Statistical details for confidence interval of equivalence test (Fit Curve Platform)

[#1]

Hello,

Regarding the equivalence test of the Fit Curve Platform: How does JMP calculate the confidence interval for the ratio of model parameters (e.g. slope of a linear fit)? Could you please provide statistical details and a literature reference? Thank you.

[#2]

From the JMP documentation: "The equality of the parameters is tested by analyzing the ratio of the parameters. The default decision lines are placed at ratio values of 0.8 and 1.25, representing a 25% difference." The 25% difference by ratio is commonly used to determine equivalence of curves used to fit dose-response curves and exhibit parallelism. You can change these settings if you have your own criterion.

I cannot find the statistical details about the confidence interval of the estimates. It is not the same as the least squares interval estimate.

[#3]

Dear Markbailey,

Thank you for your reply. I was aware of the JMP documentation, where I could not find any literature references and statistical details.

One guess: Could the confidence interval calculations e.g. be based on Fieller's theorem? If yes, what would be the details used for Fieller's formula (standard errors, covariance and degrees of freedom)?

[#4]

There are no references because it is common practice. It might be suggested in a guidance from ICH, though, about method development and validation.

There are no statistical details. The limits are not statistical, as I already said. They are determined by the user. They are practical limits, usually based on a failure point. That is, if the parameter estimates vary by more than the ratio, they are deemed practically different.

[#5]

Dear Markbailey,
 
Again thank you for your reply. Maybe there is a misunderstanding.

For the equivalence test to reject the null hypothesis (of "no equivalence"), the confidence interval calculated by JMP and reported in table "Equivalence Summary" in columns "Lower Confidence Limit" and "Upper Confidence Limit", must be within the "decision limits" set by the user (default: 0.8 and 1.25).

I am interested in the statistical details and literature references of calculating the confidence interval, that is, the "Lower Confidence Limit" and the "Upper Confidence Limit". Thank you.

[#6 · Accepted solution]

I got an answer from Development: "We just use the delta method as described here:

https://en.wikipedia.org/wiki/Delta_method"

[#7]

Thank you, this is helpful.