kkmann/farringtonmanning

farringtonmanning's Issues

Discrepancy between P value and 95%CI for non-inferiority analysis

I am conducting a non-inferiority trial analysis, using your code as below:

library(DescrTab2)
x <- c(rep(TRUE, 52), rep(FALSE, 4))
y <- c(rep(TRUE, 54), rep(FALSE, 1))

farrington.manning(x, y, -.15,alpha = 0.025)

the non-inferiority margin is -0.15, alpha=0.25, alternative using default setting greater.

the result is the following

Farrington-Manning test for non-inferiority of rates

data: group 1: x, group 2: y
Z-statistic = 1.8949, noninferiority margin = -0.15, p-value = 0.02905
alternative hypothesis: true rate difference (group 1 - group 2) is greater than -0.15
95 percent confidence interval:
-0.1542330 0.0328274
sample estimates:
rate difference (group 1 - group 2)
-0.05324675

My question is , how can we understand the discrepancy between the 95%CI and the p value. The p value showed that the alternative hypothesis: true rate difference (group 1 - group 2) is greater than -0.15 is justified, and the study reach the non-inferiority. However, the 95%CI cover the -0.15 margin, suggesting the non-inferiority not reached.

How to understand this? What is the final conclusion for this analysis?