How to perform a ANOVA for statistical equivalence?
I red about the two one-sided test (TOST) for equivalence, but (I think) for this study design it is not possible to perform a classical t-test, so a repeated measures ANOVA is needed.
The study design is a common pre-post treatment-control design: There are two different groups (control / treatment) and dependent two measure points at the baseline and a followup (MP1 / MP2). The research question is, if the treatments are equal.
My thought is, that the ANOVA analyses the differences between the groups. Is there a post-hoc for equivalence, special in R?
Thanks to D_Williams, I red the using-lsmeans vignette and the lsmeans reference manual. There is a function called test. With this function you can do equivalence / noninferiority or nonsuperiority tests. Now I got stuck with a new problem. Because of the study design I need a linear regression with repeated measures. So here is a example dataset:
dataset <- data.frame (ID = rep(1:16), GROUP = factor(rep(c("A","B"),8)), MP1 = c(15,12,20,17,28,24,17,10,14,10,25,23,9,18,19,20), MP2 = c(12,9,19,10,20,15,12,5,12,10,22,15,8,17,10,19), )
The linear regression should be:
data.lm <- lm (MP2 - MP1 ~ GROUP, data=dataset)
As far as I understood this answer right, Case 2b is the correct one for me. Because there are two quantitative variables and a one dichotomous variable.
Afterwards I run these commands:
library("lme4","lsmeans","estimablity") data.lsm <- lsmeans(data.lm,"GROUP") test(data.lsm, null = log(100), delta = 0.20, side="equivalence")
Delta is the equivalence margin or the range of similarity. But I am not sure what the log(100) is.
My questions are:
Is this approach right?
To be honest: I don't really understand the last steps. Does anybody got some code example for studying them?