opt.info.dorf: Find the characteristics of an informative two-stage...
In binGroup: Evaluation and Experimental Design for Binomial Group Testing
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Find the characteristics of an informative
two-stage hierarchical (Dorfman) decoding process using Optimal
Dorfman (OD), Thresholded Optimal Dorfman (TOD), or Pool-Specific
Optimal Dorfman (PSOD) algorithms.
Usage
1
2
opt.info.dorf(prob, se = 1, sp = 1, method = "OD", max.pool = 15,
thresh.pool = 8, threshold = NULL)
Arguments
prob
a vector of all subjects' infection probabilities.
se
the sensitivity of the diagnostic test.
sp
the specificity of the diagnostic test.
method
character string defining the specific screening
procedure for implementation of Dorfman retesting in a
heterogeneous population. Options include Optimal Dorfman
("OD"), Thresholded Optimal Dorfman ("TOD"), and
Pool-Specific Optimal Dorfman ("PSOD"). Further details
are given under 'Details'.
max.pool
the maximum allowable pool size. Further details
are given under 'Details'.
thresh.pool
the initial pool size used for TOD, if
threshold is not specified. Further details are given
under 'Details'.
threshold
the threshold value for TOD. If a threshold
value is not specified, one is found algorithmically. Further
details are given under 'Details'.
Details
This function finds the characteristics of an informative
two-stage hierarchical (Dorfman) decoding process. Characteristics
found include the expected expenditure of the decoding process,
the variance of the expenditure of the decoding process, and the
pooling sensitivity, pooling specificity, pooling positive predictive
value, and pooling negative predictive value for each individual.
Calculations of these characteristics are done using equations
presented in McMahan et al. (2012).
Optimal Dorfman (OD) is an informative Dorfman algorithm in
which the common pool size c=c_{opt} minimizes
E(T^(c)), the expected number of tests needed to decode
all N individuals when pools of size c are used.
Thresholded Optimal Dorfman (TOD) is an informative Dorfman
algorithm in which all N individuals are partitioned
into two classes, low-risk and high-risk individuals, based
on whether their risk probability falls below or above a
particular threshold value. The threshold can be specified
using the threshold argument or the TOD algorithm can
identify the optimal threshold value. The low-risk individuals
are tested using a optimal common pool size, and high-risk
individuals are tested individually.
Pool-Specific Optimal Dorfman (PSOD) is an informative Dorfman
algorithm in which optimal sizes are determined for each pool.
A total of N individuals are tested in pools that minimize
the expected number of tests per individual, on a pool-by-pool
basis. If desired, the user can add the constraint of a maximum
allowable pool size, so that each pool will contain no more
than the maximum allowable number of individuals.
All three informative Dorfman procedures described above require
individuals to be ordered from smallest to largest probability
of infection. See McMahan et al. (2012) for additional details
on the implementation of informative two-stage hierarchical
(Dorfman) testing algorithms.
Value
A list containing:
tv
the threshold value used for TOD, if applicable.
e
the expected expenditure of the decoding process.
v
the variance of the expenditure of the decoding
process.
summary
a matrix of summary measures that includes
each individual's infection probability, pool (pool to which
they belong), pooling sensitivity, pooling specificity,
pooling positive predictive value, and pooling negative
predictive value.
Author(s)
This function was originally written by Christopher S.
McMahan for McMahan et al. (2012). The function was obtained
from http://chrisbilder.com/grouptesting.
References
\insertRefDorfman1943binGroup
\insertRefMcMahan2012abinGroup
See Also
http://chrisbilder.com/grouptesting
Other Informative Dorfman functions: accuracy.dorf,
characteristics.pool,
inf.dorf.measures,
opt.pool.size,
pool.specific.dorf,
thresh.val.dorf
Examples
1
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# Find the characteristics of an informative
# Dorfman algorithm, using the OD procedure.
# 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 i7-6500U processor.
opt.info.dorf(prob=rbeta(1000,1,10), se=1, sp=1,
method ="OD", max.pool=15, thresh.pool=8, threshold=NULL)
# Find the characteristics of an informative
# Dorfman algorithm, using the TOD procedure.
# 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 i7-6500U processor.
set.seed(1002)
p.vec <- p.vec.func(p=0.01, alpha=2, grp.sz=20)
opt.info.dorf(prob=p.vec, se=0.95, sp=0.95,
method="TOD", max.pool=5, threshold=0.015)
Example output
$tv
NULL
$e
[1] 528.542
$v
[1] 830.7245
$summary
pool probability PSe PSp PPV NPV
1 90 5.713448e-02 1 1 1 1
2 119 8.617677e-02 1 1 1 1
3 21 9.413351e-03 1 1 1 1
4 22 9.580256e-03 1 1 1 1
5 180 2.009023e-01 1 1 1 1
6 155 1.299131e-01 1 1 1 1
7 125 9.093821e-02 1 1 1 1
8 127 9.411240e-02 1 1 1 1
9 157 1.319011e-01 1 1 1 1
10 168 1.585252e-01 1 1 1 1
11 48 2.572500e-02 1 1 1 1
12 133 1.019658e-01 1 1 1 1
13 154 1.286472e-01 1 1 1 1
14 171 1.700930e-01 1 1 1 1
15 140 1.092673e-01 1 1 1 1
16 77 4.728254e-02 1 1 1 1
17 168 1.586861e-01 1 1 1 1
18 29 1.326867e-02 1 1 1 1
19 69 4.205200e-02 1 1 1 1
20 180 1.993282e-01 1 1 1 1
21 160 1.425508e-01 1 1 1 1
22 157 1.335909e-01 1 1 1 1
23 43 2.253594e-02 1 1 1 1
24 196 3.183416e-01 1 1 1 1
25 137 1.056328e-01 1 1 1 1
26 149 1.211072e-01 1 1 1 1
27 43 2.267089e-02 1 1 1 1
28 125 9.068730e-02 1 1 1 1
29 56 3.075639e-02 1 1 1 1
30 195 3.061099e-01 1 1 1 1
31 29 1.327351e-02 1 1 1 1
32 160 1.429223e-01 1 1 1 1
33 30 1.419224e-02 1 1 1 1
34 59 3.392966e-02 1 1 1 1
35 126 9.274470e-02 1 1 1 1
36 22 9.731184e-03 1 1 1 1
37 38 1.916536e-02 1 1 1 1
38 106 7.212268e-02 1 1 1 1
39 45 2.385023e-02 1 1 1 1
40 13 6.646096e-03 1 1 1 1
41 143 1.138545e-01 1 1 1 1
42 146 1.194932e-01 1 1 1 1
43 128 9.598831e-02 1 1 1 1
44 106 7.173353e-02 1 1 1 1
45 122 8.866715e-02 1 1 1 1
46 33 1.590795e-02 1 1 1 1
47 132 1.008704e-01 1 1 1 1
48 108 7.486038e-02 1 1 1 1
49 33 1.590789e-02 1 1 1 1
50 10 5.090108e-03 1 1 1 1
51 19 8.919201e-03 1 1 1 1
52 161 1.452904e-01 1 1 1 1
53 7 3.280906e-03 1 1 1 1
54 11 5.398500e-03 1 1 1 1
55 19 9.112091e-03 1 1 1 1
56 34 1.707677e-02 1 1 1 1
57 145 1.168349e-01 1 1 1 1
58 153 1.255596e-01 1 1 1 1
59 130 9.809622e-02 1 1 1 1
60 178 1.915294e-01 1 1 1 1
61 36 1.806045e-02 1 1 1 1
62 76 4.682849e-02 1 1 1 1
63 192 2.674742e-01 1 1 1 1
64 88 5.631400e-02 1 1 1 1
65 174 1.754162e-01 1 1 1 1
66 167 1.558782e-01 1 1 1 1
67 124 9.021047e-02 1 1 1 1
68 62 3.539815e-02 1 1 1 1
69 95 6.258160e-02 1 1 1 1
70 24 1.041411e-02 1 1 1 1
71 53 2.832548e-02 1 1 1 1
72 200 4.403164e-01 1 1 1 1
73 180 1.964198e-01 1 1 1 1
74 1 1.940680e-04 1 1 1 1
75 124 8.986838e-02 1 1 1 1
76 3 1.470292e-03 1 1 1 1
77 176 1.814428e-01 1 1 1 1
78 177 1.896618e-01 1 1 1 1
79 90 5.809532e-02 1 1 1 1
80 112 7.937145e-02 1 1 1 1
81 83 5.245560e-02 1 1 1 1
82 48 2.547658e-02 1 1 1 1
83 138 1.076801e-01 1 1 1 1
84 67 3.985886e-02 1 1 1 1
85 27 1.207109e-02 1 1 1 1
86 161 1.430045e-01 1 1 1 1
87 32 1.545739e-02 1 1 1 1
88 72 4.383370e-02 1 1 1 1
89 178 1.897670e-01 1 1 1 1
90 54 2.881002e-02 1 1 1 1
91 157 1.344427e-01 1 1 1 1
92 190 2.469937e-01 1 1 1 1
93 189 2.433841e-01 1 1 1 1
94 104 7.102047e-02 1 1 1 1
95 140 1.090240e-01 1 1 1 1
96 160 1.406214e-01 1 1 1 1
97 22 9.873339e-03 1 1 1 1
98 97 6.503658e-02 1 1 1 1
99 186 2.229597e-01 1 1 1 1
100 97 6.463121e-02 1 1 1 1
101 136 1.045924e-01 1 1 1 1
102 120 8.722968e-02 1 1 1 1
103 141 1.108545e-01 1 1 1 1
104 130 9.822377e-02 1 1 1 1
105 142 1.126200e-01 1 1 1 1
106 115 8.151379e-02 1 1 1 1
107 2 9.891642e-04 1 1 1 1
108 135 1.035250e-01 1 1 1 1
109 140 1.097453e-01 1 1 1 1
110 56 3.056584e-02 1 1 1 1
111 192 2.736227e-01 1 1 1 1
112 89 5.672440e-02 1 1 1 1
113 99 6.660025e-02 1 1 1 1
114 130 9.817378e-02 1 1 1 1
115 82 5.194085e-02 1 1 1 1
116 55 3.038195e-02 1 1 1 1
117 37 1.892605e-02 1 1 1 1
118 108 7.436978e-02 1 1 1 1
119 25 1.058131e-02 1 1 1 1
120 155 1.301736e-01 1 1 1 1
121 96 6.449469e-02 1 1 1 1
122 147 1.197295e-01 1 1 1 1
123 168 1.620193e-01 1 1 1 1
124 169 1.641975e-01 1 1 1 1
125 112 7.926894e-02 1 1 1 1
126 4 1.900129e-03 1 1 1 1
127 196 3.269081e-01 1 1 1 1
128 159 1.401625e-01 1 1 1 1
129 192 2.715168e-01 1 1 1 1
130 122 8.869448e-02 1 1 1 1
131 53 2.860046e-02 1 1 1 1
132 83 5.229160e-02 1 1 1 1
133 89 5.637404e-02 1 1 1 1
134 6 2.739655e-03 1 1 1 1
135 80 4.865390e-02 1 1 1 1
136 134 1.022723e-01 1 1 1 1
137 50 2.703206e-02 1 1 1 1
138 69 4.201859e-02 1 1 1 1
139 2 1.001703e-03 1 1 1 1
140 97 6.516856e-02 1 1 1 1
141 107 7.335187e-02 1 1 1 1
142 70 4.230942e-02 1 1 1 1
143 190 2.485727e-01 1 1 1 1
144 179 1.920468e-01 1 1 1 1
145 93 6.088306e-02 1 1 1 1
146 56 3.132537e-02 1 1 1 1
147 72 4.337437e-02 1 1 1 1
148 67 4.022920e-02 1 1 1 1
149 154 1.272861e-01 1 1 1 1
150 47 2.508988e-02 1 1 1 1
151 193 2.871338e-01 1 1 1 1
152 152 1.247919e-01 1 1 1 1
153 3 1.593865e-03 1 1 1 1
154 14 6.701679e-03 1 1 1 1
155 23 1.009225e-02 1 1 1 1
156 51 2.734792e-02 1 1 1 1
157 188 2.388287e-01 1 1 1 1
158 141 1.103964e-01 1 1 1 1
159 8 3.902647e-03 1 1 1 1
160 15 7.290469e-03 1 1 1 1
161 10 5.374275e-03 1 1 1 1
162 26 1.122259e-02 1 1 1 1
163 114 8.119051e-02 1 1 1 1
164 5 2.545351e-03 1 1 1 1
165 38 1.930531e-02 1 1 1 1
166 142 1.132781e-01 1 1 1 1
167 135 1.037538e-01 1 1 1 1
168 8 3.983811e-03 1 1 1 1
169 14 6.664158e-03 1 1 1 1
170 126 9.260282e-02 1 1 1 1
171 145 1.160764e-01 1 1 1 1
172 52 2.778868e-02 1 1 1 1
173 155 1.290579e-01 1 1 1 1
174 188 2.357483e-01 1 1 1 1
175 126 9.221851e-02 1 1 1 1
176 175 1.809974e-01 1 1 1 1
177 82 5.189902e-02 1 1 1 1
178 28 1.256926e-02 1 1 1 1
179 158 1.370359e-01 1 1 1 1
180 160 1.418873e-01 1 1 1 1
181 173 1.740309e-01 1 1 1 1
182 105 7.117048e-02 1 1 1 1
183 189 2.409973e-01 1 1 1 1
184 25 1.052284e-02 1 1 1 1
185 68 4.051746e-02 1 1 1 1
186 163 1.505164e-01 1 1 1 1
187 100 6.761745e-02 1 1 1 1
188 65 3.841971e-02 1 1 1 1
189 117 8.380190e-02 1 1 1 1
190 183 2.090084e-01 1 1 1 1
191 71 4.268375e-02 1 1 1 1
192 190 2.563584e-01 1 1 1 1
193 91 5.906645e-02 1 1 1 1
194 117 8.377208e-02 1 1 1 1
195 172 1.720011e-01 1 1 1 1
196 63 3.679484e-02 1 1 1 1
197 80 4.911560e-02 1 1 1 1
198 29 1.313965e-02 1 1 1 1
199 186 2.215965e-01 1 1 1 1
200 197 3.431066e-01 1 1 1 1
201 147 1.198472e-01 1 1 1 1
202 71 4.258392e-02 1 1 1 1
203 179 1.923268e-01 1 1 1 1
204 103 7.009811e-02 1 1 1 1
205 182 2.058522e-01 1 1 1 1
206 25 1.050397e-02 1 1 1 1
207 37 1.860075e-02 1 1 1 1
208 37 1.884540e-02 1 1 1 1
209 63 3.663959e-02 1 1 1 1
210 76 4.688994e-02 1 1 1 1
211 103 6.927031e-02 1 1 1 1
212 165 1.518094e-01 1 1 1 1
213 72 4.336420e-02 1 1 1 1
214 32 1.511159e-02 1 1 1 1
215 39 2.055845e-02 1 1 1 1
216 31 1.440724e-02 1 1 1 1
217 148 1.204232e-01 1 1 1 1
218 176 1.841258e-01 1 1 1 1
219 9 4.100537e-03 1 1 1 1
220 85 5.349627e-02 1 1 1 1
221 184 2.127665e-01 1 1 1 1
222 191 2.651435e-01 1 1 1 1
223 123 8.908217e-02 1 1 1 1
224 167 1.563599e-01 1 1 1 1
225 25 1.042493e-02 1 1 1 1
226 166 1.551005e-01 1 1 1 1
227 77 4.708392e-02 1 1 1 1
228 58 3.342040e-02 1 1 1 1
229 149 1.210400e-01 1 1 1 1
230 127 9.336430e-02 1 1 1 1
231 181 2.017891e-01 1 1 1 1
232 181 2.022719e-01 1 1 1 1
233 102 6.913110e-02 1 1 1 1
234 199 4.235728e-01 1 1 1 1
235 87 5.492685e-02 1 1 1 1
236 187 2.278435e-01 1 1 1 1
237 46 2.408046e-02 1 1 1 1
238 123 8.911847e-02 1 1 1 1
239 141 1.115547e-01 1 1 1 1
240 184 2.117435e-01 1 1 1 1
241 128 9.462641e-02 1 1 1 1
242 103 6.913925e-02 1 1 1 1
243 11 5.550840e-03 1 1 1 1
244 151 1.235796e-01 1 1 1 1
245 106 7.214655e-02 1 1 1 1
246 98 6.537677e-02 1 1 1 1
247 107 7.340038e-02 1 1 1 1
248 195 3.027359e-01 1 1 1 1
249 166 1.536210e-01 1 1 1 1
250 92 6.049005e-02 1 1 1 1
251 48 2.580639e-02 1 1 1 1
252 163 1.506697e-01 1 1 1 1
253 200 4.474909e-01 1 1 1 1
254 32 1.532908e-02 1 1 1 1
255 95 6.350321e-02 1 1 1 1
256 90 5.719615e-02 1 1 1 1
257 146 1.171081e-01 1 1 1 1
258 164 1.513537e-01 1 1 1 1
259 184 2.146571e-01 1 1 1 1
260 143 1.136174e-01 1 1 1 1
261 31 1.511031e-02 1 1 1 1
262 176 1.835130e-01 1 1 1 1
263 79 4.854702e-02 1 1 1 1
264 64 3.741279e-02 1 1 1 1
265 35 1.752998e-02 1 1 1 1
266 21 9.471405e-03 1 1 1 1
267 5 2.595762e-03 1 1 1 1
268 195 3.037553e-01 1 1 1 1
269 60 3.444813e-02 1 1 1 1
270 102 6.907113e-02 1 1 1 1
271 16 7.470520e-03 1 1 1 1
272 91 6.000254e-02 1 1 1 1
273 81 5.019991e-02 1 1 1 1
274 15 7.071607e-03 1 1 1 1
275 46 2.404050e-02 1 1 1 1
276 87 5.557225e-02 1 1 1 1
277 143 1.132847e-01 1 1 1 1
278 143 1.145711e-01 1 1 1 1
279 62 3.570560e-02 1 1 1 1
280 59 3.397044e-02 1 1 1 1
281 106 7.162178e-02 1 1 1 1
282 112 7.903128e-02 1 1 1 1
283 144 1.152602e-01 1 1 1 1
284 92 6.036890e-02 1 1 1 1
285 174 1.765541e-01 1 1 1 1
286 187 2.267395e-01 1 1 1 1
287 146 1.175049e-01 1 1 1 1
288 20 9.352001e-03 1 1 1 1
289 55 2.953680e-02 1 1 1 1
290 14 6.787753e-03 1 1 1 1
291 187 2.276744e-01 1 1 1 1
292 94 6.223956e-02 1 1 1 1
293 101 6.804675e-02 1 1 1 1
294 111 7.842976e-02 1 1 1 1
295 90 5.870679e-02 1 1 1 1
296 170 1.685389e-01 1 1 1 1
297 159 1.391734e-01 1 1 1 1
298 73 4.461434e-02 1 1 1 1
299 54 2.870477e-02 1 1 1 1
300 173 1.751213e-01 1 1 1 1
301 109 7.563758e-02 1 1 1 1
302 54 2.921965e-02 1 1 1 1
303 134 1.031305e-01 1 1 1 1
304 95 6.309104e-02 1 1 1 1
305 155 1.295037e-01 1 1 1 1
306 27 1.206541e-02 1 1 1 1
307 30 1.356427e-02 1 1 1 1
308 67 4.046577e-02 1 1 1 1
309 190 2.560812e-01 1 1 1 1
310 90 5.829043e-02 1 1 1 1
311 109 7.556315e-02 1 1 1 1
312 162 1.458467e-01 1 1 1 1
313 131 9.902913e-02 1 1 1 1
314 188 2.334429e-01 1 1 1 1
315 57 3.231864e-02 1 1 1 1
316 122 8.869213e-02 1 1 1 1
317 157 1.337036e-01 1 1 1 1
318 16 7.397138e-03 1 1 1 1
319 114 8.104890e-02 1 1 1 1
320 198 3.666277e-01 1 1 1 1
321 91 5.888472e-02 1 1 1 1
322 61 3.477076e-02 1 1 1 1
323 63 3.649460e-02 1 1 1 1
324 57 3.227639e-02 1 1 1 1
325 159 1.378698e-01 1 1 1 1
326 81 5.104470e-02 1 1 1 1
327 173 1.752333e-01 1 1 1 1
328 184 2.118882e-01 1 1 1 1
329 81 5.053644e-02 1 1 1 1
330 39 2.066330e-02 1 1 1 1
331 25 1.042143e-02 1 1 1 1
332 147 1.200037e-01 1 1 1 1
333 183 2.072920e-01 1 1 1 1
334 19 8.933970e-03 1 1 1 1
335 113 8.044075e-02 1 1 1 1
336 97 6.473600e-02 1 1 1 1
337 194 2.965634e-01 1 1 1 1
338 60 3.435572e-02 1 1 1 1
339 173 1.748349e-01 1 1 1 1
340 189 2.403739e-01 1 1 1 1
341 64 3.697004e-02 1 1 1 1
342 3 1.111719e-03 1 1 1 1
343 45 2.393092e-02 1 1 1 1
344 55 3.011946e-02 1 1 1 1
345 30 1.431547e-02 1 1 1 1
346 31 1.453219e-02 1 1 1 1
347 200 5.053390e-01 1 1 1 1
348 34 1.702009e-02 1 1 1 1
349 150 1.226950e-01 1 1 1 1
350 43 2.266241e-02 1 1 1 1
351 57 3.217060e-02 1 1 1 1
352 121 8.814452e-02 1 1 1 1
353 145 1.157816e-01 1 1 1 1
354 58 3.358633e-02 1 1 1 1
355 14 6.880940e-03 1 1 1 1
356 178 1.901969e-01 1 1 1 1
357 15 7.258902e-03 1 1 1 1
358 137 1.051626e-01 1 1 1 1
359 42 2.193078e-02 1 1 1 1
360 35 1.739630e-02 1 1 1 1
361 52 2.795744e-02 1 1 1 1
362 62 3.551411e-02 1 1 1 1
363 12 6.206950e-03 1 1 1 1
364 125 9.063955e-02 1 1 1 1
365 179 1.938071e-01 1 1 1 1
366 83 5.277953e-02 1 1 1 1
367 198 3.498767e-01 1 1 1 1
368 21 9.439612e-03 1 1 1 1
369 29 1.261809e-02 1 1 1 1
370 60 3.433059e-02 1 1 1 1
371 24 1.037691e-02 1 1 1 1
372 18 8.806771e-03 1 1 1 1
373 114 8.133471e-02 1 1 1 1
374 65 3.892730e-02 1 1 1 1
375 153 1.254536e-01 1 1 1 1
376 36 1.833673e-02 1 1 1 1
377 196 3.166849e-01 1 1 1 1
378 114 8.145541e-02 1 1 1 1
379 118 8.532617e-02 1 1 1 1
380 98 6.535319e-02 1 1 1 1
381 102 6.866653e-02 1 1 1 1
382 177 1.853820e-01 1 1 1 1
383 9 4.626063e-03 1 1 1 1
384 88 5.597333e-02 1 1 1 1
385 156 1.311868e-01 1 1 1 1
386 84 5.289796e-02 1 1 1 1
387 33 1.610088e-02 1 1 1 1
388 136 1.049268e-01 1 1 1 1
389 9 3.985882e-03 1 1 1 1
390 94 6.159564e-02 1 1 1 1
391 27 1.185822e-02 1 1 1 1
392 174 1.764723e-01 1 1 1 1
393 8 3.859905e-03 1 1 1 1
394 199 3.815477e-01 1 1 1 1
395 121 8.733911e-02 1 1 1 1
396 115 8.202840e-02 1 1 1 1
397 137 1.051179e-01 1 1 1 1
398 115 8.197622e-02 1 1 1 1
399 108 7.414937e-02 1 1 1 1
400 156 1.304067e-01 1 1 1 1
401 129 9.636940e-02 1 1 1 1
402 84 5.334201e-02 1 1 1 1
403 93 6.093047e-02 1 1 1 1
404 165 1.535189e-01 1 1 1 1
405 51 2.744840e-02 1 1 1 1
406 178 1.898339e-01 1 1 1 1
407 186 2.225125e-01 1 1 1 1
408 175 1.811912e-01 1 1 1 1
409 170 1.665730e-01 1 1 1 1
410 139 1.088156e-01 1 1 1 1
411 161 1.454186e-01 1 1 1 1
412 110 7.638118e-02 1 1 1 1
413 136 1.042315e-01 1 1 1 1
414 19 8.970157e-03 1 1 1 1
415 116 8.247601e-02 1 1 1 1
416 17 8.148391e-03 1 1 1 1
417 2 9.190502e-04 1 1 1 1
418 58 3.283577e-02 1 1 1 1
419 173 1.747189e-01 1 1 1 1
420 136 1.040136e-01 1 1 1 1
421 185 2.178766e-01 1 1 1 1
422 73 4.461886e-02 1 1 1 1
423 170 1.677549e-01 1 1 1 1
424 124 8.953024e-02 1 1 1 1
425 172 1.716323e-01 1 1 1 1
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942 123 8.913132e-02 1 1 1 1
943 18 8.739614e-03 1 1 1 1
944 194 2.978921e-01 1 1 1 1
945 197 3.430164e-01 1 1 1 1
946 66 3.925795e-02 1 1 1 1
947 156 1.302532e-01 1 1 1 1
948 2 1.056940e-03 1 1 1 1
949 193 2.807975e-01 1 1 1 1
950 26 1.136121e-02 1 1 1 1
951 151 1.234780e-01 1 1 1 1
952 52 2.749536e-02 1 1 1 1
953 134 1.027136e-01 1 1 1 1
954 89 5.671941e-02 1 1 1 1
955 162 1.458547e-01 1 1 1 1
956 33 1.554419e-02 1 1 1 1
957 132 9.958817e-02 1 1 1 1
958 148 1.204646e-01 1 1 1 1
959 59 3.372274e-02 1 1 1 1
960 194 2.892297e-01 1 1 1 1
961 111 7.761273e-02 1 1 1 1
962 48 2.550760e-02 1 1 1 1
963 111 7.865651e-02 1 1 1 1
964 75 4.576066e-02 1 1 1 1
965 47 2.503683e-02 1 1 1 1
966 85 5.371836e-02 1 1 1 1
967 150 1.226681e-01 1 1 1 1
968 120 8.707369e-02 1 1 1 1
969 17 8.158225e-03 1 1 1 1
970 195 3.069460e-01 1 1 1 1
971 108 7.447357e-02 1 1 1 1
972 128 9.632905e-02 1 1 1 1
973 181 2.009880e-01 1 1 1 1
974 151 1.234165e-01 1 1 1 1
975 156 1.304657e-01 1 1 1 1
976 80 5.000323e-02 1 1 1 1
977 98 6.519776e-02 1 1 1 1
978 105 7.139131e-02 1 1 1 1
979 137 1.050438e-01 1 1 1 1
980 110 7.725645e-02 1 1 1 1
981 51 2.747780e-02 1 1 1 1
982 155 1.289592e-01 1 1 1 1
983 118 8.447166e-02 1 1 1 1
984 200 4.245695e-01 1 1 1 1
985 171 1.698509e-01 1 1 1 1
986 200 5.294922e-01 1 1 1 1
987 154 1.285100e-01 1 1 1 1
988 129 9.639255e-02 1 1 1 1
989 130 9.800470e-02 1 1 1 1
990 167 1.551453e-01 1 1 1 1
991 24 1.027322e-02 1 1 1 1
992 29 1.299387e-02 1 1 1 1
993 163 1.467013e-01 1 1 1 1
994 135 1.039666e-01 1 1 1 1
995 36 1.791874e-02 1 1 1 1
996 15 7.321892e-03 1 1 1 1
997 20 9.189273e-03 1 1 1 1
998 98 6.578546e-02 1 1 1 1
999 163 1.471906e-01 1 1 1 1
1000 185 2.158297e-01 1 1 1 1
$tv
[1] 0.015
$e
[1] 9.218941
$v
[1] 4.494338
$summary
pool probability PSe PSp PPV NPV
1 1 0.001583625 0.9025 0.9970628 0.3276716 0.9998449
2 1 0.002500582 0.9025 0.9971038 0.4385710 0.9997549
3 1 0.003269132 0.9025 0.9971382 0.5084377 0.9996794
4 1 0.003976450 0.9025 0.9971699 0.5600752 0.9996098
5 2 0.004656581 0.9025 0.9966937 0.5608303 0.9995426
6 2 0.005328128 0.9025 0.9967235 0.5960398 0.9994763
7 2 0.006003726 0.9025 0.9967536 0.6267425 0.9994095
8 2 0.006693557 0.9025 0.9967843 0.6541289 0.9993413
9 3 0.007407063 0.9025 0.9963005 0.6454465 0.9992703
10 3 0.008154056 0.9025 0.9963335 0.6692676 0.9991961
11 3 0.008945696 0.9025 0.9963685 0.6916672 0.9991175
12 3 0.009795627 0.9025 0.9964062 0.7129940 0.9990329
13 4 0.010721593 0.9025 0.9957710 0.6981442 0.9989400
14 4 0.011748029 0.9025 0.9958159 0.7194277 0.9988374
15 4 0.012910694 0.9025 0.9958669 0.7406675 0.9987211
16 4 0.014265788 0.9025 0.9959265 0.7622676 0.9985852
17 5 0.015910262 0.9500 0.9500000 0.2349958 0.9991498
18 6 0.018035443 0.9500 0.9500000 0.2586921 0.9990343
19 7 0.021112395 0.9500 0.9500000 0.2906730 0.9988661
20 8 0.026981576 0.9500 0.9500000 0.3450635 0.9985427
binGroup documentation built on May 2, 2019, 8:57 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Find the characteristics of an informative two-stage hierarchical (Dorfman) decoding process using Optimal Dorfman (OD), Thresholded Optimal Dorfman (TOD), or Pool-Specific Optimal Dorfman (PSOD) algorithms.
Usage
1 2 | opt.info.dorf(prob, se = 1, sp = 1, method = "OD", max.pool = 15,
thresh.pool = 8, threshold = NULL)
|
Arguments
prob |
a vector of all subjects' infection probabilities. |
se |
the sensitivity of the diagnostic test. |
sp |
the specificity of the diagnostic test. |
method |
character string defining the specific screening procedure for implementation of Dorfman retesting in a heterogeneous population. Options include Optimal Dorfman ("OD"), Thresholded Optimal Dorfman ("TOD"), and Pool-Specific Optimal Dorfman ("PSOD"). Further details are given under 'Details'. |
max.pool |
the maximum allowable pool size. Further details are given under 'Details'. |
thresh.pool |
the initial pool size used for TOD, if threshold is not specified. Further details are given under 'Details'. |
threshold |
the threshold value for TOD. If a threshold value is not specified, one is found algorithmically. Further details are given under 'Details'. |
Details
This function finds the characteristics of an informative two-stage hierarchical (Dorfman) decoding process. Characteristics found include the expected expenditure of the decoding process, the variance of the expenditure of the decoding process, and the pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value for each individual. Calculations of these characteristics are done using equations presented in McMahan et al. (2012).
Optimal Dorfman (OD) is an informative Dorfman algorithm in which the common pool size c=c_{opt} minimizes E(T^(c)), the expected number of tests needed to decode all N individuals when pools of size c are used.
Thresholded Optimal Dorfman (TOD) is an informative Dorfman algorithm in which all N individuals are partitioned into two classes, low-risk and high-risk individuals, based on whether their risk probability falls below or above a particular threshold value. The threshold can be specified using the threshold argument or the TOD algorithm can identify the optimal threshold value. The low-risk individuals are tested using a optimal common pool size, and high-risk individuals are tested individually.
Pool-Specific Optimal Dorfman (PSOD) is an informative Dorfman algorithm in which optimal sizes are determined for each pool. A total of N individuals are tested in pools that minimize the expected number of tests per individual, on a pool-by-pool basis. If desired, the user can add the constraint of a maximum allowable pool size, so that each pool will contain no more than the maximum allowable number of individuals.
All three informative Dorfman procedures described above require individuals to be ordered from smallest to largest probability of infection. See McMahan et al. (2012) for additional details on the implementation of informative two-stage hierarchical (Dorfman) testing algorithms.
Value
A list containing:
tv |
the threshold value used for TOD, if applicable. |
e |
the expected expenditure of the decoding process. |
v |
the variance of the expenditure of the decoding process. |
summary |
a matrix of summary measures that includes each individual's infection probability, pool (pool to which they belong), pooling sensitivity, pooling specificity, pooling positive predictive value, and pooling negative predictive value. |
Author(s)
This function was originally written by Christopher S. McMahan for McMahan et al. (2012). The function was obtained from http://chrisbilder.com/grouptesting.
References
\insertRefDorfman1943binGroup
\insertRefMcMahan2012abinGroup
See Also
http://chrisbilder.com/grouptesting
Other Informative Dorfman functions: accuracy.dorf,
characteristics.pool,
inf.dorf.measures,
opt.pool.size,
pool.specific.dorf,
thresh.val.dorf
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | # Find the characteristics of an informative
# Dorfman algorithm, using the OD procedure.
# 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 i7-6500U processor.
opt.info.dorf(prob=rbeta(1000,1,10), se=1, sp=1,
method ="OD", max.pool=15, thresh.pool=8, threshold=NULL)
# Find the characteristics of an informative
# Dorfman algorithm, using the TOD procedure.
# 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 i7-6500U processor.
set.seed(1002)
p.vec <- p.vec.func(p=0.01, alpha=2, grp.sz=20)
opt.info.dorf(prob=p.vec, se=0.95, sp=0.95,
method="TOD", max.pool=5, threshold=0.015)
|
Example output
$tv
NULL
$e
[1] 528.542
$v
[1] 830.7245
$summary
pool probability PSe PSp PPV NPV
1 90 5.713448e-02 1 1 1 1
2 119 8.617677e-02 1 1 1 1
3 21 9.413351e-03 1 1 1 1
4 22 9.580256e-03 1 1 1 1
5 180 2.009023e-01 1 1 1 1
6 155 1.299131e-01 1 1 1 1
7 125 9.093821e-02 1 1 1 1
8 127 9.411240e-02 1 1 1 1
9 157 1.319011e-01 1 1 1 1
10 168 1.585252e-01 1 1 1 1
11 48 2.572500e-02 1 1 1 1
12 133 1.019658e-01 1 1 1 1
13 154 1.286472e-01 1 1 1 1
14 171 1.700930e-01 1 1 1 1
15 140 1.092673e-01 1 1 1 1
16 77 4.728254e-02 1 1 1 1
17 168 1.586861e-01 1 1 1 1
18 29 1.326867e-02 1 1 1 1
19 69 4.205200e-02 1 1 1 1
20 180 1.993282e-01 1 1 1 1
21 160 1.425508e-01 1 1 1 1
22 157 1.335909e-01 1 1 1 1
23 43 2.253594e-02 1 1 1 1
24 196 3.183416e-01 1 1 1 1
25 137 1.056328e-01 1 1 1 1
26 149 1.211072e-01 1 1 1 1
27 43 2.267089e-02 1 1 1 1
28 125 9.068730e-02 1 1 1 1
29 56 3.075639e-02 1 1 1 1
30 195 3.061099e-01 1 1 1 1
31 29 1.327351e-02 1 1 1 1
32 160 1.429223e-01 1 1 1 1
33 30 1.419224e-02 1 1 1 1
34 59 3.392966e-02 1 1 1 1
35 126 9.274470e-02 1 1 1 1
36 22 9.731184e-03 1 1 1 1
37 38 1.916536e-02 1 1 1 1
38 106 7.212268e-02 1 1 1 1
39 45 2.385023e-02 1 1 1 1
40 13 6.646096e-03 1 1 1 1
41 143 1.138545e-01 1 1 1 1
42 146 1.194932e-01 1 1 1 1
43 128 9.598831e-02 1 1 1 1
44 106 7.173353e-02 1 1 1 1
45 122 8.866715e-02 1 1 1 1
46 33 1.590795e-02 1 1 1 1
47 132 1.008704e-01 1 1 1 1
48 108 7.486038e-02 1 1 1 1
49 33 1.590789e-02 1 1 1 1
50 10 5.090108e-03 1 1 1 1
51 19 8.919201e-03 1 1 1 1
52 161 1.452904e-01 1 1 1 1
53 7 3.280906e-03 1 1 1 1
54 11 5.398500e-03 1 1 1 1
55 19 9.112091e-03 1 1 1 1
56 34 1.707677e-02 1 1 1 1
57 145 1.168349e-01 1 1 1 1
58 153 1.255596e-01 1 1 1 1
59 130 9.809622e-02 1 1 1 1
60 178 1.915294e-01 1 1 1 1
61 36 1.806045e-02 1 1 1 1
62 76 4.682849e-02 1 1 1 1
63 192 2.674742e-01 1 1 1 1
64 88 5.631400e-02 1 1 1 1
65 174 1.754162e-01 1 1 1 1
66 167 1.558782e-01 1 1 1 1
67 124 9.021047e-02 1 1 1 1
68 62 3.539815e-02 1 1 1 1
69 95 6.258160e-02 1 1 1 1
70 24 1.041411e-02 1 1 1 1
71 53 2.832548e-02 1 1 1 1
72 200 4.403164e-01 1 1 1 1
73 180 1.964198e-01 1 1 1 1
74 1 1.940680e-04 1 1 1 1
75 124 8.986838e-02 1 1 1 1
76 3 1.470292e-03 1 1 1 1
77 176 1.814428e-01 1 1 1 1
78 177 1.896618e-01 1 1 1 1
79 90 5.809532e-02 1 1 1 1
80 112 7.937145e-02 1 1 1 1
81 83 5.245560e-02 1 1 1 1
82 48 2.547658e-02 1 1 1 1
83 138 1.076801e-01 1 1 1 1
84 67 3.985886e-02 1 1 1 1
85 27 1.207109e-02 1 1 1 1
86 161 1.430045e-01 1 1 1 1
87 32 1.545739e-02 1 1 1 1
88 72 4.383370e-02 1 1 1 1
89 178 1.897670e-01 1 1 1 1
90 54 2.881002e-02 1 1 1 1
91 157 1.344427e-01 1 1 1 1
92 190 2.469937e-01 1 1 1 1
93 189 2.433841e-01 1 1 1 1
94 104 7.102047e-02 1 1 1 1
95 140 1.090240e-01 1 1 1 1
96 160 1.406214e-01 1 1 1 1
97 22 9.873339e-03 1 1 1 1
98 97 6.503658e-02 1 1 1 1
99 186 2.229597e-01 1 1 1 1
100 97 6.463121e-02 1 1 1 1
101 136 1.045924e-01 1 1 1 1
102 120 8.722968e-02 1 1 1 1
103 141 1.108545e-01 1 1 1 1
104 130 9.822377e-02 1 1 1 1
105 142 1.126200e-01 1 1 1 1
106 115 8.151379e-02 1 1 1 1
107 2 9.891642e-04 1 1 1 1
108 135 1.035250e-01 1 1 1 1
109 140 1.097453e-01 1 1 1 1
110 56 3.056584e-02 1 1 1 1
111 192 2.736227e-01 1 1 1 1
112 89 5.672440e-02 1 1 1 1
113 99 6.660025e-02 1 1 1 1
114 130 9.817378e-02 1 1 1 1
115 82 5.194085e-02 1 1 1 1
116 55 3.038195e-02 1 1 1 1
117 37 1.892605e-02 1 1 1 1
118 108 7.436978e-02 1 1 1 1
119 25 1.058131e-02 1 1 1 1
120 155 1.301736e-01 1 1 1 1
121 96 6.449469e-02 1 1 1 1
122 147 1.197295e-01 1 1 1 1
123 168 1.620193e-01 1 1 1 1
124 169 1.641975e-01 1 1 1 1
125 112 7.926894e-02 1 1 1 1
126 4 1.900129e-03 1 1 1 1
127 196 3.269081e-01 1 1 1 1
128 159 1.401625e-01 1 1 1 1
129 192 2.715168e-01 1 1 1 1
130 122 8.869448e-02 1 1 1 1
131 53 2.860046e-02 1 1 1 1
132 83 5.229160e-02 1 1 1 1
133 89 5.637404e-02 1 1 1 1
134 6 2.739655e-03 1 1 1 1
135 80 4.865390e-02 1 1 1 1
136 134 1.022723e-01 1 1 1 1
137 50 2.703206e-02 1 1 1 1
138 69 4.201859e-02 1 1 1 1
139 2 1.001703e-03 1 1 1 1
140 97 6.516856e-02 1 1 1 1
141 107 7.335187e-02 1 1 1 1
142 70 4.230942e-02 1 1 1 1
143 190 2.485727e-01 1 1 1 1
144 179 1.920468e-01 1 1 1 1
145 93 6.088306e-02 1 1 1 1
146 56 3.132537e-02 1 1 1 1
147 72 4.337437e-02 1 1 1 1
148 67 4.022920e-02 1 1 1 1
149 154 1.272861e-01 1 1 1 1
150 47 2.508988e-02 1 1 1 1
151 193 2.871338e-01 1 1 1 1
152 152 1.247919e-01 1 1 1 1
153 3 1.593865e-03 1 1 1 1
154 14 6.701679e-03 1 1 1 1
155 23 1.009225e-02 1 1 1 1
156 51 2.734792e-02 1 1 1 1
157 188 2.388287e-01 1 1 1 1
158 141 1.103964e-01 1 1 1 1
159 8 3.902647e-03 1 1 1 1
160 15 7.290469e-03 1 1 1 1
161 10 5.374275e-03 1 1 1 1
162 26 1.122259e-02 1 1 1 1
163 114 8.119051e-02 1 1 1 1
164 5 2.545351e-03 1 1 1 1
165 38 1.930531e-02 1 1 1 1
166 142 1.132781e-01 1 1 1 1
167 135 1.037538e-01 1 1 1 1
168 8 3.983811e-03 1 1 1 1
169 14 6.664158e-03 1 1 1 1
170 126 9.260282e-02 1 1 1 1
171 145 1.160764e-01 1 1 1 1
172 52 2.778868e-02 1 1 1 1
173 155 1.290579e-01 1 1 1 1
174 188 2.357483e-01 1 1 1 1
175 126 9.221851e-02 1 1 1 1
176 175 1.809974e-01 1 1 1 1
177 82 5.189902e-02 1 1 1 1
178 28 1.256926e-02 1 1 1 1
179 158 1.370359e-01 1 1 1 1
180 160 1.418873e-01 1 1 1 1
181 173 1.740309e-01 1 1 1 1
182 105 7.117048e-02 1 1 1 1
183 189 2.409973e-01 1 1 1 1
184 25 1.052284e-02 1 1 1 1
185 68 4.051746e-02 1 1 1 1
186 163 1.505164e-01 1 1 1 1
187 100 6.761745e-02 1 1 1 1
188 65 3.841971e-02 1 1 1 1
189 117 8.380190e-02 1 1 1 1
190 183 2.090084e-01 1 1 1 1
191 71 4.268375e-02 1 1 1 1
192 190 2.563584e-01 1 1 1 1
193 91 5.906645e-02 1 1 1 1
194 117 8.377208e-02 1 1 1 1
195 172 1.720011e-01 1 1 1 1
196 63 3.679484e-02 1 1 1 1
197 80 4.911560e-02 1 1 1 1
198 29 1.313965e-02 1 1 1 1
199 186 2.215965e-01 1 1 1 1
200 197 3.431066e-01 1 1 1 1
201 147 1.198472e-01 1 1 1 1
202 71 4.258392e-02 1 1 1 1
203 179 1.923268e-01 1 1 1 1
204 103 7.009811e-02 1 1 1 1
205 182 2.058522e-01 1 1 1 1
206 25 1.050397e-02 1 1 1 1
207 37 1.860075e-02 1 1 1 1
208 37 1.884540e-02 1 1 1 1
209 63 3.663959e-02 1 1 1 1
210 76 4.688994e-02 1 1 1 1
211 103 6.927031e-02 1 1 1 1
212 165 1.518094e-01 1 1 1 1
213 72 4.336420e-02 1 1 1 1
214 32 1.511159e-02 1 1 1 1
215 39 2.055845e-02 1 1 1 1
216 31 1.440724e-02 1 1 1 1
217 148 1.204232e-01 1 1 1 1
218 176 1.841258e-01 1 1 1 1
219 9 4.100537e-03 1 1 1 1
220 85 5.349627e-02 1 1 1 1
221 184 2.127665e-01 1 1 1 1
222 191 2.651435e-01 1 1 1 1
223 123 8.908217e-02 1 1 1 1
224 167 1.563599e-01 1 1 1 1
225 25 1.042493e-02 1 1 1 1
226 166 1.551005e-01 1 1 1 1
227 77 4.708392e-02 1 1 1 1
228 58 3.342040e-02 1 1 1 1
229 149 1.210400e-01 1 1 1 1
230 127 9.336430e-02 1 1 1 1
231 181 2.017891e-01 1 1 1 1
232 181 2.022719e-01 1 1 1 1
233 102 6.913110e-02 1 1 1 1
234 199 4.235728e-01 1 1 1 1
235 87 5.492685e-02 1 1 1 1
236 187 2.278435e-01 1 1 1 1
237 46 2.408046e-02 1 1 1 1
238 123 8.911847e-02 1 1 1 1
239 141 1.115547e-01 1 1 1 1
240 184 2.117435e-01 1 1 1 1
241 128 9.462641e-02 1 1 1 1
242 103 6.913925e-02 1 1 1 1
243 11 5.550840e-03 1 1 1 1
244 151 1.235796e-01 1 1 1 1
245 106 7.214655e-02 1 1 1 1
246 98 6.537677e-02 1 1 1 1
247 107 7.340038e-02 1 1 1 1
248 195 3.027359e-01 1 1 1 1
249 166 1.536210e-01 1 1 1 1
250 92 6.049005e-02 1 1 1 1
251 48 2.580639e-02 1 1 1 1
252 163 1.506697e-01 1 1 1 1
253 200 4.474909e-01 1 1 1 1
254 32 1.532908e-02 1 1 1 1
255 95 6.350321e-02 1 1 1 1
256 90 5.719615e-02 1 1 1 1
257 146 1.171081e-01 1 1 1 1
258 164 1.513537e-01 1 1 1 1
259 184 2.146571e-01 1 1 1 1
260 143 1.136174e-01 1 1 1 1
261 31 1.511031e-02 1 1 1 1
262 176 1.835130e-01 1 1 1 1
263 79 4.854702e-02 1 1 1 1
264 64 3.741279e-02 1 1 1 1
265 35 1.752998e-02 1 1 1 1
266 21 9.471405e-03 1 1 1 1
267 5 2.595762e-03 1 1 1 1
268 195 3.037553e-01 1 1 1 1
269 60 3.444813e-02 1 1 1 1
270 102 6.907113e-02 1 1 1 1
271 16 7.470520e-03 1 1 1 1
272 91 6.000254e-02 1 1 1 1
273 81 5.019991e-02 1 1 1 1
274 15 7.071607e-03 1 1 1 1
275 46 2.404050e-02 1 1 1 1
276 87 5.557225e-02 1 1 1 1
277 143 1.132847e-01 1 1 1 1
278 143 1.145711e-01 1 1 1 1
279 62 3.570560e-02 1 1 1 1
280 59 3.397044e-02 1 1 1 1
281 106 7.162178e-02 1 1 1 1
282 112 7.903128e-02 1 1 1 1
283 144 1.152602e-01 1 1 1 1
284 92 6.036890e-02 1 1 1 1
285 174 1.765541e-01 1 1 1 1
286 187 2.267395e-01 1 1 1 1
287 146 1.175049e-01 1 1 1 1
288 20 9.352001e-03 1 1 1 1
289 55 2.953680e-02 1 1 1 1
290 14 6.787753e-03 1 1 1 1
291 187 2.276744e-01 1 1 1 1
292 94 6.223956e-02 1 1 1 1
293 101 6.804675e-02 1 1 1 1
294 111 7.842976e-02 1 1 1 1
295 90 5.870679e-02 1 1 1 1
296 170 1.685389e-01 1 1 1 1
297 159 1.391734e-01 1 1 1 1
298 73 4.461434e-02 1 1 1 1
299 54 2.870477e-02 1 1 1 1
300 173 1.751213e-01 1 1 1 1
301 109 7.563758e-02 1 1 1 1
302 54 2.921965e-02 1 1 1 1
303 134 1.031305e-01 1 1 1 1
304 95 6.309104e-02 1 1 1 1
305 155 1.295037e-01 1 1 1 1
306 27 1.206541e-02 1 1 1 1
307 30 1.356427e-02 1 1 1 1
308 67 4.046577e-02 1 1 1 1
309 190 2.560812e-01 1 1 1 1
310 90 5.829043e-02 1 1 1 1
311 109 7.556315e-02 1 1 1 1
312 162 1.458467e-01 1 1 1 1
313 131 9.902913e-02 1 1 1 1
314 188 2.334429e-01 1 1 1 1
315 57 3.231864e-02 1 1 1 1
316 122 8.869213e-02 1 1 1 1
317 157 1.337036e-01 1 1 1 1
318 16 7.397138e-03 1 1 1 1
319 114 8.104890e-02 1 1 1 1
320 198 3.666277e-01 1 1 1 1
321 91 5.888472e-02 1 1 1 1
322 61 3.477076e-02 1 1 1 1
323 63 3.649460e-02 1 1 1 1
324 57 3.227639e-02 1 1 1 1
325 159 1.378698e-01 1 1 1 1
326 81 5.104470e-02 1 1 1 1
327 173 1.752333e-01 1 1 1 1
328 184 2.118882e-01 1 1 1 1
329 81 5.053644e-02 1 1 1 1
330 39 2.066330e-02 1 1 1 1
331 25 1.042143e-02 1 1 1 1
332 147 1.200037e-01 1 1 1 1
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850 131 9.906232e-02 1 1 1 1
851 141 1.105291e-01 1 1 1 1
852 144 1.151143e-01 1 1 1 1
853 120 8.691417e-02 1 1 1 1
854 192 2.710986e-01 1 1 1 1
855 109 7.600458e-02 1 1 1 1
856 129 9.787854e-02 1 1 1 1
857 46 2.476354e-02 1 1 1 1
858 61 3.503830e-02 1 1 1 1
859 43 2.242980e-02 1 1 1 1
860 96 6.389754e-02 1 1 1 1
861 23 1.006052e-02 1 1 1 1
862 61 3.482632e-02 1 1 1 1
863 74 4.481793e-02 1 1 1 1
864 52 2.772706e-02 1 1 1 1
865 172 1.720883e-01 1 1 1 1
866 150 1.224266e-01 1 1 1 1
867 87 5.558897e-02 1 1 1 1
868 70 4.209168e-02 1 1 1 1
869 20 9.336668e-03 1 1 1 1
870 196 3.110917e-01 1 1 1 1
871 162 1.457712e-01 1 1 1 1
872 159 1.384960e-01 1 1 1 1
873 81 5.064875e-02 1 1 1 1
874 107 7.326889e-02 1 1 1 1
875 39 2.019056e-02 1 1 1 1
876 148 1.208099e-01 1 1 1 1
877 77 4.717309e-02 1 1 1 1
878 34 1.673723e-02 1 1 1 1
879 46 2.416669e-02 1 1 1 1
880 78 4.741071e-02 1 1 1 1
881 198 3.719787e-01 1 1 1 1
882 165 1.520370e-01 1 1 1 1
883 180 1.950655e-01 1 1 1 1
884 99 6.582834e-02 1 1 1 1
885 181 2.021726e-01 1 1 1 1
886 135 1.039883e-01 1 1 1 1
887 192 2.707097e-01 1 1 1 1
888 37 1.906888e-02 1 1 1 1
889 187 2.296850e-01 1 1 1 1
890 101 6.830067e-02 1 1 1 1
891 166 1.549195e-01 1 1 1 1
892 110 7.634719e-02 1 1 1 1
893 197 3.408628e-01 1 1 1 1
894 89 5.651171e-02 1 1 1 1
895 64 3.707010e-02 1 1 1 1
896 83 5.244475e-02 1 1 1 1
897 32 1.539975e-02 1 1 1 1
898 138 1.073876e-01 1 1 1 1
899 183 2.076714e-01 1 1 1 1
900 194 2.933525e-01 1 1 1 1
901 199 3.820789e-01 1 1 1 1
902 1 7.705191e-05 1 1 1 1
903 35 1.717893e-02 1 1 1 1
904 92 6.017662e-02 1 1 1 1
905 191 2.633963e-01 1 1 1 1
906 135 1.037754e-01 1 1 1 1
907 189 2.417757e-01 1 1 1 1
908 175 1.810256e-01 1 1 1 1
909 11 5.453330e-03 1 1 1 1
910 49 2.619338e-02 1 1 1 1
911 10 4.756554e-03 1 1 1 1
912 153 1.258176e-01 1 1 1 1
913 187 2.233616e-01 1 1 1 1
914 152 1.246143e-01 1 1 1 1
915 40 2.101875e-02 1 1 1 1
916 50 2.672739e-02 1 1 1 1
917 4 2.199843e-03 1 1 1 1
918 4 2.240093e-03 1 1 1 1
919 78 4.756708e-02 1 1 1 1
920 7 3.130236e-03 1 1 1 1
921 85 5.352118e-02 1 1 1 1
922 53 2.803225e-02 1 1 1 1
923 166 1.538455e-01 1 1 1 1
924 132 1.004902e-01 1 1 1 1
925 12 5.915029e-03 1 1 1 1
926 18 8.444782e-03 1 1 1 1
927 94 6.166959e-02 1 1 1 1
928 88 5.633594e-02 1 1 1 1
929 150 1.224985e-01 1 1 1 1
930 145 1.170649e-01 1 1 1 1
931 5 2.374370e-03 1 1 1 1
932 137 1.058365e-01 1 1 1 1
933 138 1.071293e-01 1 1 1 1
934 116 8.305816e-02 1 1 1 1
935 20 9.274582e-03 1 1 1 1
936 36 1.766317e-02 1 1 1 1
937 142 1.132826e-01 1 1 1 1
938 74 4.521378e-02 1 1 1 1
939 166 1.541987e-01 1 1 1 1
940 153 1.268972e-01 1 1 1 1
941 154 1.279067e-01 1 1 1 1
942 123 8.913132e-02 1 1 1 1
943 18 8.739614e-03 1 1 1 1
944 194 2.978921e-01 1 1 1 1
945 197 3.430164e-01 1 1 1 1
946 66 3.925795e-02 1 1 1 1
947 156 1.302532e-01 1 1 1 1
948 2 1.056940e-03 1 1 1 1
949 193 2.807975e-01 1 1 1 1
950 26 1.136121e-02 1 1 1 1
951 151 1.234780e-01 1 1 1 1
952 52 2.749536e-02 1 1 1 1
953 134 1.027136e-01 1 1 1 1
954 89 5.671941e-02 1 1 1 1
955 162 1.458547e-01 1 1 1 1
956 33 1.554419e-02 1 1 1 1
957 132 9.958817e-02 1 1 1 1
958 148 1.204646e-01 1 1 1 1
959 59 3.372274e-02 1 1 1 1
960 194 2.892297e-01 1 1 1 1
961 111 7.761273e-02 1 1 1 1
962 48 2.550760e-02 1 1 1 1
963 111 7.865651e-02 1 1 1 1
964 75 4.576066e-02 1 1 1 1
965 47 2.503683e-02 1 1 1 1
966 85 5.371836e-02 1 1 1 1
967 150 1.226681e-01 1 1 1 1
968 120 8.707369e-02 1 1 1 1
969 17 8.158225e-03 1 1 1 1
970 195 3.069460e-01 1 1 1 1
971 108 7.447357e-02 1 1 1 1
972 128 9.632905e-02 1 1 1 1
973 181 2.009880e-01 1 1 1 1
974 151 1.234165e-01 1 1 1 1
975 156 1.304657e-01 1 1 1 1
976 80 5.000323e-02 1 1 1 1
977 98 6.519776e-02 1 1 1 1
978 105 7.139131e-02 1 1 1 1
979 137 1.050438e-01 1 1 1 1
980 110 7.725645e-02 1 1 1 1
981 51 2.747780e-02 1 1 1 1
982 155 1.289592e-01 1 1 1 1
983 118 8.447166e-02 1 1 1 1
984 200 4.245695e-01 1 1 1 1
985 171 1.698509e-01 1 1 1 1
986 200 5.294922e-01 1 1 1 1
987 154 1.285100e-01 1 1 1 1
988 129 9.639255e-02 1 1 1 1
989 130 9.800470e-02 1 1 1 1
990 167 1.551453e-01 1 1 1 1
991 24 1.027322e-02 1 1 1 1
992 29 1.299387e-02 1 1 1 1
993 163 1.467013e-01 1 1 1 1
994 135 1.039666e-01 1 1 1 1
995 36 1.791874e-02 1 1 1 1
996 15 7.321892e-03 1 1 1 1
997 20 9.189273e-03 1 1 1 1
998 98 6.578546e-02 1 1 1 1
999 163 1.471906e-01 1 1 1 1
1000 185 2.158297e-01 1 1 1 1
$tv
[1] 0.015
$e
[1] 9.218941
$v
[1] 4.494338
$summary
pool probability PSe PSp PPV NPV
1 1 0.001583625 0.9025 0.9970628 0.3276716 0.9998449
2 1 0.002500582 0.9025 0.9971038 0.4385710 0.9997549
3 1 0.003269132 0.9025 0.9971382 0.5084377 0.9996794
4 1 0.003976450 0.9025 0.9971699 0.5600752 0.9996098
5 2 0.004656581 0.9025 0.9966937 0.5608303 0.9995426
6 2 0.005328128 0.9025 0.9967235 0.5960398 0.9994763
7 2 0.006003726 0.9025 0.9967536 0.6267425 0.9994095
8 2 0.006693557 0.9025 0.9967843 0.6541289 0.9993413
9 3 0.007407063 0.9025 0.9963005 0.6454465 0.9992703
10 3 0.008154056 0.9025 0.9963335 0.6692676 0.9991961
11 3 0.008945696 0.9025 0.9963685 0.6916672 0.9991175
12 3 0.009795627 0.9025 0.9964062 0.7129940 0.9990329
13 4 0.010721593 0.9025 0.9957710 0.6981442 0.9989400
14 4 0.011748029 0.9025 0.9958159 0.7194277 0.9988374
15 4 0.012910694 0.9025 0.9958669 0.7406675 0.9987211
16 4 0.014265788 0.9025 0.9959265 0.7622676 0.9985852
17 5 0.015910262 0.9500 0.9500000 0.2349958 0.9991498
18 6 0.018035443 0.9500 0.9500000 0.2586921 0.9990343
19 7 0.021112395 0.9500 0.9500000 0.2906730 0.9988661
20 8 0.026981576 0.9500 0.9500000 0.3450635 0.9985427
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