Parallelism Testing for Groups of 4PL Curves

Question

Hello All,

I have what may be a very naïve question: is it valid to do parallelism testing on a group of independent curves (4PL in this case) at one time?

I have a subset of potency data where all of the individual fits are good.  p values for both both F test and Chi square well below 0.05...so the test is indicating non-parallelism.  Now...what I am wondering, is this something that needs to be done on a pairwise bases (i.e., iteratively)?  If there is one outlier (a non-parallel response)...does this impact the whole output?  I have about 20 curves in each subset.

Thanks in advance!

Chris

Mark_Bailey · Answer

At a minimum, the question of parallel curves is one check that the binding of an unknown sample is the same as the binding of a known sample. What is the standard in each subset? What is the nature of the rest of the subset? Are the other samples of the same analyte at unknown concentrations? Are they replicate assays?

MRB3855 · Answer

To unpack this a little further; if you have 20 curves to compare for parallelism, just the sample size alone will increase your power (correctly concluding they are not parallel) so much, that you may get a low p-value (<0.05, say) when the differences  between the curves is tiny (real, but tiny and meaningless).  This is sometimes called an overpowered experiment; i.e., in general, if you have enough data you increase the chances of rejecting the null hypothesis (the null here is curves are parallel) because large sample sizes can identify small (and perhaps negligible) differences. This is another good reason to not use that method to test parallelism.

MRB3855 · Answer

Lot's to unpack here. But...to answer your question about "If there is one outlier (a non-parallel response)...does this impact the whole output? ". Yes, one bad actor can reject (p-value < 0.05, say). your parallelism test.  And, FWIW, this is the "old" way of determining parallelism.  The most appropriate way is to test for equivalence between model parameters (for parallelism in the 4p logistic model, this is growth rate, and asymptotes). This can be done via the Equivalence Test option in the red triangle pull down menu of the Fit Curve results. Therein, you can also define your equivalence bounds for the ratio (Decision Limits as they are called in the Fit Curve platform). If desired, you can look at all pairwise comparisons (caution: if you have 20 curves, that is 190 pairwise comparisons) if you perform the equivalence test several times since you have to choose a reference curve (reference will be in the denominator of all confidence intervals for ratios). Equivalence testing tests for practical equivalence (ratio within Decision Limits) rather than a difference (as tested via the p-value for parallelism). i.e., "are the curves 'parallel enough' such that any differences are of no practical significance?" is the appropriate question, rather than "are they different"?.  As I said, there is a lot to unpack here; there is a load of info out there on testing for parallelism, and see attached for a fairly readable explanation on the details.

Parallelism_2012Yang262-9.pdf