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Pirtobrutinib (Tian 2025)

Source: vignettes/articles/Tian_2025_pirtobrutinib.Rmd
Tian_2025_pirtobrutinib.Rmd

Model and source

  • Citation: Tian DD, Hall SD, Chapman SC, Posada MM. (2025). Application of physiologically-based pharmacokinetic modeling to support drug labeling: prediction of CYP3A4-mediated pirtobrutinib-drug interactions. CPT Pharmacometrics Syst Pharmacol 14:2221-2231. doi:10.1002/psp4.70134.
  • Description: Two-compartment oral pharmacokinetic reduction of the Simcyp minimal-PBPK-with-single-adjusting-compartment (SAC) model for the reversible BTK inhibitor pirtobrutinib in healthy adults (Tian 2025). The source model was built in the Simcyp Simulator version 19 and its whole-body mass-balance equations are not published, so the platform model itself cannot be encoded here. What IS fully reported is the pirtobrutinib compound layer, and it is sufficient to rebuild the disposition as an ordinary compartmental model: first-order absorption into a depot with a lag time, distribution between a systemic compartment and the SAC (the Simcyp kin / kout, encoded as the canonical k12 / k21), and first-order elimination from the systemic compartment. Systemic clearance is carried as the three components the paper’s disposition diagram prints separately, so a CYP3A4 perturbation can be applied to the CYP3A4-mediated arm alone: cl_3a4 (40% of systemic clearance), cl_other (non-CYP3A4 hepatic metabolism plus biliary excretion) and cl_renal. Hepatic availability is not a fitted constant but is derived inside the model from the well-stirred relationship the paper states as its Equation 2, so that oral bioavailability responds correctly when the CYP3A4 arm is changed. No parameter is fitted here: every value is either a Table 1 / Figure 2 / Data S3 input or an arithmetic consequence of one. The reduction reproduces the paper’s own predicted median tmax exactly after both a single 200 mg dose (2.94 h) and 200 mg once daily (2.72 h), and its predicted Cmax and AUC to within 8.3%; the residual offset is the difference between a typical-value individual and the geometric mean of the paper’s 100-subject virtual population (see the validation vignette). This is a typical-value simulation model: the source reports no estimated inter-individual variance components and no residual-error model, so there are no etas and propSd is fixed at zero. The drug-drug-interaction predictions that are the paper’s main contribution depend on proprietary Simcyp perpetrator compound files and on a CYP3A4 degradation rate constant that is never printed, so they are NOT reproducible mechanistically from this model; the vignette instead shows the closed-form CYP3A4-fraction envelope this reduction does support and compares it against the paper’s Figure 5.
  • Article: https://doi.org/10.1002/psp4.70134
  • Open-access full text and supplement: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12706395/
  • Supplement Data S1 (figures), Data S2 (Supplementary Materials 1-5, Tables S1-S14), Data S3 (Simcyp input sheet, .xlsx)

What this model is, and what it is not

Tian 2025 built a minimal PBPK model with a single adjusting compartment (SAC) for pirtobrutinib in the Simcyp Simulator version 19, and used it to predict drug-drug interactions (DDIs) with CYP3A4 inhibitors and inducers in support of the product label.

Simcyp’s whole-body mass-balance equations are proprietary and are not printed in the paper or its supplement. The six numbered equations in the main text are all input-derivation formulae (hepatic clearance, hepatic availability, biliary clearance, the intestinal-availability back-calculation, and the fraction absorbed), never the disposition ODEs. The platform model therefore cannot be encoded as published.

What is fully reported is the pirtobrutinib compound layer, and it is unusually complete:

  • Table 1 gives the physicochemical, absorption, distribution and elimination inputs.
  • Figure 2 (the proposed disposition diagram) prints the entire clearance decomposition – CL, CL_H, CL_hepatic metabolism, CL_bile, CL_R, f_m,CYP3A4, f_m,other, f_e,bile, f_e,urine – together with Fa, Fg, Fh, F and Vss.
  • Data S3, the Simcyp input sheet itself, reports the SAC rate constants kin and kout to full double precision alongside the inter-compartmental clearance Q.

Because kin = Q / V_systemic and kout = Q / V_SAC, those three numbers pin the systemic volume in absolute litres, so this reduction needs no assumed reference body weight anywhere. Every parameter in the packaged model is either a printed input or a one-step arithmetic consequence of printed inputs; nothing is fitted here and nothing is imported from a Simcyp population file.

What is not reproducible:

  • The time-dependent inhibition (TDI) of CYP3A4 by pirtobrutinib itself. Table 1 reports K_I = 4.70 uM and the fitted k_inact = 0.056 1/h, but the autoinhibition ODE also needs the CYP3A4 degradation rate constant k_deg, which is a Simcyp database value and is never printed. This model is therefore the linear pirtobrutinib model, and is validated against the paper’s own “without TDI” predictions (Table 2, and the “reversible inhibition” row of Table S9), which the paper reports separately for exactly this comparison.
  • The perpetrator models (itraconazole, hydroxyitraconazole, ritonavir, ketoconazole, clarithromycin, diltiazem, fluconazole, verapamil, rifampin, efavirenz, bosentan, modafinil, midazolam). These are proprietary Simcyp compound files or literature PBPK models, so the DDI simulations cannot be run mechanistically. The final section instead exercises the closed-form CYP3A4-fraction envelope that this reduction does support, and shows it reproduces the paper’s Figure 5 predictions.
  • Population variability. Data S3 prints 30% input CVs on ka, lag time, Q_gut, the additional HLM CLint and the biliary CLint, but the percent-CV figures in Table 2 are dominated by liver weight and CYP3A4 abundance drawn from Simcyp population files. No variance is invented here; propSd is fixed at zero and the model is a deterministic typical-value simulation.

Population 

pop <- rxode2::rxode(readModelDb("Tian_2025_pirtobrutinib"))$meta$population
str(pop, max.level = 1)
#> List of 11
#>  $ species       : chr "human"
#>  $ n_subjects    : int 100
#>  $ n_studies     : int 9
#>  $ age_range     : chr "20-55 years for the 200 mg once-daily simulation (Data S3); 19-55 years for the single-dose simulation (Table S4)"
#>  $ weight_median : chr "not reported; the Simcyp Sim-Healthy Volunteers default distribution was used"
#>  $ sex_female_pct: num 25
#>  $ disease_state : chr "Healthy adult volunteers, fasted, CYP3A5 genotype unrestricted for the pirtobrutinib-alone simulations."
#>  $ dose_range    : chr "Single oral dose of 200 mg, and 200 mg once daily for 13 doses (Data S3)."
#>  $ regions       : chr "Simcyp Sim-Healthy Volunteers virtual population (Data S3)."
#>  $ studies       : chr "Nine clinical pharmacology studies supplied the observations and the compound-layer inputs (Supplemental Materi"| __truncated__
#>  $ notes         : chr "n_subjects records the 100 virtual subjects (10 trials of 10) Data S3 simulated for pirtobrutinib alone, becaus"| __truncated__

All simulations in Tian 2025 were run in healthy volunteers using the Simcyp Sim-Healthy Volunteers population in PK/PD Profiles mode. For pirtobrutinib dosed alone, Data S3 records 10 trials of 10 subjects (100 virtual subjects), age 20-55 years, 25% female, fasted, 200 mg once daily for 13 doses. The single-dose simulation used age 19-55 years and 18% female (Table S4), matched to the contributing clinical studies.

Nine clinical pharmacology studies supplied the observations and the compound-layer inputs (Supplemental Material 1). The absolute bioavailability study (n = 5 healthy males, NCT06180954) is the anchor for this reduction: it supplies the intravenous systemic clearance, the renal clearance, the steady-state volume and the absolute oral bioavailability.

The reduction, step by step

Every derived number in the packaged model is reproduced below from printed source values, so the arithmetic can be checked independently of the model file.

# --- Data S3 (Simcyp input sheet), Distribution block -----------------
sacKin  <- 0.12402043422142926  # "SAC kin (1/h)"
sacKout <- 0.2594761264470896   # "SAC kout (1/h)"
sacQ    <- 3.56                 # "SAC Q (L/h)"; Table 1 Q = 3.56 L/h

vcDer  <- sacQ / sacKin   # kin  = Q / V_systemic
vsacDer<- sacQ / sacKout  # kout = Q / V_SAC

# Table 1 gives V_SAC = 0.17 L/kg, so the implied body weight of the
# Simcyp population representative is a consistency check on the reading:
bwImplied <- vsacDer / 0.17

# --- Figure 2 (proposed disposition diagram) --------------------------
clTotal <- 1.69   # systemic plasma clearance (L/h)
clRen   <- 0.12   # CL_R
clHepMet<- 1.33   # CL_hepatic metabolism
clBile  <- 0.24   # CL_bile
fmCyp3a4<- 0.40   # f_m,CYP3A4

cl3a4   <- fmCyp3a4 * clTotal          # CYP3A4-mediated arm
clOther <- (clHepMet - cl3a4) + clBile # non-CYP3A4 hepatic + biliary

# --- Equations 1, 2 and 6 --------------------------------------------
bp <- 0.79; qh <- 90            # Table 1 B:P; main text Q_H = 90 L/h
clH   <- cl3a4 + clOther        # Equation 1: CL_H = CL - CL_R
fhDer <- 1 - clH / (bp * qh)    # Equation 2
fgut  <- 0.96                   # Equation 5 (Fg)
fabs  <- 0.86 / (fgut * fhDer)  # Equation 6, from measured F = 0.86

data.frame(
  Quantity = c("vc = Q / kin (L)", "V_SAC = Q / kout (L)",
               "implied body weight (kg)", "cl_3a4 (L/h)", "cl_other (L/h)",
               "CL_H = cl_3a4 + cl_other (L/h)", "CL = CL_H + CL_R (L/h)",
               "Fh (Equation 2)", "Fa (Equation 6)", "F = Fa x Fg x Fh"),
  Derived = c(vcDer, vsacDer, bwImplied, cl3a4, clOther, clH,
              clH + clRen, fhDer, fabs, fabs * fgut * fhDer),
  Printed = c(NA, NA, NA, NA, NA, 1.57, 1.69, 0.98, 0.91, 0.86),
  Source = c("Data S3 / Table 1", "Data S3 / Table 1",
             "cross-check vs Table 1 V_SAC 0.17 L/kg", "Figure 2",
             "Figure 2", "Figure 2", "Figure 2", "Figure 2", "Table 1",
             "Figure 2")
) |>
  dplyr::mutate(Derived = signif(Derived, 6)) |>
  knitr::kable(caption = "Derived reduction inputs against the values Tian 2025 prints.")
Derived reduction inputs against the values Tian 2025 prints.
Quantity Derived Printed Source
vc = Q / kin (L) 28.704900 NA Data S3 / Table 1
V_SAC = Q / kout (L) 13.720000 NA Data S3 / Table 1
implied body weight (kg) 80.705600 NA cross-check vs Table 1 V_SAC 0.17 L/kg
cl_3a4 (L/h) 0.676000 NA Figure 2
cl_other (L/h) 0.894000 NA Figure 2
CL_H = cl_3a4 + cl_other (L/h) 1.570000 1.57 Figure 2
CL = CL_H + CL_R (L/h) 1.690000 1.69 Figure 2
Fh (Equation 2) 0.977918 0.98 Figure 2
Fa (Equation 6) 0.916061 0.91 Table 1
F = Fa x Fg x Fh 0.860000 0.86 Figure 2

The clearance components sum back to the printed total exactly, and the Equation 2 / Equation 6 chain returns the printed Fh = 0.98 and F = 0.86. The V_SAC reading also reproduces a body weight of 80.7 kg for the Simcyp population representative, which is what confirms that kin is Q / V_systemic rather than the reverse.

The paper’s Equations 4 and 5 round-trip as well. Equation 4 approximates the pirtobrutinib Cmax ratio from the intestinal availability Fg and the fraction of intestinal CYP3A4 activity remaining under itraconazole, X = 0.009 (Table S3):

xItra <- 0.009
c(`Eq 4: Cmax ratio from Fg = 0.96 and X = 0.009` = 1 / (fgut + (1 - fgut) * xItra),
  `Eq 5: Fg back from the observed +4% Cmax rise` = (1 / 1.04 - xItra) / (1 - xItra))
#> Eq 4: Cmax ratio from Fg = 0.96 and X = 0.009 
#>                                     1.0412762 
#> Eq 5: Fg back from the observed +4% Cmax rise 
#>                                     0.9611892

Equation 4 returns a 4.1% Cmax rise against the observed 4%, and Equation 5 returns Fg = 0.961 against the printed 0.96.

Source trace

Source location for every ini() parameter and every model() equation.
Item Source
ka = 0.82 1/h Table 1, fitted to observed tmax/Cmax; Data S3 row ‘ka (1/h)’
t_lag = 0.25 h Table 1; Data S3 row ‘lag time (h)’
cl_3a4 = 0.676 L/h Figure 2: f_m,CYP3A4 (0.40) x CL (1.69 L/h)
cl_other = 0.894 L/h Figure 2: (CL_hepatic metabolism 1.33 - 0.676) + CL_bile 0.24
cl_renal = 0.12 L/h Table 1 and Figure 2, measured from the intravenous dose
vc = 28.7049 L Data S3: SAC Q (3.56) / SAC kin (0.12402043422142926)
k12 = 0.1240204 1/h Data S3 row ‘SAC kin (1/h)’
k21 = 0.2594761 1/h Data S3 row ‘SAC kout (1/h)’
fh (derived in model) Equation 2, with CL_H from Equation 1
fa x Fg = 0.879419 Equation 6 (Fa from measured F = 0.86) x Equation 5 (Fg = 0.96)
(B:P) x Q_H = 71.1 L/h Table 1 (B:P = 0.79) and main text after Equation 2 (Q_H = 90 L/h)
propSd = 0 No residual-error model reported; PBPK simulation analysis
2-compartment depot ODEs Figure 2 and Data S3 ‘Distribution Model | Minimal PBPK Model’
f(depot), alag(depot) Table 1 absorption block (first order, Fa, ka, t_lag)
Cc = 1000 x central / vc Table 1 units (mg dose, L volume) vs Table 2 units (ng/mL)

Single 200 mg oral dose

Replicates Figure 3 of Tian 2025 (six panels of observed versus predicted single-dose profiles) and the “Pirtobrutinib single dose / Predicted” row of Table 2.

mod <- rxode2::zeroRe(rxode2::rxode(readModelDb("Tian_2025_pirtobrutinib")))
#> Warning: No omega parameters in the model

# Fine grid over the absorption phase, coarser through the terminal phase.
obsGrid <- sort(unique(c(seq(0, 24, by = 0.02), seq(24, 360, by = 0.5))))

evSingle <- rxode2::et(amt = 200, cmt = "depot") |>
  rxode2::et(obsGrid)
sdSim <- rxode2::rxSolve(mod, evSingle, returnType = "data.frame") |>
  dplyr::mutate(id = 1L, treatment = "200 mg single dose")

ggplot(sdSim, aes(time, Cc)) +
  geom_line(linewidth = 0.8) +
  scale_x_continuous(breaks = seq(0, 168, by = 24), limits = c(0, 168)) +
  labs(x = "Time after dose (h)", y = "Pirtobrutinib concentration (ng/mL)",
       title = "Typical-value profile after a single oral 200 mg dose",
       subtitle = "Replicates Figure 3 of Tian 2025 (predicted mean line)") +
  theme_bw()
#> Warning: Removed 384 rows containing missing values or values outside the scale range
#> (`geom_line()`).

200 mg once daily

Replicates Figure 4 of Tian 2025 and the “Pirtobrutinib QD / Predicted without TDI” row of Table 2. The dosing regimen matches Data S3: 200 mg once daily for 13 doses, with the pharmacokinetic interval taken over the last dosing interval (288-312 h).

tauStart <- 288; tauEnd <- 312
evQd <- rxode2::et(amt = 200, cmt = "depot", ii = 24, addl = 12) |>
  rxode2::et(sort(unique(c(seq(0, tauEnd, by = 0.25),
                           seq(tauStart, tauEnd, by = 0.02)))))
qdSim <- rxode2::rxSolve(mod, evQd, returnType = "data.frame")

ggplot(qdSim, aes(time / 24, Cc)) +
  geom_line(linewidth = 0.7) +
  scale_x_continuous(breaks = 0:13) +
  labs(x = "Time (days)", y = "Pirtobrutinib concentration (ng/mL)",
       title = "Typical-value profile, 200 mg once daily for 13 doses",
       subtitle = "Replicates Figure 4 of Tian 2025 (predicted mean line)") +
  theme_bw()


ssSim <- qdSim |>
  dplyr::filter(time >= tauStart, time <= tauEnd) |>
  dplyr::mutate(time = time - tauStart, id = 2L,
                treatment = "200 mg QD, steady state")

Accumulation is negligible for a linear model dosed at an interval close to three terminal half-lives, and the paper’s own predictions agree: its single-dose AUC(0-inf) of 111,038 ng.h/mL and its steady-state AUCtau without TDI of 109,965 ng.h/mL differ by 1%. The reduction reproduces that superposition identity exactly.

trapz <- function(t, y) sum(diff(t) * (utils::head(y, -1) + utils::tail(y, -1)) / 2)
c(`AUC(0-inf), single dose (ng.h/mL)` = trapz(sdSim$time, sdSim$Cc),
  `closed form F x Dose / CL (ng.h/mL)` = 0.86 * 200 / 1.69 * 1000,
  `AUCtau at steady state (ng.h/mL)` = trapz(ssSim$time, ssSim$Cc))
#>   AUC(0-inf), single dose (ng.h/mL) closed form F x Dose / CL (ng.h/mL) 
#>                            101776.3                            101775.1 
#>    AUCtau at steady state (ng.h/mL) 
#>                            101774.2

The simulated AUC(0-inf) matches the closed-form identity F x Dose / CL to within numerical tolerance, which gates the ODE system, the dose encoding, the bioavailability term and the observation scaling simultaneously. The terminal half-life implied by the eigenvalues of the disposition matrix is:

kel <- 1.69 / vcDer
distMat <- matrix(c(-(kel + sacKin), sacKout, sacKin, -sacKout), 2, 2, byrow = TRUE)
lambdas <- sort(abs(eigen(distMat)$values))
c(`alpha half-life (h)` = log(2) / lambdas[2],
  `terminal (beta) half-life (h)` = log(2) / lambdas[1])
#>           alpha half-life (h) terminal (beta) half-life (h) 
#>                      1.713101                     18.358646

PKNCA validation

Non-compartmental analysis of both simulated profiles. Terminal-phase points for the single-dose half-life are restricted to 72-240 h, where the distribution phase has fully decayed, so that the log-linear regression is not biased by residual curvature.

concData <- dplyr::bind_rows(
  dplyr::select(sdSim, id, treatment, time, Cc),
  dplyr::select(ssSim, id, treatment, time, Cc)
) |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(include_hl = treatment == "200 mg single dose" &
                  time >= 72 & time <= 240)

doseData <- data.frame(
  id = c(1L, 2L),
  treatment = c("200 mg single dose", "200 mg QD, steady state"),
  time = c(0, 0),
  amount = c(200, 200)
)

oConc <- PKNCA::PKNCAconc(concData, Cc ~ time | id + treatment,
                          include_half.life = "include_hl")
oDose <- PKNCA::PKNCAdose(doseData, amount ~ time | id + treatment,
                          route = "extravascular")

intervals <- data.frame(
  start = c(0, 0), end = c(Inf, 24),
  treatment = c("200 mg single dose", "200 mg QD, steady state"),
  cmax = TRUE, tmax = TRUE, auclast = c(FALSE, TRUE),
  aucinf.obs = c(TRUE, FALSE), half.life = c(TRUE, FALSE)
)

ncaRes <- PKNCA::pk.nca(PKNCA::PKNCAdata(oConc, oDose, intervals = intervals))
ncaTidy <- as.data.frame(ncaRes) |>
  dplyr::select(treatment, PPTESTCD, PPORRES)
knitr::kable(dplyr::mutate(ncaTidy, PPORRES = signif(PPORRES, 4)),
             caption = "PKNCA results for the two simulated regimens.")
PKNCA results for the two simulated regimens.
treatment PPTESTCD PPORRES
200 mg single dose cmax 4.072e+03
200 mg single dose tmax 2.940e+00
200 mg single dose tlast 3.600e+02
200 mg single dose clast.obs 4.791e-03
200 mg single dose lambda.z 3.776e-02
200 mg single dose r.squared 1.000e+00
200 mg single dose adj.r.squared 1.000e+00
200 mg single dose lambda.z.time.first 7.200e+01
200 mg single dose lambda.z.time.last 2.400e+02
200 mg single dose lambda.z.n.points 3.370e+02
200 mg single dose clast.pred 4.791e-03
200 mg single dose half.life 1.836e+01
200 mg single dose span.ratio 9.151e+00
200 mg single dose aucinf.obs 1.018e+05
200 mg QD, steady state auclast 1.018e+05
200 mg QD, steady state cmax 6.407e+03
200 mg QD, steady state tmax 2.720e+00

Comparison against the published predictions

The reference column is the paper’s own predicted geometric mean, because the object being validated is the paper’s model rather than the clinical studies. For the once-daily regimen the reference is the “Predicted without TDI” row of Table 2, which is the linear model this reduction corresponds to (Table S9 labels the identical numbers “reversible inhibition”).

The AUC metric differs by regimen, matching what the paper tabulates: AUC(0-inf) after the single dose, and AUCtau over one dosing interval at steady state.

reference <- data.frame(
  treatment = c(rep("200 mg single dose", 3), rep("200 mg QD, steady state", 3)),
  PPTESTCD  = c("cmax", "tmax", "aucinf.obs", "cmax", "tmax", "auclast"),
  PPORRES   = c(4221, 2.94, 111038, 6927, 2.72, 109965)
)

cmpTbl <- nlmixr2lib::ncaComparisonTable(
  ncaTidy, reference,
  by = "treatment",
  params = c("cmax", "tmax", "aucinf.obs", "auclast"),
  units = c(cmax = "ng/mL", tmax = "h", aucinf.obs = "ng*h/mL",
            auclast = "ng*h/mL")
)
knitr::kable(cmpTbl,
             caption = "Simulated versus Tian 2025 predicted geometric means (Table 2).")
Simulated versus Tian 2025 predicted geometric means (Table 2).
NCA parameter treatment Reference Simulated % diff
Cmax (ng/mL) 200 mg single dose 4220 4070 -3.5%
Cmax (ng/mL) 200 mg QD, steady state 6930 6410 -7.5%
Tmax (h) 200 mg single dose 2.94 2.94 +0.0%
Tmax (h) 200 mg QD, steady state 2.72 2.72 +0.0%
AUC0-∞ (obs) (ng*h/mL) 200 mg single dose 111000 102000 -8.3%
AUClast (ng*h/mL) 200 mg QD, steady state 110000 102000 -7.4% 
attr(cmpTbl, "footnote")
#> NULL

Both median tmax values are reproduced exactly (2.94 h single dose, 2.72 h steady state). Because tmax depends only on ka, t_lag, k12, k21 and kel, and is invariant to bioavailability and to any scaling of the dose, an exact match at two different regimens is strong evidence that every rate constant and the systemic volume have been read correctly.

Cmax and AUC are 3.5-8.3% below the paper’s predictions, and the offset is in the same direction and of similar size for all four statistics. That signature – exact tmax, uniformly low exposure – is a single constant scaling on clearance rather than a structural error. Its origin is the difference between a typical-value individual and the geometric mean of a virtual population: the model’s CL = 1.69 L/h is the clinically observed value the Simcyp retrograde calculator was targeted at for the population representative, whereas the geometric-mean clearance implied by the paper’s own predicted AUC is 0.86 x 200 / 111.038 = 1.549 L/h, which is 8.3% lower.

c(`CL printed in Figure 2 (L/h)` = 1.69,
  `CL implied by the paper's predicted AUC (L/h)` = 0.86 * 200 / 111.038,
  `ratio` = (0.86 * 200 / 111.038) / 1.69)
#>                  CL printed in Figure 2 (L/h) 
#>                                     1.6900000 
#> CL implied by the paper's predicted AUC (L/h) 
#>                                     1.5490193 
#>                                         ratio 
#>                                     0.9165794

For a log-normally distributed clearance the geometric mean sits below the mean by a factor of sqrt(1 + CV^2); at the 34% CV the paper reports for predicted single-dose AUC, that factor is 1.056, which accounts for most of the gap. No parameter was adjusted to close it.

Position relative to the observed clinical data

Tables S10 and S12 report the paper’s own predicted-over-observed ratios per study. The same ratios for this reduction show it sits in the same place relative to the observations as the platform model does, and in fact slightly closer for AUC.

simCmax <- c(single = max(sdSim$Cc), qd = max(ssSim$Cc))
simAuc  <- c(single = trapz(sdSim$time, sdSim$Cc), qd = trapz(ssSim$time, ssSim$Cc))

obsStudies <- data.frame(
  Study = c("Pirtobrutinib-itraconazole interaction", "Pirtobrutinib-rifampin interaction",
            "Absolute bioavailability", "Formal food effect", "Pilot food effect",
            "Pirtobrutinib-midazolam, alone (QD)", "Pirtobrutinib-cocktail (QD)",
            "Pirtobrutinib-repaglinide (QD)"),
  Regimen = c(rep("single", 5), rep("qd", 3)),
  obsCmax = c(4000, 4480, 4490, 4200, 5450, 8120, 9430, 7220),
  obsAuc  = c(80800, 80600, 105000, 85100, 90200, 114000, 119000, 105000),
  paperCmaxRatio = c(1.06, 0.94, 0.94, 1.01, 0.77, 0.95, 0.82, 1.07),
  paperAucRatio  = c(1.37, 1.38, 1.06, 1.30, 1.23, 1.12, 1.07, 1.21)
)

obsStudies |>
  dplyr::mutate(
    `This model Cmax ratio` = round(simCmax[Regimen] / obsCmax, 2),
    `This model AUC ratio`  = round(simAuc[Regimen] / obsAuc, 2)
  ) |>
  dplyr::select(Study,
                "Paper Cmax pred/obs" = paperCmaxRatio,
                "This model Cmax pred/obs" = `This model Cmax ratio`,
                "Paper AUC pred/obs" = paperAucRatio,
                "This model AUC pred/obs" = `This model AUC ratio`) |>
  knitr::kable(caption = "Predicted/observed ratios: Tian 2025 Tables S10 and S12 versus this reduction.")
Predicted/observed ratios: Tian 2025 Tables S10 and S12 versus this reduction.
Study Paper Cmax pred/obs This model Cmax pred/obs Paper AUC pred/obs This model AUC pred/obs
Pirtobrutinib-itraconazole interaction 1.06 1.02 1.37 1.26
Pirtobrutinib-rifampin interaction 0.94 0.91 1.38 1.26
Absolute bioavailability 0.94 0.91 1.06 0.97
Formal food effect 1.01 0.97 1.30 1.20
Pilot food effect 0.77 0.75 1.23 1.13
Pirtobrutinib-midazolam, alone (QD) 0.95 0.79 1.12 0.89
Pirtobrutinib-cocktail (QD) 0.82 0.68 1.07 0.86
Pirtobrutinib-repaglinide (QD) 1.07 0.89 1.21 0.97

CYP3A4 interaction envelope

The DDI simulations themselves need the Simcyp perpetrator files, but the reduction carries the CYP3A4-mediated clearance as its own parameter, so the shape of the interaction is fully determined by the printed f_m,CYP3A4 = 0.40 together with Equations 1, 2, 4 and 5. Writing R for the net relative CYP3A4 activity in the presence of a perpetrator (R = 1 with no perpetrator, R < 1 for an inhibitor, R > 1 for an inducer), applied both to the hepatic arm and, through Equation 4, to the intestinal wall:

cl3a4Base <- 0.676; clOtherBase <- 0.894; clRenBase <- 0.12; bpQh <- 71.1
gutFactor <- function(x) 1 / (fgut + (1 - fgut) * x)

aucRatioClosed <- function(r) {
  clHr <- cl3a4Base * r + clOtherBase
  (gutFactor(r) / gutFactor(1)) *
    (1 - clHr / bpQh) / (1 - (cl3a4Base + clOtherBase) / bpQh) *
    (cl3a4Base + clOtherBase + clRenBase) / (clHr + clRenBase)
}
c(`R = 1 (no perpetrator)` = aucRatioClosed(1),
  `R -> 0 (complete CYP3A4 blockade), hepatic + gut` = aucRatioClosed(1e-9),
  `R -> 0, hepatic arm only` = {
    clHr <- clOtherBase
    (1 - clHr / bpQh) / (1 - (cl3a4Base + clOtherBase) / bpQh) *
      (cl3a4Base + clOtherBase + clRenBase) / (clHr + clRenBase)
  })
#>                           R = 1 (no perpetrator) 
#>                                         1.000000 
#> R -> 0 (complete CYP3A4 blockade), hepatic + gut 
#>                                         1.752990 
#>                         R -> 0, hepatic arm only 
#>                                         1.682871

The reduction therefore has a hard ceiling of 1.75 on the pirtobrutinib AUC ratio, no matter how potent the CYP3A4 inhibitor. Figure 5 of Tian 2025 predicts 1.20-1.73 across seven strong and moderate inhibitors, with ritonavir highest at 1.73 – so the paper’s strongest prediction sits 1% under the ceiling this reduction implies, and every other inhibitor sits below it. Note also that the hepatic arm alone caps out at 1.68, below the paper’s ketoconazole (1.69) and ritonavir (1.73) predictions: the intestinal term of Equation 4 is required to reach them, which independently corroborates the Fg = 0.96 reading.

Reproducing Figure 5

For each perpetrator, R is solved from the paper’s predicted AUC ratio, and the resulting Cmax ratio is then predicted by the model and compared with the paper’s predicted Cmax ratio. The Cmax comparison is out of sample – nothing about it was used in solving for R – so it tests whether the reduction’s absorption and distribution kinetics couple AUC and Cmax the same way the full Simcyp model does.

uiPirto <- rxode2::rxode(readModelDb("Tian_2025_pirtobrutinib"))
ddiGrid <- sort(unique(c(seq(0, 24, by = 0.02), seq(24, 400, by = 0.5))))

solveWithActivity <- function(r) {
  m <- rxode2::zeroRe(rxode2::ini(uiPirto, lcl_3a4 = log(cl3a4Base * max(r, 1e-9))))
  ev <- rxode2::et(amt = 200 * gutFactor(r), cmt = "depot") |> rxode2::et(ddiGrid)
  d <- rxode2::rxSolve(m, ev, returnType = "data.frame")
  c(cmax = max(d$Cc), auc = trapz(d$time, d$Cc))
}
ddiBase <- solveWithActivity(1)
#> ℹ change initial estimate of `lcl_3a4` to `-0.391562202939173`
#> Warning: No omega parameters in the model

fig5 <- data.frame(
  Perpetrator = c("Itraconazole capsule", "Itraconazole solution", "Ritonavir",
                  "Ketoconazole", "Clarithromycin", "Diltiazem", "Fluconazole",
                  "Verapamil", "Rifampin", "Efavirenz", "Bosentan",
                  "Modafinil 400 mg", "Modafinil 200 mg"),
  Class = c(rep("inhibitor", 8), rep("inducer", 5)),
  paperAuc = c(1.43, 1.46, 1.73, 1.69, 1.55, 1.33, 1.37, 1.47,
               0.27, 0.52, 0.72, 0.78, 0.84),
  paperCmax = c(1.09, 1.09, 1.10, 1.09, 1.08, 1.06, 1.06, 1.08,
                0.62, 0.88, 0.86, 0.94, 0.95)
)
fig5$R <- vapply(fig5$paperAuc, function(target) {
  stats::uniroot(function(r) aucRatioClosed(r) - target,
                 c(1e-9, 2000), tol = 1e-12)$root
}, numeric(1))
fig5$modelCmax <- vapply(fig5$R, function(r) solveWithActivity(r)[["cmax"]],
                         numeric(1)) / ddiBase[["cmax"]]
#> ℹ change initial estimate of `lcl_3a4` to `-1.56294011172412`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-1.67955038603278`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-4.38192068767232`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-3.35222684234078`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-2.10179004090337`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-1.2266406780961`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-1.35315003456355`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-1.72057174123685`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `1.37992717347863`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `0.669018258961907`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `0.214412629356758`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `0.084795997091261`
#> Warning: No omega parameters in the model
#> ℹ change initial estimate of `lcl_3a4` to `-0.0439504855625008`
#> Warning: No omega parameters in the model
fig5$pctDiff <- 100 * (fig5$modelCmax / fig5$paperCmax - 1)

fig5 |>
  dplyr::transmute(Perpetrator, Class,
                   "Paper AUC ratio" = paperAuc,
                   "Implied net CYP3A4 activity R" = round(R, 3),
                   "Paper Cmax ratio" = paperCmax,
                   "Model Cmax ratio" = round(modelCmax, 3),
                   "% diff" = round(pctDiff, 1)) |>
  knitr::kable(caption = "Tian 2025 Figure 5 reproduced. R is fitted to the AUC ratio; the Cmax ratio is an out-of-sample prediction.")
Tian 2025 Figure 5 reproduced. R is fitted to the AUC ratio; the Cmax ratio is an out-of-sample prediction.
Perpetrator Class Paper AUC ratio Implied net CYP3A4 activity R Paper Cmax ratio Model Cmax ratio % diff
Itraconazole capsule inhibitor 1.43 0.310 1.09 1.065 -2.3
Itraconazole solution inhibitor 1.46 0.276 1.09 1.069 -2.0
Ritonavir inhibitor 1.73 0.018 1.10 1.095 -0.5
Ketoconazole inhibitor 1.69 0.052 1.09 1.091 0.1
Clarithromycin inhibitor 1.55 0.181 1.08 1.078 -0.2
Diltiazem inhibitor 1.33 0.434 1.06 1.053 -0.7
Fluconazole inhibitor 1.37 0.382 1.06 1.058 -0.2
Verapamil inhibitor 1.47 0.265 1.08 1.070 -1.0
Rifampin inducer 0.27 5.880 0.62 0.677 9.2
Efavirenz inducer 0.52 2.888 0.88 0.851 -3.3
Bosentan inducer 0.72 1.833 0.86 0.930 8.1
Modafinil 400 mg inducer 0.78 1.610 0.94 0.948 0.8
Modafinil 200 mg inducer 0.84 1.416 0.95 0.964 1.5 

c(`max abs % difference on the out-of-sample Cmax ratio` = round(max(abs(fig5$pctDiff)), 1),
  `max abs % difference, inhibitors only` =
    round(max(abs(fig5$pctDiff[fig5$Class == "inhibitor"])), 1))
#> max abs % difference on the out-of-sample Cmax ratio 
#>                                                  9.2 
#>                max abs % difference, inhibitors only 
#>                                                  2.3

All eight inhibitors reproduce the paper’s predicted Cmax ratio to within 2.3%, and the five inducers to within 9.2%. The implied net CYP3A4 activities are also mechanistically sensible: ritonavir, a potent mechanism-based CYP3A4 inactivator, resolves to R = 0.02, essentially complete inactivation, while rifampin resolves to a roughly 6-fold induction against the 18-fold increase in CYP3A4 activity the Discussion cites for rifampin in vitro. Both bracket correctly.

fig5Long <- fig5 |>
  dplyr::select(Perpetrator, Class, paperAuc, paperCmax, modelCmax) |>
  tidyr::pivot_longer(c(paperCmax, modelCmax), names_to = "Source",
                      values_to = "cmaxRatio") |>
  dplyr::mutate(Source = dplyr::recode(Source, paperCmax = "Tian 2025 Figure 5",
                                       modelCmax = "This reduction"),
                Perpetrator = factor(Perpetrator, levels = rev(fig5$Perpetrator)))

ggplot(fig5Long, aes(cmaxRatio, Perpetrator, shape = Source, colour = Source)) +
  geom_vline(xintercept = 1, linetype = "dashed", colour = "grey50") +
  geom_point(size = 2.6, alpha = 0.85) +
  labs(x = "Pirtobrutinib Cmax ratio", y = NULL,
       title = "Out-of-sample Cmax ratios versus Tian 2025 Figure 5",
       subtitle = "Net CYP3A4 activity fitted to the AUC ratio only") +
  theme_bw() +
  theme(legend.position = "bottom")

Assumptions and deviations

  • Linear model only. The packaged model omits pirtobrutinib’s time-dependent inhibition of its own CYP3A4-mediated clearance. K_I = 4.70 uM and the fitted k_inact = 0.056 1/h are printed in Table 1, but the autoinhibition ODE additionally requires the CYP3A4 degradation rate constant k_deg, which is a Simcyp database default and is not printed anywhere in the paper, the supplement or the Data S3 input sheet. Validation is therefore against the paper’s “Predicted without TDI” row (Table 2) and the “reversible inhibition” row of Table S9, which are the same numbers and are reported by the authors for exactly this comparison. The paper notes that a population-PK analysis in patients with cancer did not detect the time-dependent clearance change at all.
  • Exposure 3.5-8.3% below the paper’s predictions. Discussed and quantified above: CL = 1.69 L/h is the printed clinical value, while the geometric-mean clearance of the paper’s 100-subject virtual population is 1.549 L/h. No parameter was tuned to close the gap.
  • Steady-state volume. The reduction’s steady-state volume is vc + V_SAC = 42.4 L, or 0.526 L/kg at the implied 80.7 kg, against the 0.536 L/kg in Data S3 (0.54 L/kg in Table 1). The 1.8% shortfall is the liver and portal-vein volume that the Simcyp minimal-PBPK layout carries as separate compartments and that this two-compartment reduction lumps into vc.
  • No inter-individual variability. Data S3 prints 30% input CVs on ka, lag time, Q_gut, the additional HLM CLint and the biliary CLint, but no CV on the recombinant CYP3A4 CLint and no variance on total clearance. The percent CVs in Table 2 (28-36%) are the spread of the Simcyp virtual population, driven by liver weight and CYP3A4 abundance sampled from population files that are not published. Rather than invent an omega, this is a deterministic typical-value model with propSd fixed at zero; all comparisons above are typical-value against published geometric means.
  • No covariates. Body weight, age and sex are recorded in covariatesDataExcluded: they set the Simcyp population sampling ranges but no covariate relationship on any pirtobrutinib parameter is printed. Because Data S3 gives kin, kout and Q, vc is an absolute volume and no reference body weight has to be assumed anywhere in this reduction.
  • Fa uses the unrounded Equation 6 value. Table 1 prints Fa = 0.91 and the Method column states it was “calculated using Equation (6)”, i.e. from the measured absolute bioavailability F = 0.86. This model carries the unrounded Fa = 0.91606 so that Fa x Fg x Fh returns exactly the printed F = 0.86; using the rounded 0.91 would give 0.8544, 0.7% low.
  • Renal clearance from the intravenous dose. CL_R = 0.12 L/h is used, as in the paper. Section 3.1 records that a [14C]-pirtobrutinib oral solution gave 0.29 L/h instead, and Figure S2 shows the f_m,CYP3A4 estimate of 0.40 is insensitive to the choice.
  • Biliary clearance folded into cl_other. Figure 2 reports CL_bile = 0.24 L/h separately, on the assumption that unchanged pirtobrutinib recovered in feces after intravenous dosing is biliary excretion. The paper itself flags the alternative that this material is degraded pirtobrutinib glucuronide, which would move the same 0.14 fraction from biliary excretion into f_m,other (0.39 becomes 0.534). Both readings give the identical cl_other = 0.894 L/h, so folding the two routes into one parameter makes the model robust to that ambiguity. Neither route is a CYP3A4 interaction target.
  • R in the Figure 5 analysis is a lumped net activity. A single relative activity is applied to both the hepatic and intestinal CYP3A4 pools. The paper’s own split for itraconazole capsule is more extreme in the gut (X = 0.009, Table S3) than in the liver, so the recovered R values should be read as a net effective activity rather than as a hepatic-specific one. The out-of-sample Cmax agreement shows the lumping is adequate for reproducing the paper’s predictions but does not identify the liver/gut split. R values are not model parameters and are not stored in the model file.
  • DDI predictions are not mechanistic here. The perpetrator PBPK models (itraconazole and hydroxyitraconazole from Chen 2019, ketoconazole, bosentan and modafinil from the cited literature, and the Simcyp-supplied rifampin, ritonavir, clarithromycin, diltiazem, fluconazole, verapamil, efavirenz and midazolam files) are not reproducible. Nothing in this vignette predicts a DDI from perpetrator pharmacokinetics; the Figure 5 section reproduces the paper’s predictions given a CYP3A4 activity, which is a different and weaker claim.
  • Midazolam and repaglinide victim predictions are out of scope. The paper’s Table S13 midazolam ratios and the repaglinide study characterise pirtobrutinib as a perpetrator, which needs the pirtobrutinib TDI layer that is not reproducible.
  • No erratum. No correction notice was found for doi:10.1002/psp4.70134 at the time of extraction; the article was published 2025 after acceptance on 6 October 2025.