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NEW WORKING PAPER @arxiv

A retrospective, model-based analysis of a fatal dose-finding trial. [THREAD] 1/
arxiv.org/abs/2004.12755
@arxiv The trial in question came to my attention 1.5 years ago, thanks (as is so often the case) to @Lymphomation: 2/
@arxiv @Lymphomation As you see in the thread linked above, my immediate response was in terms of the #PrecautionaryCoherence principle, explained in the quick video below: 3/
@arxiv @Lymphomation This latest paper, however, advances past the generalities and abstraction of the PC principle, into the more concrete realm of a model-based analysis grounded in mechanistic realism and using actual trial data. 4/
@arxiv @Lymphomation But let me stress I’m not abandoning the PC principle, but rather pursuing its natural development: Technically, the key to a useful model was using #latentvariables—an idea at the core of this Letter published last month on #PrecautionaryCoherence 5/
But before laying out the model, we need background story. 6a/

8 Oct 2018
affimed.com/affimed-places…
$AFMD puts 2 #AFM11 trials on clinical hold for SAEs in 3 patients:
• 2 life-threatening AEs in clinicaltrials.gov/ct2/show/NCT02… (R/R NHL)
• 1 death in clinicaltrials.gov/ct2/show/NCT02… (R/R B-ALL)
12 Oct 2018: @US_FDA places a full clinical hold on #AFM11 program. 6b/
@US_FDA 17 Apr 2019: $AFMD Regulatory Update indicates ongoing discussions with FDA over the clinical hold. 6c/
affimed.com/affimed-provid…
@US_FDA 22 May 2019: $AFMD terminates #AFM11 Phase 1 program. 6d/
affimed.com/affimed-announ…
@US_FDA So here we have a phase 1 oncology trial that vividly contravenes the commonplace description of such trials as “primarily concerned with safety.”

A trial such as this demands the closest and most concrete analysis we can bring to it. 7/
[my abstract below]
@US_FDA For my analysis, I’ve abstracted (as best I can) doses and toxicities from the B-ALL trial, which was reported at #ASH2018. (AFAIK, the NHL trial has not been reported at a scientific meeting or in the literature.) 8/
Here’s Table 1 from my paper, where I abstract, for each of the N=17 participants:
• a low dose causing no tox
• highest dose received
• CTCAE Grade at high dose.

Of note, the step-up dosing used in this trial was crucial for yielding these dose pairs. 9/
My primary data come from the SAFETY section of the #ASH2018 poster by Salogub et al. 10/
affimed.com/wp-content/upl…
[images below]
I’ve tried to be quite transparent about my uncertainties in this abstraction. (See esp. the note about Patient 16 highlighted below.) 11/
THE MODEL

So now I need a dose-response model for toxicity that incorporates BOTH:
(a) ordinal toxicities AND
(b) inter-individual heterogeneity.

Several extant models already do (a), and I’ll discuss their connections with my own model below.

But (b) is a new requirement. 12/
My approach is to take the MTDᵢ notion at the heart of my opening #DTAT argument 3+ years ago, and extend it to ordinal toxicities.

The key to this notationally is to posit that a DLT occurs at the boundary between CTCAE grades 2–3, and to write: 13/

MTDᵢ ≡ MTDᵢᵍ, g=3
Thus, we have {MTDᵢᵍ | g=1,…,5}:

MTDᵢ¹ = max dose patient i can tolerate before getting a Grade 1 toxicity

MTDᵢ² = max dose patient i can tolerate before getting a Grade 2 toxicity


MTDᵢ⁵ = max dose patient i can tolerate before getting a Grade 5 (fatal) toxicity. 14/
Whereas in previous work I have supposed a Gamma distribution for MTDᵢ (remember, this is the same as MTDᵢ³), here a lognormal distribution proves more convenient: 15/

log MTDᵢ ~ 𝒩(μ,τ), τ ≡ 1/σ².
From a #trialsafety perspective, a model of ordinal toxic dose-response will be useless unless it supports extrapolation from the low-grade toxicities we may be willing to encounter during careful #titration, to the higher-grade toxicities we hope to avoid. 16/
So (as you see above), I’ve posited a link between the {MTDᵢᵍ | g=1,…,5}. The manner in which I do this:

MTDᵢᵍ = rᵢ⁽ᵍ⁻³⁾·MTDᵢᵍ (Eq. 3)

effectively assumes that the grading system is superbly aligned with the underlying dose-response. 17/
That is, each individual i’s toxic response is characterized by a ratio rᵢ that links—in a geometric sequence—the maximum tolerable doses within each toxicity grade. (Equivalently, the logarithms of these doses are an arithmetic sequence with constant difference log rᵢ.) 18/
Now you know I wouldn’t be caught dead NOT subscripting rᵢ to indicate its likely inter-individual heterogeneity. But in this analysis, with so few participants—and even fewer toxicities—I’ve required a further identifying restriction: 19/

log rᵢ ~ 𝒩(log r₀, τᵣ) , τᵣ≫1.
Before explaining the priors I’ve placed on the parameters in this Bayesian model, it’s worth skipping ahead a bit in the paper, to its discussion of some formal connections with an ordinal toxicity model of Bekele & Thall (2004) 20/
odin.mdacc.tmc.edu/~pfthall/main/…
The first thing to note about the Bekele & Thall model is that it incorporates *multiple* toxicities, in contrast to the neurotoxicity of chief concern in the AFM11 trials. Thus, their model has an extra j index. (Note too that they adopt a logarithmic dose scaling as I did.) 21/
The key point, however, is that they introduce a normally distributed #latentvariable Z that serves exactly the same role *formally* as my log MTDᵢ: 22/
The difference is, however, that this Bekele & Thall treat Z as a mere technical convenience. Thus, they overlook the opportunity to lend it a realistic, pharmacologic interpretation such as I give to MTDᵢ. 23/
This easy dismissal of #latentvariables pervades the statistical #dosefinding literature. I tend to see it as the symptom of a fecklessness pervading medical statistics as a whole. 24/

[WARNING DO NOT READ THREAD:]
More to the present point, this results in Bekele & Thall’s failure to acknowledge PKPD heterogeneity in their model. Their model remains, for all the weight of its matrix notation, a 1-size-fits-all #dosefinding model. 25/
One notable methodologic implication of this is that they must conduct their prior elicitation with physicians in terms of statisticians’ dose-cohort abstractions.

How much easier would this elicitation be, conducted in terms of #titration in the individual patient! 26/
THE PRIORS

But now back to my own priors, inferred from the actual design of the trial. To begin, the prior on μ:

μ ~ 𝒰[2.9, 7.5]

aimed to center

log MTDᵢ ~ 𝒩(μ,τ)

at a median of log(180), the Cohort 5 target dose [ng/kg/week] ±1 order of magnitude either side. 27/
In earlier work on the #economics of #dosefinding, I focused attention on the coefficient of variation, CV(MTDᵢ). 28/
So I have chosen to place my prior on this CV instead of the much less intuitive τ:

CV ~ 𝒩(0.5, σ=1/6).

I argue that adopting a dose-escalation design requires holding an expectation that CV is modest. The σ=1/6 puts CV>1 in the normal distribution’s 3σ upper tail. 29/
Finally (for the priors) I place a vague uniform prior on r₀, centered on 3 (which is the ratio between the trial’s dose levels, as well as the step-up dosing ratio) and extending ±2:

r₀ ~ 𝒰(1, 5).

Both endpoints here are safely outside the bounds of reason. 30/
This all comes together in the following JAGS model: 31/
As someone who delights in the clarity of thought one can achieve through declarative programming, I absolutely adore JAGS. Thank you @martyn_plummer for this magnificent tool! 32/

sourceforge.net/projects/mcmc-…
@martyn_plummer The model runs fast, yielding effective samples sizes in the 1000’s in just seconds. 33/
@martyn_plummer Figs. 1 and 2 show the posterior densities of MTDᵢ for the patients who experienced toxicities and for those who didn’t. 34/
The contrast between those Figures [note also the change of scale] clearly shows that we learn most from the patients who experience toxicities.

Judicious #titration yields better dose-finding trials by every measure—including #informativeness! 35/
How about them #hyperparameters?

While μ≈5 puts median MTDᵢ around e⁵≈150 ng/kg weekly, close to the Cohort 5 dose of 180, finding CV≈1 is a ‘surprise’, and the r₀≈1.3 deserves at least some comment. 36/
Recall that we had placed a low prior probability on CV≈1. Otherwise, this dose-escalation trial would have looked neither ethical nor economical ex ante. 37/
Of course, our ex post ‘discovery’ of the substantial heterogeneity represented by CV≈1 is the formal correlate of the dismay that would have attended the severe toxicities in the AFM11 trials. 38/
The finding r₀≈1.3 isn’t at all surprising to pharmacologic intuition, since it means that a 30% increase in dose bumps up the CTCAE Grade by 1 level.

But it DOES conflict in retrospect with the 3⨉ multiplier between dose levels (and the 3⨉ step-up dosing) in this trial. 39/
Even under circumstances of low inter-individual heterogeneity (CV≪1), using dose increments within or between individuals that greatly exceed r₀ would be manifestly unsafe. (I would like to think even a #OneSizeFitsAllogist would know better.) 40/
The final bit of the analysis exploits a lovely feature of JAGS (declarative programming FTW!) to ask what might have been known before the escalation to Cohort 6, and whether this might have averted the fatal toxicity of Patient 17. 41/
Here, conditional on what was known at the end of Cohort 5, are the (forward-looking HT @f2harrell) #probabilities of each grade of toxicity, during the 1st (step-up) week of dosing, and upon graduation (after no toxicity) to the target dose. 42/
Would YOU have enrolled Cohort 6, facing these probabilities? 43/
IN CONCLUSION

Beneath the retrospective surface of this discussion is a prospective opportunity:

Since this model may be used in this same way at EVERY dosing decision, it actually forms a basis for designing and implementing dose-#titration trials with ordinal outcomes! /44
I may extend this thread sometime soon with #PhilSci aspects of the paper. There is e.g. an interesting 2012 paper journals.sagepub.com/doi/10.1177/17… by @EmilyVDressler @LGM_Biostats & @bandipu that, though not formally aligned with my model, aims similarly at pharmacologic #realism. 45/
@EmilyVDressler @LGM_Biostats @bandipu The code is of course available as always @OSFramework under the permissive MIT License: 46/
osf.io/9x6j7/
@EmilyVDressler @LGM_Biostats @bandipu @OSFramework In closing, I’d like to thank especially @dhovekamp42 for engaging me over several extended and extensive convos here, helping orient me to available data sources. (All errors are mine alone, however!) 47/
@EmilyVDressler @LGM_Biostats @bandipu @OSFramework @dhovekamp42 And finally, this is a WORKING PAPER!

I will be most glad for your engagement here or @PubPeer, and will be eager to update/qualify/rectify my analysis as needed. 48/48

THANKS FOR READING!
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