## Desultory thoughts [R for BE/BA]

Hi ElMaestro,

» to me it is exactly the opposite way around:
» A model with more than one variance component is a mixed model.

Not necessarily. It depends on what you believe [sic] is a random effect. Treatment, sequence, and period are fixed effects, right? IMHO, subject is random. When we think about interaction(s) we enter the gray zone, of course.

» I am of the impression that FDA and EMA have both been in a slight predicament with their guidances because they have both been "somewhat" aware of the specification/convergence issues with REML; hence both went in a direction with all effect s fixed as done explicitly by EMA and implicitly by FDA (when they use GLM for swr) in the guidance.

Well, the EMA’s models are wacky because they assume equal intra-subject variances of T and R. An assumption which was shown to be false in many cases. Essentially most of the information obtainable in a replicate design is thrown away.
I don’t know why the FDA does not directly estimate $$s_{wR}^2$$ from the mixed model but work with the intra-subject contrasts of R instead. More below.

» My contribution here is solely to open someone's eyes to the fact that we may not need to rely on a normal linear model for s2wr in a TRR/RTR/RRT design.

OK.

» I would much more like to think of this thread as a contribution to regulators defining the next iteration of giudelines/guidances. Whether they will see it as an advantage to use REML to derive s2wr now it is shown to be doable (not causing convergence issues, because it is not involving the silly and unestimable s2wt component), is of course their decision solely. I have done my part.

With the current guidance one gets always an estimate of $$s_{wR}^2$$. No problems in the RSABE-part if ≥0.0294. Only in the mixed-model for ABE and the partial replicate designs one may run into the convergence issues. That’s not resolved yet, unless one uses a simpler1 variance-covariance structure, which is against the guidance. But – again and again – there are cases were nothing helped, neither in SAS nor in Phoenix. Duno whether it is possible to specify Nelder-Mead in SAS or Phoenix.2 That’s why I still hold that the partial replicates are lousy designs because one might end up with no result for ABE unless one opts for the EMA’s models (which are wrong, IMHO).
OK, one step back. Since the mixed model for ABE is recommended by the FDA for ages, I wonder what people have done when they faced convergence problems…

» For consideration further down the line, for those who enter discussions about estimator bias being catastrophic: Which estimator is more biased when handling RRT/RTR/TRR: the s2wr you get from the linear model or the one you get via REML?

Good question, next question. Maybe REML…

» What would your answer imply for any future recommendations for guidelines/guidances?

Oh dear! I participated in all GBHI workshops. The discussions about reference-scaling (Rockville 2016, Amsterdam 2018) were disastrous. What do we have?
• US and China
• RSABE (any PK metric)
• No clinical justification required.3
• No upper cap on scaling.
• Mixed model for ABE, ISC for RSABE.
• EMA, WHO, and many more
• ABEL (Cmax; for modified release additionally Cmin/Cτ, partial AUCs).
• Upper cap of expansion at CVwR 50%.
• All effects fixed.
• Clinical justification (no safety issues wider wider limits).
• Demonstration that CVwR is not caused by outliers.
• Like above but AUC only and upper cap 57.4%.
• Mixed effects model.
• Outliers can be excluded if procedure specified in the protocol (irrespective of the treatment).
And yes, problems with inflation of the Type I Error, which all regulators prefer to ignore. Kudos to some companies taking the issue more seriously and adjusting α downwards.

» (I am not a hardliner myself: I am usually thinking biased estimators are still useful estimators)

Agree.

1. Actually it is the other way ’round. The model of the guidance is overspecified (read: wrong) for partial replicates.
2. I played around with a lot of optimizers / settings in R the last three days. Only the grid search was stable (though slow). All others ran into singularities even with tweaked parameter constraints.
3. Yeah, highly variable drugs are safe drugs. Instead of coming up with guidances for the “highly variable narrow therapeutic index drugs” dagibatran and rivaroxaban, IMHO, they should be taken off the market. Regulators should be concerned about protecting the public health and not the profits of the industry.

Dif-tor heh smusma 🖖
Helmut Schütz

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