*This thread introduces a Dec 2020 paper I posted on arXiv, containing several important elements including the advent of what I have since termed complete path enumeration (CPE), and the maturation of a therapeutic index concept I had introduced in April 2020.*

This latest #DTAT paper @arXiv sets out to reverse-engineer the unstated (∴ unexamined!) pharmacologic intuitions that underlie the #trialsafety claim implicit in the decision to conduct a dose-escalation trial. 2/ pic.twitter.com/Fs3UXZbbwC

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

So we need a mind-bending contest of sorts. Has dose escalation gone soft after all that time in the tank? Let’s find out, shall we?

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

En garde! 4/https://t.co/wXnX0KFjPP

Given the full 3-D information from a CT scan, one can easily reconstruct a plain X-ray taken from any angle. Likewise, starting from a fully articulated set of priors about a drug’s pharmacology, we can easily project the safety characteristics of any trial design. 6/ pic.twitter.com/tBjmj30k08

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

We’ll need plenty of #computation here, too. Ultimately, we will obtain F⁻¹ by a graphical technique requiring thousands of (forwards) calculations of F. The usual approach of approximating F via discrete-event simulation is both too slow and too noisy for this purpose. 8/

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

For a task such as this, there is no better tool than Prolog. This definite clause grammar (DCG) — which at 526 characters would fit into 2 tweets! — is an EXECUTABLE SPECIFICATION that contains all the essential logic: 10/ pic.twitter.com/D3tUv6nZIq

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

What I’ve learned from Markus is that Prolog remains an active research area, with ongoing work to develop and incorporate new language constructs that expand the (logically) pure core of the language—which is its truly powerful aspect. 12/https://t.co/wLvsvVTscJ

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Also notable is that Scryer is itself implemented in @rustlang, a language designed to support #safe, #reliable programming — the very same advantages of #LogicProgramming that so strongly recommend Prolog for #clinicaltrials applications. 14/https://t.co/Zox7SSyAZQ

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

What’s more, my current application barely scratches the surface of what could be done with Prolog in this problem domain.

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Constraint logic programming (CLP) might well support a unified treatment subsuming the whole field of dose escalation. 16/ pic.twitter.com/irOAZpaNfo

In terms of these matrices, the J-vector π of path probabilities can be obtained from a simple matrix equation involving a J-vector b and J×2D matrix U that are

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020constantsfor each value of D. 18/ pic.twitter.com/0PdgdRbdUm

As I’ve done previously, I now ‘ordinalize’ the binary DLTs of the 3+3 trial, obtaining ordinal toxicities in terms of which safety outcomes such as severe or fatal toxicities may be explored. 20/https://t.co/Pd8hpatLYB

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Crucially, the expected number of fatal toxicities in the trial now also reduces to matrix operations that R can perform almost instantaneously. 22/ pic.twitter.com/Sfua0QXyVC

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Now complete, F apparently has many dimensions. But one of them can be factored out if we keep hammering the logarithmic theme.

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

The trick? Use our prespecified doses as a natural scale for dose measurement, effectively setting δ≡1.

24/ pic.twitter.com/HcROTQS2xr

We can! Through a #minimax framing of our #trialsafety question, we can ‘slice’ Figure 1 along a plausible worst-case scenario:

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

What if our 2nd dose level coincided with median MTDᵢ? 26/https://t.co/Q7DOFUyMRh pic.twitter.com/49JGgxhr79

κ/σ characterizes the drug itself, according to how its dosing safety margin κ compares to inter-individual variability in optimal dosing.

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

As such, it measures how suited the drug is to 1-size-fits-all dosing—a #OneSizeFitsAllogist’s #TherapeuticIndex. 28/ pic.twitter.com/ljNwx3laCd

Phase 1 trialists are called upon, I think, to consider questions posed by the axes of this plot.

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Fortunately, this is #pharmacology not #metaphysics—nothing here threatens to “transcend every faculty of the mind”! 30/https://t.co/y9ZFE9COKT

That trial had a dose-level ratio of 3, while our model gave posterior median estimates 1/σ² ≡ τ ≈ 1.31 and r₀ ≈ 1.33. Pulling out our desk calculator…

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

σ = 1/√1.31 = 0.874

δ = log 3 = 1.1

κ = log 1.33 = 0.285 32/

Of course, a calculator-based ‘postmortem’ of this kind serves only to demonstrate a continuity with earlier work. The proper use of Figure 3 is to promote PROSPECTIVE thinking that yields #smarter and #safer trials. 34/ pic.twitter.com/fSfMmNmvYG

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

Other dose-escalation designs surely have their own Fig 3’s, perhaps more favorable than the one I’ve drawn for 3+3. The methods I used in this paper ought to be adaptable to any design (such as @koaeraser’s mTPI) for which rules can be pretabulated: 36/https://t.co/qWerGe9Vf6 pic.twitter.com/DAB8qiyJgm

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020

2021 will be a year of so much renewal, and I hope this includes renewed attention to #pharmacologic thinking in #oncology #dosefinding, and the renewed commitment to #trialsafety this will make possible. 38/38

— David C. Norris, MD moved to Mastodon 🦣 (@davidcnorrismd) December 16, 2020