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This is my first time using an equivalency test.

I am using the tost() function in the 'equivalence' R package, and I want to test the hypothesis that these two groups are equivalent:

treated <- c(0.8488640, -1.0857180,  0.6125256, -2.3915139)
untreated <- c(-1.09906748, -0.35318684, -0.06985595,  0.57647817)

tost(treated, untreated, paired=F, epsilon = 1)

The values represent relative concentrations of a molecule (concentration at a certain time point relative to time 0), in the log2 scale. I have two treatment groups (treated and untreated.

This is the output I am getting with epsilon = 1:

    Welch Two Sample TOST

data:  treated and untreated
df = 4.1924
sample estimates:
 mean of x  mean of y 
-0.5039606 -0.2364080 

Epsilon: 1 
95 percent two one-sided confidence interval (TOST interval):
 -2.030468  1.495363
Null hypothesis of statistical difference is: not rejected 
TOST p-value: 0.2146223

First, does the epsilon = 2 mean we allow for a +/- 2% difference in means to consider equivalency? Or does it mean a 2 'unit' difference, instead of percent (%)?

From the data above, how can I determine a reasonable value for the epsilon parameter? I do not have prior knowledge of an expected range, especially since I am working with a large dataset with many different molecules that all have very different ranges of concentrations. From the box plot below, the two groups appear to have very similar means, so I would expect the result of the tost to be significant in this case.

Any advice would be very helpful, thank you!!

enter image description here

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  • The equivalence margin has to be selected before looking at the data, typically based on medical/domain-specific reasoning. Differences within the margin really count as equivalent from scientific perspective.

  • The value 1 is on the scale of the values, not 1%. In you case of log values, a difference of 1 seems extremely high. Like: a median survival of 4 versus 10 years.

  • Furthermore, the selected equivalence test does not test if the values are equivalent (spoiler: they are not), but rather is about the two means.

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  • $\begingroup$ Thanks a lot for your input! What do you think the reason is for the two means not being considered equivalent, since they look equal to me from the boxplot? Is it because of the very small sample size? If so, would another similar test be more appropriate for such small samples? $\endgroup$
    – arielle
    Commented Aug 16 at 14:51
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    $\begingroup$ The boxplots show medians, not means. Typically, reasonably small equivalence margins require quite large sample sizes. Basically, the usual 90% confidence interval for the mean difference has to sit within +-margin to claim "equivalence" at the 5% level. $\endgroup$
    – Michael M
    Commented Aug 17 at 9:36
  • $\begingroup$ I see! Thank you for this information, this was helpful! $\endgroup$
    – arielle
    Commented Aug 19 at 15:04

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