Perm.CI.RLH {RI2by2}

Permutation test confidence interval for a treatment effect on a binary outcome

Description

Computes permutation-based confidence intervals for the average treatment effect on a binary outcome in an experiment where m of n individuals are randomized to treatment by design. This function is based on the modified approach (RLH) in Rigdon, Loh and Hudgens (forthcoming). The Chiba (2015) and Blaker (2000) intervals are also returned. There is an additional option of specifying the maximum number of hypothesis tests to be carried out.

Usage

Perm.CI.RLH(data, level, verbose=FALSE, total_tests=NA)

Arguments

data

observed 2 by 2 table in matrix form where row 1 is the treatment assignment Z=1 and column 1 is the binary outcome Y=1

level

significance level of hypothesis tests, i.e., method yields a 100(1-level)% confidence interval

verbose

If TRUE, returns an additional data frame listing all the values of (n_{11},n_{10},n_{01},n_{00}) tested, and the corresponding p-values; default = FALSE.

total_tests

maximum number of hypotheses to be tested in total, with a minimum of two for each possible value of (n_{10}-n_{01})/n; default = NA. By default, all hypotheses are evaluated until the minimum and maximum values of (n_{10}-n_{01})/n with p-values \ge level (or level/2 for the Chiba intervals) are found.

Value

A list with the following items:

Chiba

Chiba confidence interval

RLH

RLH confidence interval

Blaker

Blaker confidence interval

tau.hat

estimated average treatment effect

p_values

if verbose=TRUE, a data frame with all the p-values from the hypothesis tests; default=FALSE

Author(s)

Wen Wei Loh [e-mail]

References

Rigdon, J.R. and Hudgens, M.G. (2015). Randomization inference for treatment effects on a binary outcome. Statistics in Medicine, 34(6), 924-935.

Chiba, Y. (2015). Exact tests for the weak causal null hypothesis on a binary outcome in randomized trials. Journal of Biometrics & Biostatistics, 6(244).

Chiba, Y. (2016). A note on exact confidence interval for causal effects on a binary outcome in randomized trials. Statistics in Medicine, 35(10), 1739-1741.

Blaker, H. (2000). Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics, 28(4), 783-798.

Rigdon, J.R., Loh W.W. and Hudgens, M.G. (forthcoming). Response to comment on "Randomization inference for treatment effects on a binary outcome."

Examples

ex = matrix(c(11,1,7,21),2,2,byrow=TRUE)
Perm.CI.RLH(ex,0.05)

ex = matrix(c(7,5,1,27),2,2,byrow=TRUE)
Perm.CI.RLH(ex,0.05)
Perm.CI.RLH(ex,0.05, verbose=TRUE)

ex = matrix(c(33,15,11,37),2,2,byrow=TRUE)
Perm.CI.RLH(ex,0.05, total_tests=1000)
Perm.CI.RLH(ex,0.05)