Likelihood Ratio confidence interval for Binomial proportion

This function calculates the Likelihood Ratio (LRT) confidence interval for a Binomial proportion. It is vectorized, allowing the evaluation of single values or vectors.

ci_p_LRT(x, n, conf.level = 0.95)

Arguments

x: A number or a vector with the number of successes.
n: A number or a vector with the number of trials.
conf.level: Confidence level for the returned confidence interval. By default, it is 0.95.

Value

A vector with the lower and upper limits.

Details

This function computes the confidence interval for a Binomial proportion based on the Likelihood Ratio Test (LRT). The confidence interval is defined as the set of values for $p$ that satisfy the following condition:

$$-2 \log \left(\frac{L(p)}{L(\hat{p}_{ML})}\right) \leq \chi^2_{\gamma}(1),$$

where $L(p)$ is the likelihood function for the binomial model, $\hat{p}_{ML} = x / n$ is the maximum likelihood estimator for $p$, and $\chi^2_{\gamma}(1)$ is the $1-\gamma$ quantile of the chi-square distribution with 1 degree of freedom.

The confidence limits are calculated numerically using the uniroot function in R. Special care is taken to handle edge cases where $x = 0$ or $x = n$, setting the limits to 0 or 1, respectively.

References

Somerville, M. C., & Brown, R. S. (2013). Exact likelihood ratio and score confidence intervals for the binomial proportion. Pharmaceutical statistics, 12(3), 120-128.

Author

David Esteban Cartagena Mejía, dcartagena@unal.edu.co

Examples

ci_p_LRT(x = 15, n = 50, conf.level = 0.95)
#>           [,1]
#> [1,] 0.1851811
#> [2,] 0.4348277