poolbinom.logit {binomSamSize} | R Documentation |
Calculate logit based confidence interval for the 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.
poolbinom.wald(x, k, n, conf.level=0.95) poolbinom.logit(x, k, n, conf.level=0.95)
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 |
Assume the individual probability of experiencing the event for each of k\cdot n individuals is π, i.e. the response is Bernoulli distributed X_i \sim B(π). For example π could be the prevalence of a disease in veterinary epidemiology.
Now, instead of considering each individual the k\cdot n samples are pooled into n pools each of size k. A pool is positive if there is at least one positive in the pool. Let X be the number of positive pools. Then
X \sim Bin(n, 1-(1-π)^k)
.
The present function computes an estimator and confidence interval for
π by computing the MLE and standard error for
\hat{π}. A Wald confidence interval is formed using
\hat{π} \pm z_{1-α/2}\cdot se(\hat{π}). In case of
poolbinom.logit
a logit transformation is used, i.e. the
standard error for logit(\hat{π}) is computed and the Wald-CI
is derived on the logit-scale which is then backtransformed using the
inverse logit function. In case x=0 or x=n the logit of
\hat{π} is not defined and hence the confidence interval is
not defined in these two situation. To fix the problem we use the
intervals (0,
\hat{π}_u(x=0)) and (\hat{π}_l(x=n),1), respectively, where
π_u and π_o are the respective borders of a
corresponding LRT interval.
The poolbinom.wald
approach corresponds to method 2 in the
Cowling et al. (1999). The logit transformation improves on this
procedure, because the method ensures that the interval is in the
range (0,1).
A data.frame containing the observed proportions and the lower and
upper bounds of the confidence interval. The style is similar
to the binom.confint
function of the binom
package
M. Höhle
D. W. Cowling, I. A. Gardner, W. O. Johnson (1999), Comparison of methods for estimation of individual level prevalence based on pooled samples, Preventive Veterinary Medicine, 39:211–225
poolbinom.wald(x=0, k=10, n=34, conf.level=0.95) poolbinom.logit(x=0:1, k=10, n=34, conf.level=0.95) poolbinom.logit(x=1, k=seq(10,100,by=10), n=34, conf.level=0.95) poolbinom.logit(x=0:34,k=1,n=34)