This thread introduces an April 2020 paper I posted on arXiv, introducing a therapeutic index concept has become crucial to several later developments.
The trial in question came to my attention 1.5 years ago, thanks (as is so often the case) to @Lymphomation: 2/https://t.co/DLVOsKD5rk
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
But before laying out the model, we need background story. 6a/
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
8 Oct 2018https://t.co/GHZQ3skY4h$AFMD puts 2 #AFM11 trials on clinical hold for SAEs in 3 patients:
• 2 life-threatening AEs in https://t.co/PGwSrK7ABx (R/R NHL)
• 1 death in https://t.co/Wg9LCxoQdB (R/R B-ALL)
17 Apr 2019: $AFMD Regulatory Update indicates ongoing discussions with FDA over the clinical hold. 6c/https://t.co/C0wQOXLREf
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
17 Apr 2019: $AFMD Regulatory Update indicates ongoing discussions with FDA over the clinical hold. 6c/https://t.co/C0wQOXLREf
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
Here’s Table 1 from my paper, where I abstract, for each of the N=17 participants:
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
• 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/ pic.twitter.com/EDLRuVvnqn
I’ve tried to be quite transparent about my uncertainties in this abstraction. (See esp. the note about Patient 16 highlighted below.) 11/ pic.twitter.com/6mHKrTQs0x
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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.
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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
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/
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
log MTDᵢ ~ 𝒩(μ,τ), τ ≡ 1/σ².
So (as you see above), I’ve posited a link between the {MTDᵢᵍ | g=1,…,5}. The manner in which I do this:
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
MTDᵢᵍ = rᵢ⁽ᵍ⁻³⁾·MTDᵢᵍ (Eq. 3)
effectively assumes that the grading system is superbly aligned with the underlying dose-response. 17/
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/
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
log rᵢ ~ 𝒩(log r₀, τᵣ) , τᵣ≫1.
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/ pic.twitter.com/hDbw45dv0d
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/ pic.twitter.com/BxI1fHIThb
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
THE PRIORS
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/
So I have chosen to place my prior on this CV instead of the much less intuitive τ:
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/
This all comes together in the following JAGS model: 31/ pic.twitter.com/sb4NSgvEMC
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
The model runs fast, yielding effective samples sizes in the 1000’s in just seconds. 33/ pic.twitter.com/gqxOO1wCgr
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
The model runs fast, yielding effective samples sizes in the 1000’s in just seconds. 33/ pic.twitter.com/gqxOO1wCgr
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/https://t.co/v1XpNoYuk4
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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.
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
But it DOES conflict in retrospect with the 3⨉ multiplier between dose levels (and the 3⨉ step-up dosing) in this trial. 39/
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/ pic.twitter.com/IeUOibSPFb
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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/ pic.twitter.com/IeUOibSPFb
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
I may extend this thread sometime soon with #PhilSci aspects of the paper. There is e.g. an interesting 2012 paper https://t.co/P8wFMG235d by @EmilyVDressler @LGM_Biostats & @bandipu that, though not formally aligned with my model, aims similarly at pharmacologic #realism. 45/ pic.twitter.com/WDlg0eH6Ss
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
I may extend this thread sometime soon with #PhilSci aspects of the paper. There is e.g. an interesting 2012 paper https://t.co/P8wFMG235d by @EmilyVDressler @LGM_Biostats & @bandipu that, though not formally aligned with my model, aims similarly at pharmacologic #realism. 45/ pic.twitter.com/WDlg0eH6Ss
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
And finally, this is a WORKING PAPER!
— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) April 28, 2020
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!