HPLC Equivalence Study: Simultaneous Change of Instrument and Column

[#1]

Hello everyone,

I would appreciate your advice on the most appropriate statistical approach for an HPLC equivalence study.

Background

We need to demonstrate equivalence between our current and future HPLC systems. However, two factors are changing simultaneously:

• the HPLC instrument;
• the chromatographic column.

In routine use, these changes will not necessarily be implemented simultaneously, but the study is intended to support the transition to the new configuration.

Configurations Evaluated

• A: Old instrument + old column (current routine configuration)
• B: New instrument + new column (target configuration)
• C: Old instrument + new column (intermediate configuration)

The same samples will be analyzed under all three conditions, so the data will be paired.

Question

Which statistical approach would you recommend to demonstrate equivalence between the systems and, if possible, distinguish the effect of the instrument from the effect of the column?

I am considering several options.

Option 1: Equivalence Testing (TOST)

• A vs B
• A vs C

Option 2: Mixed Model Followed by TOST

For JMP users, have you implemented this approach using the Repeated Structure option, particularly with an Unequal Variances covariance structure? If so, what were the benefits and limitations?

Option 3: Alternative Approach

• Design of Experiments (DOE);
• Any other methodology you have successfully applied in a similar context.

Sample Size Determination

I would also be interested in recommendations regarding sample size calculations for this type of equivalence study

Study Limitation

We do not have the additional configuration:

• D: New instrument + old column

Thank you in advance for your insights, experience, and recommendations.

[#2]

Hi @BayesKnight : I lot to upack here. But, in no particular order:

1. If you had only two configurations, a mixed model with sample as a random effect and configuration as a fixed effect (Option 2 as you've described) is exactly a paried t-test. So, that is easily extendable with more than two confgurations via the mixed model. Then you can carry out pairwise TOSTs. within that mixed model structure (whatever the covariance structure).  In general, this would be more powerful than option 1.

2. Sample size; for greater than two configurations, this will take simulation for the mixed model appoach. Since the data are "paired", you may be able to get a pretty good idea of sample size via the "Power for One Sample Equivalence of Means" platform. 

3. Distinguishing the effect of the instrument from the effect of the column will, generally speaking, take some assumptions (no interaction).