PTA, CFR, and virtual populations
Once you have an exposure rule and an MIC, a single “typical patient” calculation is rarely enough. Real people differ in clearance, volume, kidney function, and body size. Virtual populations, PTA, and CFR are the tools we use to ask how often a regimen works across that spread.
Think of it as moving from one drawn curve to a cloud of curves, then counting how many of those curves pass the test you chose.
Method intuition for simulation. Not software documentation and not a bedside calculator.
Virtual populations are controlled variation
A virtual population is a set of simulated individuals. For each person you draw pharmacokinetic parameters from distributions that are supposed to reflect interindividual variability. If the literature reports correlated clearances, or clearances that depend on eGFR, that structure belongs in the draw. If you invent tidy independent normals because they look neat, you are no longer studying the published system. You are studying your drawing habits.
Useful discipline looks like this:
- cite the IIV source,
- keep covariate rules explicit,
- record the random seed and the sample size,
- say which population the parameters came from (ICU, healthy volunteers, dialysis, and so on).
Why sample size shows up in methods sections
Too few virtual subjects and the PTA estimate jitters. Extremely large N can look impressive while hiding a bad structural assumption. Report both N and a quick stability check.PTA: fix the MIC, count the successes
Probability of target attainment (PTA) answers a conditional question:
If MIC equals this value, what fraction of virtual subjects meet the PK/PD target?
You usually compute PTA across a grid of MIC values and plot a declining curve. The interesting part is often the cliff: the MIC region where success falls apart.
PTA is a curve over MIC, not a single trophy number.
CFR: bring the local microbiology back in
Cumulative fraction of response (CFR) folds PTA over an MIC distribution from surveillance or local epidemiology:
[ = _i (_i)P(_i) ]
PTA asks “what if MIC is X?”
CFR asks “given the MICs we actually see around here, how often do we succeed?”
That second question is only as honest as the MIC weights. A distribution from another country, another year, or a mixed species group can make CFR look decisive while answering the wrong question.
Use PTA when you want to see regimen strength across a MIC grid, compare dosing strategies, or find the MIC where performance collapses.
Use CFR when you have a trustworthy local or regional MIC distribution and you want one summary of expected success under that ecology.
Show PTA curves for mechanism insight, then report CFR under one or more dated MIC priors. Sensitivity to the prior is part of the scientific result.
A minimal workflow you can defend
- Define regimen and PK model, with provenance.
- Define free-drug target or targets.
- Simulate N virtual subjects.
- Compute PTA on an MIC grid.
- Optionally weight by an MIC distribution to get CFR.
- Stress-test the fragile inputs: binding, IIV, renal strata, MIC source.
If the target is joint (two drugs, two conditions), success is the intersection inside each virtual subject. Averaging two separate PTA values is not the same thing. A later lesson walks through that case.
Takeaway
Virtual populations turn “does this look fine on paper?” into “how often does this pass under realistic variability?” PTA keeps MIC fixed. CFR brings epidemiology back. Neither repairs a bad target choice or a mismatched population.
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