poolbinom.lrt: Calculate LRT based confidence interval for binomial...

Description Usage Arguments Details Value Author(s) Examples

Description

Calculate LRT based confidence interval for the Bernoulli proportion of k*n individuals, which are pooled into n pools each of size k. Observed is the number of positive pools x.

Usage

1
poolbinom.lrt(x, k, n, conf.level=0.95, bayes=FALSE, conf.adj=FALSE)

Arguments

x

Number of positive pools (can be a vector).

k

Pool size (can be a vector).

n

Number of pools (can be a vector).

conf.level

The level of confidence to be used in the confidence interval

bayes

See binom.bayes

conf.adj

See binom.bayes

Details

Compute LRT based intervals for the binomial response X \sim Bin(n, θ), where θ = 1 - (1-π)^k. As a consequence,

π = g(θ) = 1 - (1-π)^{1/k}

.

One then knows that the borders for π are just transformations of the borders of theta using the above g(θ) function.

For further details about the pooling setup see poolbinom.logit.

Value

A data.frame containing the observed proportions and the lower and upper bounds of the confidence interval. The output is similar to the binom.confint function of the binom package

Author(s)

M. H<f6>hle

Examples

1
2
3
binom.lrt(x=0:34,n=34)
poolbinom.lrt(x=0:34,k=1,n=34)
poolbinom.lrt(x=0:34,k=10,n=34)

Example output

Loading required package: binom
   method  x  n       mean      lower     upper
1     lrt  0 34 0.00000000 0.00000000 0.0549260
2     lrt  1 34 0.02941176 0.00172715 0.1232101
3     lrt  2 34 0.05882353 0.01003468 0.1707730
4     lrt  3 34 0.08823529 0.02267441 0.2131131
5     lrt  4 34 0.11764706 0.03809867 0.2524963
6     lrt  5 34 0.14705882 0.05538987 0.2898577
7     lrt  6 34 0.17647059 0.07420031 0.3256911
8     lrt  7 34 0.20588235 0.09421155 0.3602949
9     lrt  8 34 0.23529412 0.11519935 0.3938651
10    lrt  9 34 0.26470588 0.13709301 0.4265548
11    lrt 10 34 0.29411765 0.15977785 0.4583825
12    lrt 11 34 0.32352941 0.18318363 0.4895578
13    lrt 12 34 0.35294118 0.20725749 0.5200322
14    lrt 13 34 0.38235294 0.23195958 0.5498753
15    lrt 14 34 0.41176471 0.25726018 0.5791178
16    lrt 15 34 0.44117647 0.28313780 0.6077818
17    lrt 16 34 0.47058824 0.30957792 0.6358823
18    lrt 17 34 0.50000000 0.33657220 0.6634278
19    lrt 18 34 0.52941176 0.36411773 0.6904221
20    lrt 19 34 0.55882353 0.39221824 0.7168622
21    lrt 20 34 0.58823529 0.42088220 0.7427398
22    lrt 21 34 0.61764706 0.45012467 0.7680404
23    lrt 22 34 0.64705882 0.47996781 0.7927425
24    lrt 23 34 0.67647059 0.51044218 0.8168164
25    lrt 24 34 0.70588235 0.54161753 0.8402221
26    lrt 25 34 0.73529412 0.57344519 0.8629070
27    lrt 26 34 0.76470588 0.60613487 0.8848006
28    lrt 27 34 0.79411765 0.63970506 0.9057885
29    lrt 28 34 0.82352941 0.67430886 0.9257997
30    lrt 29 34 0.85294118 0.71014227 0.9446101
31    lrt 30 34 0.88235294 0.74750367 0.9619013
32    lrt 31 34 0.91176471 0.78688685 0.9773256
33    lrt 32 34 0.94117647 0.82922704 0.9899653
34    lrt 33 34 0.97058824 0.87678987 0.9982729
35    lrt 34 34 1.00000000 0.94507400 1.0000000
   method  x k  n        mle      lower     upper
1   logit  0 1 34 0.00000000 0.00000000 0.0549260
2   logit  1 1 34 0.02941176 0.00172715 0.1232101
3   logit  2 1 34 0.05882353 0.01003468 0.1707730
4   logit  3 1 34 0.08823529 0.02267441 0.2131131
5   logit  4 1 34 0.11764706 0.03809867 0.2524963
6   logit  5 1 34 0.14705882 0.05538987 0.2898577
7   logit  6 1 34 0.17647059 0.07420031 0.3256911
8   logit  7 1 34 0.20588235 0.09421155 0.3602949
9   logit  8 1 34 0.23529412 0.11519935 0.3938651
10  logit  9 1 34 0.26470588 0.13709301 0.4265548
11  logit 10 1 34 0.29411765 0.15977785 0.4583825
12  logit 11 1 34 0.32352941 0.18318363 0.4895578
13  logit 12 1 34 0.35294118 0.20725749 0.5200322
14  logit 13 1 34 0.38235294 0.23195958 0.5498753
15  logit 14 1 34 0.41176471 0.25726018 0.5791178
16  logit 15 1 34 0.44117647 0.28313780 0.6077818
17  logit 16 1 34 0.47058824 0.30957792 0.6358823
18  logit 17 1 34 0.50000000 0.33657220 0.6634278
19  logit 18 1 34 0.52941176 0.36411773 0.6904221
20  logit 19 1 34 0.55882353 0.39221824 0.7168622
21  logit 20 1 34 0.58823529 0.42088220 0.7427398
22  logit 21 1 34 0.61764706 0.45012467 0.7680404
23  logit 22 1 34 0.64705882 0.47996781 0.7927425
24  logit 23 1 34 0.67647059 0.51044218 0.8168164
25  logit 24 1 34 0.70588235 0.54161753 0.8402221
26  logit 25 1 34 0.73529412 0.57344519 0.8629070
27  logit 26 1 34 0.76470588 0.60613487 0.8848006
28  logit 27 1 34 0.79411765 0.63970506 0.9057885
29  logit 28 1 34 0.82352941 0.67430886 0.9257997
30  logit 29 1 34 0.85294118 0.71014227 0.9446101
31  logit 30 1 34 0.88235294 0.74750367 0.9619013
32  logit 31 1 34 0.91176471 0.78688685 0.9773256
33  logit 32 1 34 0.94117647 0.82922704 0.9899653
34  logit 33 1 34 0.97058824 0.87678987 0.9982729
35  logit 34 1 34 1.00000000 0.94507400 1.0000000
   method  x  k  n         mle        lower       upper
1   logit  0 10 34 0.000000000 0.0000000000 0.005633278
2   logit  1 10 34 0.002980845 0.0001728494 0.013062724
3   logit  2 10 34 0.006044123 0.0010080278 0.018551884
4   logit  3 10 34 0.009194799 0.0022909151 0.023682152
5   logit  4 10 34 0.012438311 0.0038768058 0.028682233
6   logit  5 10 34 0.015780630 0.0056820954 0.033649810
7   logit  6 10 34 0.019228333 0.0076800951 0.038640358
8   logit  7 10 34 0.022788690 0.0098461555 0.043691582
9   logit  8 10 34 0.026469767 0.0121646964 0.048832665
10  logit  9 10 34 0.030280544 0.0146366644 0.054091362
11  logit 10 10 34 0.034231063 0.0172582367 0.059477323
12  logit 11 10 34 0.038332605 0.0200307617 0.065036502
13  logit 12 10 34 0.042597899 0.0229580417 0.070774304
14  logit 13 10 34 0.047041391 0.0260460855 0.076720311
15  logit 14 10 34 0.051679568 0.0293030374 0.082901347
16  logit 15 10 34 0.056531362 0.0327392434 0.089347302
17  logit 16 10 34 0.061618669 0.0363674370 0.096092098
18  logit 17 10 34 0.066967008 0.0402030480 0.103174756
19  logit 18 10 34 0.072606374 0.0442646021 0.110641218
20  logit 19 10 34 0.078572363 0.0485745459 0.118545731
21  logit 20 10 34 0.084907677 0.0531597935 0.126953738
22  logit 21 10 34 0.091664174 0.0580530947 0.135945310
23  logit 22 10 34 0.098905720 0.0632946017 0.145620097
24  logit 23 10 34 0.106712253 0.0689341474 0.156104509
25  logit 24 10 34 0.115185750 0.0750403237 0.167562459
26  logit 25 10 34 0.124459260 0.0816727224 0.180212047
27  logit 26 10 34 0.134711151 0.0889656485 0.194352610
28  logit 27 10 34 0.146188672 0.0970456056 0.210394049
29  logit 28 10 34 0.159249308 0.1061171716 0.229024506
30  logit 29 10 34 0.174439113 0.1164757195 0.251239310
31  logit 30 10 34 0.192656957 0.1285840445 0.278741438
32  logit 31 10 34 0.215551867 0.1432363655 0.315215994
33  logit 32 10 34 0.246722305 0.1620040674 0.368824208
34  logit 33 10 34 0.297167059 0.1889182275 0.470662083
35  logit 34 10 34 1.000000000 0.2518687492 1.000000000

binomSamSize documentation built on May 1, 2019, 10:14 p.m.