Empirical Methods and Cheminformatics Approaches Together Can Improve Human PK Predictions and The Confidence in Human PK Predictions

A guest post by Hakan Gunaydin
The problem
Before a molecule ever reaches the clinic, we want to know roughly how fast the body will clear it. In lead optimization, this prediction is the most important triage tool: it determines which compounds are good candidates for further profiling and which don’t have the legs to move forward. We rarely need high accuracy at this stage — we need to be right within a fewfold, reliably and cheaply, based on preclinical data. First-pass human PK prediction from preclinical data is how the teams try to tackle this problem.

Tang’s single-species scaling method is the most commonly used method for this purpose

The field’s default is Tang’s single-species scaling from rat (Tang et al., 2007). In that work, Tang and colleagues took a data-driven approach to predicting human clearance from a single animal species, using intravenous clearance data for 102 compounds across rat, dog, and monkey. Rather than the traditional allometric “rule of exponents,” which requires three or more species, they asked whether a single, empirically fitted proportionality constant per species would do as well or better. For rat, the answer was a simple linear scaling:

CL(human, per kg) = 0.152 x CL(rat, per kg)

The coefficient 0.152 is purely empirical — a best-fit constant across their training set — and, notably, it is not the value you would get from naive liver-blood-flow scaling (0.247 for rat). Tang showed that this fitted rat coefficient outperformed the liver-blood-flow method and that a single well-chosen species could rival multi-species allometry. That is why it became a lead-optimization staple: it needs only rat data and a single multiplication.

In practice, we run it on a free-drug basis because clearance is driven by the unbound concentration. Correcting each side for plasma protein binding — dividing plasma clearance by the free fraction (Fu) — gives the working form:

hCLp = 0.152 x (rCLp / rFu) x hFu

where rCLp is rat plasma clearance, rFu the rat free fraction, hCLp is human plasma clearance, and hFu the human free fraction. Here we evaluate everything in unbound space, where the algebra simplifies beautifully: since hCLu = hCLp / hFu, the human free fraction cancels, and Tang’s method becomes

hCLu(Tang) = 0.152 x rCLu

i.e., human unbound clearance is just rat unbound clearance scaled by a constant. Clean, mechanistic, and completely blind to what compound you hand it. It does a reasonably well job in predicting human CLu, 65% of the predictions with this method are within 3X of measured human unbound clearance on an expanded dataset that includes data on approved drugs since the initial publication of this work.

A nearest-neighbor approach (NN method) can also be used to make human PK predictions

The alternative does not use any formula at all. To predict a new compound, find the 3 drugs with the most similar preclinical PK profile — here, similarity in rat clearance, rat free fraction, and human free fraction (rCLp, rFu, hFu) — and take the geometric mean of their observed human unbound clearances. It is a prediction by analogy: you trust that compounds that behave alike in preclinical assays will clear similarly in humans.

This method also does a reasonably good job of predicting human unbound clearance; 67% of the predictions are within 3-fold of the observed human unbound clearance values.

This method is analogous to commonly used potency prediction approaches in lead optimization programs

A similar analogy is predicting potency by simply averaging the potency of the n nearest neighbors, using existing potency data. This is often the metric we use to compare all other potency prediction methods in lead optimization in drug discovery, since it’s the most obvious choice.

If you come from the free-energy-perturbation world, this maps cleanly:

Tang’s scaling is like absolute FEP. A single physics-flavored model gives you an answer for each molecule on its own, from a fixed rule, with no reference compound.

The NN approach is like relative FEP. You predict a new compound by leaning on measured values of its near-neighbors. It is only as good as the analogs available.

These analogies turn out to predict exactly how the two methods behave.

NN method and Tang’s Method are a statistical tie!

Evaluated leave-one-out on unbound clearance across all 217 drugs:

The honest reading is that the two methods are statistically tied. A paired Wilcoxon test on the fold errors is not significant (p = 0.48), and NN comes out ahead on only 52% of compounds — a coin flip. NN is marginally tighter on fold error (2.58 vs. 2.77), and Tang holds its own on within-2-fold, but none of these gaps is one you would bet a program on.

This is analogous to the potency prediction analogy with the nearest neighbors lesson in miniature: on a chemically diverse set of drugs, the “3 nearest” analogs frequently aren’t very near, so borrowing their data buys you little over the empirical relationship established by Tang et al.

So, if the question is “Does NN replace Tang?” the answer is no.

Below are two compounds that show how each method fails in different ways.

When NN misses: Warfarin

Warfarin is a case where the empirical scaling wins and the analog approach misfires. Its three nearest neighbors were selected because they share Warfarin’s distinctive, very low rat free fraction (rFu ~ 0.008) and rCLp:

The neighbors are genuinely close in the PK inputs — all four sit in a tight rFu band (0.0055–0.0081). But look at the structural similarity: on ECFP4 fingerprints, the analogs are only 0.15–0.20 similar to Warfarin — different chemotypes entirely (a coumarin borrowing from a pyrazolidinedione, an indole-acetic acid, and a naphthylpropionic acid). And their observed unbound clearances (35–130 mL/min/kg) are all far higher than Warfarin’s (7.9). The geometric mean lands at 60 — a 7.7-fold over-prediction — while Tang, working only from Warfarin’s own rat clearance, gets within 1.8-fold. Similar preclinical PK did not translate to similar human clearance.

When Tang misses: Aprepitant

Aprepitant is an example in which the empirical scaling approach led to a misprediction. Its human unbound clearance is high (1000 mL/min/kg), and Tang’s fixed scaling from rat badly under-predicts it at 236 — a 4.2-fold miss. The nearest-neighbor approach, however, is much closer to the observed value (1022, a 1.02-fold error):

Here the analogs — again structurally diverse (ECFP4 0.06–0.18) but matched on the low rat free fraction and high unbound clearance.

Together, these two compounds make the point: neither method is reliably better; they fail on different compounds.

The next question is: is the combination of both approaches better than each one on its own?

The better question: what do the two methods tell you together?

Tang and NN rely on completely different information: one comes from an empirical rat-to-human scaling, and the other from the measured behavior of similar analogs. When two independent methods agree, that agreement matters. When they diverge, at least one of them is in trouble.

The data bear this out. The disagreement between the two predictions (their fold-gap) correlates with the larger of the two errors, with a Spearman’s rho of 0.40 (p ~ 1e-9). Concretely:

The two methods agree within 2-fold on 126 of 217 drugs (58%). In that agreement band, Tang’s fold error is a respectable 2.53.

For the 91 drugs where they disagree, Tang’s fold error increases to 3.14, while NN barely moves (2.57 to 2.59).

That asymmetry is the punchline: a Tang-vs.-NN disagreement is a red flag specifically for the Tang prediction. NN’s geometric averaging pulls it toward the population center, which happens to protect it exactly in the compounds where Tang’s fixed scaling misfires (Aprepitant is one such case). So even though NN doesn’t win on average, it earns its keep as a check on Tang: run both, and when they part ways, distrust the empirical number and move toward making more elaborate mechanistic PK projections.

The practical recommendation: look at the consensus

If a disagreement warns you and an agreement reassures you, the natural summary is simply the geometric mean of the two predictions — a consensus that automatically sits between them, close together when they agree and hedged when they don’t.

The consensus beats either method alone:

The consensus lands at GMFE 2.47, 46% within 2-fold, with the best rank-ordering of the three (Spearman 0.78). For reference, an oracle that could always pick the better of the two methods per compound would reach GMFE 1.97 / 62% within 2-fold — so the simple geometric mean already recovers much of the value of knowing which method to trust, without having to know it in advance.

Takeaways

The NN approach does not outperform Tang’s single-species scaling on a diverse set of drugs. On unbound clearance, they are a statistical tie (Wilcoxon p = 0.48).

Their disagreement is diagnostic. When Tang and NN diverge, the Tang prediction is the one most likely to be badly wrong — a built-in, zero-cost confidence flag for the empirical method.

The consensus (geometric mean of both) is the number to act on. It is more accurate and better-ranked than either method alone, and it degrades gracefully by hedging exactly the compounds where the two disagree.

The framing that emerges is not “empirical versus data-driven,” but “empirical checked by data-driven”: keep Tang’s scaling as the backbone, run an NN alongside it as a cross-check, and let the two together tell you both the prediction and how much to trust it.

The data

Both the human clearance and free-fraction values come from the Lombardo et al. (2018) database — a curated compilation of intravenous human pharmacokinetic parameters for 1352 drugs, assembled from primary literature and regulatory filings and supplemented with plasma-protein-binding data. It is, at present, the most extensive and carefully curated public resource of its kind, and its explicit purpose was to give drug-metabolism and medicinal-chemistry scientists a robust dataset for exactly the kind of clearance-scaling analysis we do here. From it, combined with literature rat PK data published since the publication, we assembled 217 drugs with complete rat (rCLp, rFu) and human (hFu, measured hCLu) data.

References

Tang H, Hussain A, Leal M, Mayersohn M, Fluhler E. Interspecies prediction of human drug clearance based on scaling data from one or two animal species. Drug Metab Dispos. 2007;35(10):1886–1893. doi:10.1124/dmd.107.016188. PMID: 17646280.

Lombardo F, Berellini G, Obach RS. Trend Analysis of a Database of Intravenous Pharmacokinetic Parameters in Humans for 1352 Drug Compounds. Drug Metab Dispos. 2018;46(11):1466–1477. doi:10.1124/dmd.118.082966. PMID: 30115648.

Methods

217 drugs with complete rat (rCLp, rFu) and human (hFu, measured hCLp) data; human values from Lombardo et al. (2018). Unbound clearance hCLu = hCLp/hFu; rat rCLu = rCLp/rFu. NN similarity is computed as the Euclidean distance over log10-transformed, z-scored rCLp, rFu, and hFu; predictions are the leave-one-out geometric mean of the 3 nearest analogs. Tang’s method is parameter-free and therefore inherently out-of-sample. Physicochemical properties and ECFP4 (Morgan, r=2) Tanimoto similarities computed with RDKit. All accuracy metrics are computed on a log10 scale.