Bioassay data from customer who wants a logit function transformation before running potency test

Question

Hello folks,

I have a customer who is trying to mimic the report attached below made with combistats software to perform potency, parallelism analysis, etc. on a dose-response data (# of deaths out of total n). Please see data table attached.

The issue here is that in this report, the Y was transformed with a logit function. How can we perform this in JMP? Can JMP match the results found in this report?

The customer is familiar with the logistic regression in Fit Curve used for dose-response fitting. The need to mimic the report and perform a transformation with the logit function is the issue here.

Any insight would be appreciated.

Data.jmp

Logit in CombiStats.pdf

russ_wolfinger · Answer

This is turning out to be an intriguing little problem @yasmine_hajar   Thanks for the comments @DonMcCormack and @Chris_Kirchberg .  While the way we handle this is much better and in line with best modern statistical practices, that's not the OP.   I recall a few difficult and frustrating cases over the years trying to reproduce results from other software packages.

The ANOVA table in the CombiStats doc is old school with classic Sums of Squares &etc, but it is not clear at all how they computed it.  The doc does not appear to have sufficient detail on their exact approach.   I just quickly tried several things, including logits using continuity corrections with 0.5 and a few other values, various weights, and even the GLMM add-in https://community.jmp.com/t5/JMP-Add-Ins/Generalized-Linear-Mixed-Model-Add-in/ta-p/284627   @MeichenDong  wrote before @ElizabethClaassenimplemented it in Fit Model (which computes pseudo logits and weights), but nothing is matching their ANOVA.

If anyone is interested in a numerical/statistical puzzle, I believe it is possible to reverse engineer the exact 8 numbers they use as Ys based on results from their ANOVA table, but I haven't tried to set this up.   It would be a nonlinear system of equations with classic ANOVA formulas for sums of squares and the 8 Ys as the unknowns.  There's a chance they are also using weights--the doc mentions using inverse variance, which for a binomial would be 1/(n*p*(1-p)).

@yasmine_hajar    Wondering if the customer would be willing to contact CombiStats and ask for details on exactly how Example 5.3.2 (Logits) is computed, indicating they would like to reproduce the results independently.   Once we see that I'm sure we can rep it somehow.

DonMcCormack · Answer

Based on CombiStats web page, they're using the European Pharmacopoeia as a basis for their analysis (Quantile responses approach). I did a talk on this at Discovery EU 2019 but focused mainly on the calculation of relative potency. There are a few challenges with trying to reproduce this in JMP. First is that you'd need to use Generalized Linear Models or Generalized Regression to the the Logit fit. Your output will include Chi-squared statistics, but not sums of squares and F-tests. When I tried to do this using the process from my talk, I couldn't match the results. I'm not sure if what they're calling non-linear is the same as what I used. Are they using MLE or LS? Does it make a difference? The design used to collect the data can also make a difference and I'm unsure if what I talked about is consistent with the design from the example.

This is not the first time I've seen EP 5.3 come up. I'd be interested to hear from @SamGardner

Chris_Kirchberg · Answer

a right click on proportions and choosing new columns formula>specialty>logit will give the transform needed, but as Russ stated, 0 proportions will give -inf values (and 1 will give +inf values) and will result as a missing value. In this case it I have seen people use generalized linear models (JMP can do that) with response and total in the y, dose and sample in x. Then binomial distribution with logit link. The problem here is that one does not have the convenient methods of test for parallelism, potency, etc. and you would have to calculate all of these manually.