUE, a second axis for the conditional probability plot will be displayed on the right side of the plot.
the name of the font to be used in plots.
A list containing:
a data frame containing the mean and standard deviation of the expected number of tests for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing.
a data frame containing the probability mass function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing.
a data frame containing the cumulative distribution function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing.
a data frame containing the conditional probability mass function for the number of tests possible for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), and full informative Sterrett (FIS) testing.
a data frame containing the mean and standard deviation of the conditional moments for one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), and full informative Sterrett (FIS) testing.
a data frame containing the sum of the differences in the cumulative distribution function for each pairwise comparison of one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman testing.
a vector containing the probabilities of positivity for each individual.
This function calculates summary measures for informative Sterrett algorithms. Informative algorithms include one-stage informative Sterrett (1SIS), two-stage informative Sterrett (2SIS), full informative Sterrett (FIS), and Dorfman (two-stage hierarchical testing).
The mean and standard deviation of the number of tests, probability mass function (PMF), and cumulative distribution function (CDF) are calculated for all informative Sterrett algorithms and Dorfman testing. Conditional PMFs and conditional moments are calculated for all informative Sterrett algorithms. Subtracting the mean number of tests for two procedures gives the area difference between their CDFs. This area difference is calculated for each pairwise comparison of 1SIS, 2SIS, FIS, and Dorfman testing. CDF plots provide a visualization of how probabilities are distributed over the number of tests. CDFs that increase more rapidly to 1 correspond to more efficient retesting procedures.
Non-informative Sterrett (NIS) decodes positive groups by retesting individuals at random, so there are \(I!\) different possible NIS implementations. CDFs are found by permuting the elements in the vector of individual risk probabilities and using the FIS CDF expression without reordering the individual probabilities. That is, the FIS procedure uses the most efficient NIS implementation, which is to retest individuals in order of descending probabilities. When implementing the informative Sterrett algorithms with a large number of individuals, an algorithm is used to compute the PMF for the number of tests under FIS. This is done automatically by Sterrett for \(I>12\). The algorithm is described in detail in the Appendix of Bilder et al. (2010).
Bilder, C., Tebbs, J., Chen, P. (2010). “Informative retesting.” Journal of the American Statistical Association, 105, 942–955.
expectOrderBeta for generating a vector of individual risk
probabilities for informative group testing and opChar1 for
calculating operating characteristics with hierarchical and array-based
group testing algorithms.
Other operating characteristic functions:
GroupMembershipMatrix(),
TOD(),
halving(),
operatingCharacteristics1(),
operatingCharacteristics2()
# Example 1: FIS provides the smallest mean
# number of tests and the smallest standard
# deviation. 2SIS has slightly larger mean
# and standard deviation than FIS, but
# its performance is comparable, indicating
# 2SIS may be preferred because it is
# easier to implement.
set.seed(1231)
p.vec1 <- rbeta(n = 8, shape1 = 1, shape2 = 10)
save.it1 <- Sterrett(p = p.vec1, Sp = 0.90, Se = 0.95)
save.it1
#>
#> PMF
#> tests one.stage.IS.PMF two.stage.IS.PMF full.IS.PMF Dorfman.PMF
#> 1 1 0.48835471 0.48835471 4.883547e-01 0.4883547
#> 2 3 0.09599437 0.09599437 9.599437e-02 NA
#> 3 4 0.07394624 0.07394624 7.394624e-02 NA
#> 4 5 0.04488706 0.06729731 6.729731e-02 NA
#> 5 6 0.03972361 0.06516755 6.516755e-02 NA
#> 6 7 0.02005756 0.05073281 5.444685e-02 NA
#> 7 8 0.01199658 0.03078615 3.887818e-02 NA
#> 8 9 0.04084418 0.05308898 6.080128e-02 0.5116453
#> 9 10 0.18419568 0.03045444 3.711694e-02 NA
#> 10 11 NA 0.04417744 1.426534e-02 NA
#> 11 12 NA NA 3.262503e-03 NA
#> 12 13 NA NA 4.362291e-04 NA
#> 13 14 NA NA 3.151575e-05 NA
#> 14 15 NA NA 9.742431e-07 NA
#>
#> Mean and standard deviation
#> Method mean sd
#> 1 1SIS 3.980830 3.566401
#> 2 2SIS 3.669331 3.201135
#> 3 FIS 3.612345 3.095739
#> 4 Dorfman 5.093162 3.998915
# Example 2: One individual is "high risk" and
# the others are "low risk". Since there is
# only one high-risk individual, the three
# informative Sterrett procedures perform
# similarly. All three informative Sterrett
# procedures offer large improvements over
# Dorfman testing.
p.vec2 <- c(rep(x = 0.01, times = 9), 0.5)
save.it2 <- Sterrett(p = p.vec2, Sp = 0.99, Se = 0.99)
save.it2
#>
#> PMF
#> tests one.stage.IS.PMF two.stage.IS.PMF full.IS.PMF Dorfman.PMF
#> 1 1 0.457623451 0.457623451 4.576235e-01 0.4576235
#> 2 3 0.443665745 0.443665745 4.436657e-01 NA
#> 3 4 0.004573797 0.004573797 4.573797e-03 NA
#> 4 5 0.004527994 0.009011738 9.011738e-03 NA
#> 5 6 0.004482659 0.009010726 9.010726e-03 NA
#> 6 7 0.004437787 0.009008842 9.097171e-03 NA
#> 7 8 0.004393373 0.009006102 9.182748e-03 NA
#> 8 9 0.004349413 0.009002524 9.269199e-03 NA
#> 9 10 0.004305902 0.008998125 9.356497e-03 NA
#> 10 11 0.017294239 0.022024328 2.247606e-02 0.5423765
#> 11 12 0.050345641 0.014470169 1.501690e-02 NA
#> 12 13 NA 0.003604455 1.619568e-03 NA
#> 13 14 NA NA 9.329207e-05 NA
#> 14 15 NA NA 3.048583e-06 NA
#> 15 16 NA NA 6.026634e-08 NA
#> 16 17 NA NA 7.178150e-10 NA
#> 17 18 NA NA 4.761248e-12 NA
#> 18 19 NA NA 1.355528e-14 NA
#>
#> Mean and standard deviation
#> Method mean sd
#> 1 1SIS 2.799251 2.754353
#> 2 2SIS 2.674921 2.433704
#> 3 FIS 2.670015 2.416430
#> 4 Dorfman 6.423765 4.982010
# Example 3: Two individuals are at higher
# risk than the others. All three informative
# Sterrett procedures provide large
# improvements over Dorfman testing.
# Due to the large initial group size, an
# algorithm (described in the Appendix of
# Bilder et al. (2010)) is used for FIS.
# The Sterrett() function does this
# automatically for I>12.
p.vec3 <- c(rep(x = 0.01, times = 98), 0.1, 0.1)
save.it3 <- Sterrett(p = p.vec3, Sp = 0.99, Se = 0.99)
save.it3
#>
#> PMF
#> tests one.stage.IS.PMF two.stage.IS.PMF full.IS.PMF Dorfman.PMF
#> 1 1 0.306455946 0.306455946 3.064559e-01 0.3064559
#> 2 3 0.033353253 0.033353253 3.335325e-02 NA
#> 3 4 0.032954071 0.032954071 3.295407e-02 NA
#> 4 5 0.003045396 0.006994767 6.994767e-03 NA
#> 5 6 0.003013996 0.003742329 3.742329e-03 NA
#> 6 7 0.002982934 0.003763610 3.807238e-03 NA
#> 7 8 0.002952208 0.003784067 3.841593e-03 NA
#> 8 9 0.002921811 0.003803714 3.876891e-03 NA
#> 9 10 0.002891742 0.003822568 3.912522e-03 NA
#> 10 11 0.002861996 0.003840643 3.948500e-03 NA
#> 11 12 0.002832569 0.003857954 3.984829e-03 NA
#> 12 13 0.002803457 0.003874515 4.021513e-03 NA
#> 13 14 0.002774658 0.003890339 4.058554e-03 NA
#> 14 15 0.002746168 0.003905442 4.095957e-03 NA
#> 15 16 0.002717982 0.003919836 4.133724e-03 NA
#> 16 17 0.002690097 0.003933535 4.171859e-03 NA
#> 17 18 0.002662511 0.003946552 4.210366e-03 NA
#> 18 19 0.002635219 0.003958900 4.249249e-03 NA
#> 19 20 0.002608218 0.003970592 4.288510e-03 NA
#> 20 21 0.002581505 0.003981640 4.328154e-03 NA
#> 21 22 0.002555077 0.003992058 4.368185e-03 NA
#> 22 23 0.002528930 0.004001856 4.408605e-03 NA
#> 23 24 0.002503061 0.004011047 4.449420e-03 NA
#> 24 25 0.002477468 0.004019643 4.490632e-03 NA
#> 25 26 0.002452146 0.004027655 4.532246e-03 NA
#> 26 27 0.002427093 0.004035094 4.574265e-03 NA
#> 27 28 0.002402305 0.004041973 4.616694e-03 NA
#> 28 29 0.002377780 0.004048301 4.659536e-03 NA
#> 29 30 0.002353516 0.004054090 4.702795e-03 NA
#> 30 31 0.002329507 0.004059350 4.746476e-03 NA
#> 31 32 0.002305753 0.004064092 4.790582e-03 NA
#> 32 33 0.002282250 0.004068326 4.835118e-03 NA
#> 33 34 0.002258996 0.004072062 4.880088e-03 NA
#> 34 35 0.002235986 0.004075310 4.925495e-03 NA
#> 35 36 0.002213220 0.004078081 4.971345e-03 NA
#> 36 37 0.002190693 0.004080383 5.017641e-03 NA
#> 37 38 0.002168404 0.004082226 5.064388e-03 NA
#> 38 39 0.002146349 0.004083619 5.111590e-03 NA
#> 39 40 0.002124526 0.004084573 5.159252e-03 NA
#> 40 41 0.002102933 0.004085095 5.207378e-03 NA
#> 41 42 0.002081567 0.004085194 5.255973e-03 NA
#> 42 43 0.002060425 0.004084880 5.305040e-03 NA
#> 43 44 0.002039505 0.004084161 5.354585e-03 NA
#> 44 45 0.002018805 0.004083045 5.404613e-03 NA
#> 45 46 0.001998321 0.004081541 5.455127e-03 NA
#> 46 47 0.001978052 0.004079656 5.506134e-03 NA
#> 47 48 0.001957995 0.004077400 5.557636e-03 NA
#> 48 49 0.001938148 0.004074779 5.609640e-03 NA
#> 49 50 0.001918508 0.004071802 5.662150e-03 NA
#> 50 51 0.001899074 0.004068477 5.715171e-03 NA
#> 51 52 0.001879843 0.004064810 5.768709e-03 NA
#> 52 53 0.001860812 0.004060809 5.822767e-03 NA
#> 53 54 0.001841980 0.004056481 5.877351e-03 NA
#> 54 55 0.001823344 0.004051835 5.932466e-03 NA
#> 55 56 0.001804902 0.004046876 5.988118e-03 NA
#> 56 57 0.001786653 0.004041611 6.044311e-03 NA
#> 57 58 0.001768593 0.004036048 6.101051e-03 NA
#> 58 59 0.001750722 0.004030193 6.158343e-03 NA
#> 59 60 0.001733036 0.004024052 6.216193e-03 NA
#> 60 61 0.001715533 0.004017633 6.274605e-03 NA
#> 61 62 0.001698213 0.004010942 6.333586e-03 NA
#> 62 63 0.001681072 0.004003984 6.393140e-03 NA
#> 63 64 0.001664109 0.003996766 6.453274e-03 NA
#> 64 65 0.001647322 0.003989294 6.513992e-03 NA
#> 65 66 0.001630709 0.003981574 6.575302e-03 NA
#> 66 67 0.001614269 0.003973611 6.637207e-03 NA
#> 67 68 0.001597998 0.003965413 6.699715e-03 NA
#> 68 69 0.001581895 0.003956983 6.762831e-03 NA
#> 69 70 0.001565960 0.003948328 6.826561e-03 NA
#> 70 71 0.001550189 0.003939454 6.890911e-03 NA
#> 71 72 0.001534580 0.003930365 6.955886e-03 NA
#> 72 73 0.001519133 0.003921067 7.021494e-03 NA
#> 73 74 0.001503846 0.003911565 7.087739e-03 NA
#> 74 75 0.001488716 0.003901865 7.154629e-03 NA
#> 75 76 0.001473742 0.003891971 7.222169e-03 NA
#> 76 77 0.001458923 0.003881888 7.290366e-03 NA
#> 77 78 0.001444256 0.003871621 7.359227e-03 NA
#> 78 79 0.001429740 0.003861174 7.428757e-03 NA
#> 79 80 0.001415373 0.003850554 7.498963e-03 NA
#> 80 81 0.001401155 0.003839763 7.569851e-03 NA
#> 81 82 0.001387082 0.003828808 7.641430e-03 NA
#> 82 83 0.001373155 0.003817691 7.713704e-03 NA
#> 83 84 0.001359370 0.003806418 7.786680e-03 NA
#> 84 85 0.001345727 0.003794992 7.860367e-03 NA
#> 85 86 0.001332224 0.003783419 7.934770e-03 NA
#> 86 87 0.001318859 0.003771702 8.009896e-03 NA
#> 87 88 0.001305632 0.003759845 8.085753e-03 NA
#> 88 89 0.001292540 0.003747853 8.162347e-03 NA
#> 89 90 0.001279582 0.003735729 8.239686e-03 NA
#> 90 91 0.001266757 0.003723477 8.317776e-03 NA
#> 91 92 0.001254063 0.003711101 8.396626e-03 NA
#> 92 93 0.001241499 0.003698605 8.476243e-03 NA
#> 93 94 0.001229064 0.003685992 8.556633e-03 NA
#> 94 95 0.001216756 0.003673266 8.637805e-03 NA
#> 95 96 0.001204573 0.003660430 8.719766e-03 NA
#> 96 97 0.001192516 0.003647489 8.802524e-03 NA
#> 97 98 0.001180581 0.003634445 8.886086e-03 NA
#> 98 99 0.001168768 0.003621303 8.970461e-03 NA
#> 99 100 0.001157076 0.003608064 9.055656e-03 NA
#> 100 101 0.004782683 0.007231913 1.277886e-02 0.6935441
#> 101 102 0.435432747 0.007652733 1.329996e-02 NA
#> 102 103 NA 0.231736159 1.068667e-02 NA
#> 103 104 NA NA 6.511757e-03 NA
#> 104 105 NA NA 3.108059e-03 NA
#> 105 106 NA NA 1.203933e-03 NA
#> 106 107 NA NA 3.894191e-04 NA
#> 107 108 NA NA 1.075320e-04 NA
#> 108 109 NA NA 2.579244e-05 NA
#> 109 110 NA NA 5.448610e-06 NA
#> 110 111 NA NA 1.025161e-06 NA
#> 111 112 NA NA 1.733941e-07 NA
#> 112 113 NA NA 2.656919e-08 NA
#> 113 114 NA NA 3.712601e-09 NA
#> 114 115 NA NA 4.757506e-10 NA
#> 115 116 NA NA 5.618201e-11 NA
#> 116 117 NA NA 6.140131e-12 NA
#> 117 118 NA NA 6.233651e-13 NA
#> 118 119 NA NA 5.898293e-14 NA
#> 119 120 NA NA 5.216813e-15 NA
#> 120 121 NA NA 4.324339e-16 NA
#> 121 122 NA NA 3.367395e-17 NA
#> 122 123 NA NA 2.468602e-18 NA
#> 123 124 NA NA 1.706968e-19 NA
#> 124 125 NA NA 1.115254e-20 NA
#> 125 126 NA NA 6.895809e-22 NA
#> 126 127 NA NA 4.040977e-23 NA
#> 127 128 NA NA 2.247242e-24 NA
#> 128 129 NA NA 1.187406e-25 NA
#> 129 130 NA NA 5.967784e-27 NA
#> 130 131 NA NA 2.855818e-28 NA
#> 131 132 NA NA 1.302426e-29 NA
#> 132 133 NA NA 5.665645e-31 NA
#> 133 134 NA NA 2.352644e-32 NA
#> 134 135 NA NA 9.332165e-34 NA
#> 135 136 NA NA 3.538425e-35 NA
#> 136 137 NA NA 1.283205e-36 NA
#> 137 138 NA NA 4.453230e-38 NA
#> 138 139 NA NA 1.479650e-39 NA
#> 139 140 NA NA 4.709123e-41 NA
#> 140 141 NA NA 1.436118e-42 NA
#> 141 142 NA NA 4.198203e-44 NA
#> 142 143 NA NA 1.176782e-45 NA
#> 143 144 NA NA 3.163783e-47 NA
#> 144 145 NA NA 8.160154e-49 NA
#> 145 146 NA NA 2.019565e-50 NA
#> 146 147 NA NA 4.796855e-52 NA
#> 147 148 NA NA 1.093580e-53 NA
#> 148 149 NA NA 2.393213e-55 NA
#> 149 150 NA NA 5.027772e-57 NA
#> 150 151 NA NA 1.014017e-58 NA
#> 151 152 NA NA 1.963305e-60 NA
#> 152 153 NA NA 3.649106e-62 NA
#> 153 154 NA NA 6.510431e-64 NA
#> 154 155 NA NA 1.114836e-65 NA
#> 155 156 NA NA 1.832014e-67 NA
#> 156 157 NA NA 2.888593e-69 NA
#> 157 158 NA NA 4.369089e-71 NA
#> 158 159 NA NA 6.337728e-73 NA
#> 159 160 NA NA 8.814315e-75 NA
#> 160 161 NA NA 1.174931e-76 NA
#> 161 162 NA NA 1.500527e-78 NA
#> 162 163 NA NA 1.835276e-80 NA
#> 163 164 NA NA 2.148740e-82 NA
#> 164 165 NA NA 2.406958e-84 NA
#> 165 166 NA NA 2.578158e-86 NA
#> 166 167 NA NA 2.638983e-88 NA
#> 167 168 NA NA 2.579605e-90 NA
#> 168 169 NA NA 2.406214e-92 NA
#> 169 170 NA NA 2.140051e-94 NA
#> 170 171 NA NA 1.813149e-96 NA
#> 171 172 NA NA 1.461964e-98 NA
#> 172 173 NA NA 1.120644e-100 NA
#> 173 174 NA NA 8.156741e-103 NA
#> 174 175 NA NA 5.630204e-105 NA
#> 175 176 NA NA 3.680238e-107 NA
#> 176 177 NA NA 2.274557e-109 NA
#> 177 178 NA NA 1.326912e-111 NA
#> 178 179 NA NA 7.292705e-114 NA
#> 179 180 NA NA 3.768112e-116 NA
#> 180 181 NA NA 1.826130e-118 NA
#> 181 182 NA NA 8.278994e-121 NA
#> 182 183 NA NA 3.500954e-123 NA
#> 183 184 NA NA 1.376320e-125 NA
#> 184 185 NA NA 5.011191e-128 NA
#> 185 186 NA NA 1.682597e-130 NA
#> 186 187 NA NA 5.184140e-133 NA
#> 187 188 NA NA 1.457182e-135 NA
#> 188 189 NA NA 3.711276e-138 NA
#> 189 190 NA NA 8.494911e-141 NA
#> 190 191 NA NA 1.730261e-143 NA
#> 191 192 NA NA 3.097718e-146 NA
#> 192 193 NA NA 4.799140e-149 NA
#> 193 194 NA NA 6.303391e-152 NA
#> 194 195 NA NA 6.824821e-155 NA
#> 195 196 NA NA 5.848385e-158 NA
#> 196 197 NA NA 3.719024e-161 NA
#> 197 198 NA NA 1.560148e-164 NA
#> 198 199 NA NA 3.238585e-168 NA
#>
#> Mean and standard deviation
#> Method mean sd
#> 1 1SIS 53.81318 46.86916
#> 2 2SIS 45.57633 42.89603
#> 3 FIS 39.79628 37.32272
#> 4 Dorfman 70.35441 46.10214