ci.prat: Confidence intervals for the ratio of binomial and multinomial proportions

Description

A number of methods have been develeloped for obtaining confidence intervals for the ratio of two binomial proportions. These include the Wald/Katz-log method (Katz et al. 1978), adjusted-log (Walter 1975, Pettigrew et al. 1986), Koopman asymptotic score (Koopman 1984), Inverse hyperbolic sine transformation (Newman 2001), the Bailey method (Bailey (1987), and the Noether (1957) procedure. Koopman results are found iteratively for most intervals using root finding.

Usage

ci.prat(y1, n1, y2, n2, conf = 0.95, method = "katz.log", 
bonf = FALSE, tol = .Machine$double.eps^0.25)

Arguments

The ratio numerator number of successes. A scalar or vector.

The ratio numerator number of trials. A scalar or vector of length(y1)

The ratio denominator number of successes. A scalar or vector of length(y1)

The ratio denominator number of trials. A scalar or vector of length(y1)

conf

The level of confidence, i.e. 1 - P(type I error).

method

Confidence interval method. One of "adj.log","bailey","katz.log","koopman","sinh-1" or "noether". Partial distinct names can be used.

bonf

Logical, indicating whether or not Bonferroni corrections should be applied for simultaneous inference if y1, y2, n1 and n2 are vectors.

tol

The desired accuracy (convergence tolerance) for the iterative root finding procedure when finding Koopman and Agresti-Min intevals. The default is taken to be the smallest positive floating-point number of the workstation implementing the function, r

Details

See Aho and Bowyer (in review) for computational details. Koopman et al. (1984) suggested methods for handling extreme cases of y1, n1, y2, and n2 (see below). These are applied through exception handling here.

References

Agresti, A., Min, Y. (2001) On small-sample confidence intervals for parameters in discrete distributions. Biometrics 57: 963-971. Aho, K., and Bowyer, T. (In review) Asymptotic confidence intervals for ratios of proportions with an emphasis on ratios of multinomial random variables (selection ratios). Ecological Modelling. Bailey, B.J.R. (1987) Confidence limits to the risk ratio. Biometrics 43(1): 201-205. Katz, D., Baptista, J., Azen, S. P., and Pike, M. C. (1978) Obtaining confidence intervals for the risk ratio in cohort studies. Biometrics 34: 469-474 Koopman, P. A. R. (1984) Confidence intervals for the ratio of two binomial proportions. Biometrics 40:513-517. Manly, B. F., McDonald, L. L., Thomas, D. L., McDonald, T. L. and Erickson, W.P. (2002) Resource Selection by Animals: Statistical Design and Analysis for Field Studies. 2nd edn. Kluwer, New York, NY Newcombe, R. G. (2001) Logit confidence intervals and the inverse sinh transformation. The American Statistician 55: 200-202. Pettigrew H. M., Gart, J. J., Thomas, D. G. (1986) The bias and higher cumulants of the logarithm of a binomial variate. Biometrika 73(2): 425-435. Walter, S. D. (1975) The distribution of Levins measure of attributable risk. Biometrika 62(2): 371-374.

Examples

Run this code

# From Koopman (1984)
ci.prat(y1 = 36, n1 = 40, y2 = 16, n2 = 80, method = "katz")
ci.prat(y1 = 36, n1 = 40, y2 = 16, n2 = 80, method = "koop")