binomSamSize (version 0.1-3)

poolbinom.lrt: Calculate LRT based confidence interval for binomial proportion for pooled samples

Description

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

Usage

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

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

Details

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

$$\pi = g(\theta) = 1 - (1-\pi)^{1/k}$$.

One then knows that the borders for $\pi$ are just transformations of the borders of theta using the above $g(\theta)$ function.

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

Examples

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)