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Cenicriviroc (TBR-652) HIV-1 RNA and MCP-1 exposure-response (Marier 2011)

Source: vignettes/articles/Marier_2011_cenicriviroc.Rmd
Marier_2011_cenicriviroc.Rmd

Model and source

  • Citation: Marier JF, Trinh M, Pheng LH, Palleja SM, Martin DE. Pharmacokinetics and pharmacodynamics of TBR-652, a novel CCR5 antagonist, in HIV-1-infected, antiretroviral treatment-experienced, CCR5 antagonist-naive patients. Antimicrob Agents Chemother. 2011;55(6):2768-2774. doi:10.1128/AAC.00713-10. PMCID PMC3101382. PK/PD model form is in Methods ‘Pharmacokinetic/pharmacodynamic modeling’ (p. 2770); the parameter estimates and their standard errors are in Results (p. 2772) and are restated in the Discussion (p. 2773); the fitted curve and the individual data it was fit to are Figure 3 (p. 2773). Companion model file from the same paper: modellib(‘Marier_2011_cenicriviroc_mcp1’).
  • Article: https://doi.org/10.1128/AAC.00713-10
  • Open-access full text: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3101382/

Marier et al. (2011) report a double-blind, placebo-controlled, dose-escalating study of 10 days of once-daily oral monotherapy with the CCR5 antagonist then known only as TBR-652 in HIV-1-infected, antiretroviral treatment-experienced, CCR5-antagonist-naive adults. The compound was later assigned the INN cenicriviroc; it is a dual CCR5 / CCR2 antagonist, and this package uses the INN throughout while keeping the development code visible in each model’s description.

The paper contributes two models, fitted independently on two different biomarkers from the same cohort, so the package carries one file for each:

Model file Endpoint Emax IC50
Marier_2011_cenicriviroc_hiv1rna Day-11 change from baseline in plasma HIV-1 RNA -1.43 log10 copies/mL 13.1 ng/mL
Marier_2011_cenicriviroc_mcp1 Day-10 change from baseline in plasma MCP-1 +2.63 log10 pg/mL 29.8 ng/mL

Both have the same structural form – a simple, intercept-free, hyperbolic Emax function of the average steady-state cenicriviroc concentration:

E=Emax⋅CssIC50+Css E = E_{max} \cdot \frac{C_{ss}}{IC_{50} + C_{ss}}

Two properties of these models are unusual enough to state up front, because they determine how the rest of this vignette is written.

There is no pharmacokinetic model. Marier 2011 characterised cenicriviroc PK by noncompartmental analysis only (Methods, “Pharmacokinetics”, p. 2769). There is no compartmental structure, no CL, no V, no ka to extract. The driving exposure is therefore supplied to the model as a covariate, CSS_CVC, rather than generated from dose events – exactly as for the other static exposure-response models in this library (Riggs_2012_albinterferon_svr_gt1, Song_2013_..._dbp, Mukker_2026_tuvusertib_hERG).

Both models are deterministic. The source reports two point estimates and their standard errors per endpoint, and nothing else: no OMEGA, no SIGMA, no residual SD. Neither model carries an eta, and addSd is fixed(0) in both, so each returns a single exact curve. Every check below is consequently an exact numerical identity rather than a statistic over a simulated cohort, and is asserted at correspondingly tight tolerance.

mod_hiv  <- readModelDb("Marier_2011_cenicriviroc_hiv1rna")
mod_mcp1 <- readModelDb("Marier_2011_cenicriviroc_mcp1")

# Both models are static: no ODE states, no dose events. The event table is
# therefore a plain observation frame carrying the driving covariate, with
# cmt = NA_character_ because there is no compartment to point at. This is the
# same idiom used by Mukker_2026_tuvusertib_QTc.Rmd.
#
# NOTE on the muffled warning: rxode2 emits "multi-subject simulation without
# 'omega'" on every solve here. That is expected and correct -- these models
# have no random effects, so there is no omega to supply. Passing `omega = NA`
# is NOT the fix: for a model that declares no eta, rxode2 evaluates
# dim(NA)[1] and fails with "rep(0, dim(.omega)[1]) : invalid 'times'
# argument". Only that one message is muffled; any other warning propagates.
solve_static <- function(mod, css) {
  ev <- data.frame(
    id      = seq_along(css),
    CSS_CVC = css,
    time    = 0,
    evid    = 0,
    amt     = 0,
    cmt     = NA_character_
  )
  withCallingHandlers(
    as.data.frame(rxode2::rxSolve(mod, events = ev)),
    warning = function(w) {
      if (grepl("without.*'omega'", conditionMessage(w))) {
        invokeRestart("muffleWarning")
      }
    }
  )
}

Population

The study (protocol 652-2-201) screened and entered 54 patients at 10 sites, 9 in the United States and 1 in Argentina. Approximately 10 patients per dose level were randomised 4:1 to cenicriviroc or matching placebo at 25, 50, 75, 100 and 150 mg once daily for 10 days, followed by a 40-day observation period.

From Table 1 (p. 2770): 87% male (7 of 54 female); mean age 38.9 years (SD 7.95), inclusion range 18-65; mean weight 79.81 kg (SD 17.08); mean height 176.71 cm (SD 9.685); mean BMI 25.65 kg/m^2 (SD 5.322). Race and ethnicity were 55.6% Caucasian, 25.9% African-American, 13.0% Hispanic, 1.9% Asian and 3.7% other.

Entry required treatment experience with all antiretroviral therapy stopped at least 6 weeks earlier (actual time off therapy ranged from 6 weeks to 3 years), no prior CCR5-antagonist exposure, CCR5-tropic virus by the enhanced-sensitivity Trofile assay, plasma HIV-1 RNA of at least 5,000 copies/mL and a CD4+ count of at least 250 cells/mm^3.

Two per-patient reassignments the paper makes explicitly matter for the denominators. Patient 2007 was randomised to the 50 mg cohort but mistakenly received 25 mg and was analysed with the 25 mg cohort. Patient 5002, in the 150 mg cohort, was retrospectively found to harbour predominantly CXCR4-tropic virus at baseline, was therefore ineligible, and was omitted from the antiviral efficacy analyses. The HIV-1 RNA analysis set used here is consequently 42 treated plus 10 placebo patients; the paper states no analysis-set size for the MCP-1 model, so n_subjects is left NA in that file rather than guessed.

The same information is available programmatically:

pop <- rxode2::rxode(mod_hiv)$population
str(pop[c("species", "n_subjects", "disease_state", "endpoint")])
#> List of 4
#>  $ species      : chr "human"
#>  $ n_subjects   : int 52
#>  $ disease_state: chr "HIV-1 infection, antiretroviral treatment-experienced but off all antiretroviral therapy for at least 6 weeks ("| __truncated__
#>  $ endpoint     : chr "Change from baseline (day 1 predose) in plasma HIV-1 RNA on day 11, in log10 copies/mL. Assayed with the Cobas "| __truncated__

Source trace

Every value below is recorded as an in-file comment beside its ini() entry in inst/modeldb/specificDrugs/Marier_2011_cenicriviroc_hiv1rna.R and ..._mcp1.R. This table collects them for review. Page numbers refer to the journal pagination (the article runs pp. 2768-2774).

Model Parameter / equation Value Source location
both E = emax * Css / (ic50 + Css) n/a Methods, “Pharmacokinetic/pharmacodynamic modeling”, p. 2770; selection by AIC stated in Results, p. 2772
hiv1rna emax -1.43 log10 copies/mL Results p. 2772; restated Discussion p. 2773 and Abstract
hiv1rna SE(emax) 0.138 log10 copies/mL Results p. 2772
hiv1rna lic50 = log(13.1) 13.1 ng/mL Results p. 2772; restated Discussion p. 2773
hiv1rna SE(ic50) 6.53 ng/mL Results p. 2772
hiv1rna addSd fixed(0) not reported; see Assumptions
mcp1 emax +2.63 log10 pg/mL Results pp. 2772-2773
mcp1 SE(emax) 0.233 log10 pg/mL Results p. 2773
mcp1 lic50 = log(29.8) 29.8 ng/mL Results pp. 2772-2773
mcp1 SE(ic50) 9.45 ng/mL Results p. 2773
mcp1 addSd fixed(0) not reported; see Assumptions
both CSS_CVC definition (AUC0-24 / 24 h) see Table 2 Methods, “Pharmacokinetics”, p. 2769; values Table 2, p. 2772
hiv1rna fitted curve + individual data n/a Figure 3, p. 2773
mcp1 fitted curve + individual data n/a Figure 4, p. 2773
hiv1rna observed day-11 medians Table 3, p. 2772

Units

Because the observation of each model is a change on a log scale rather than a concentration, the dimensional bookkeeping is worth writing out explicitly.

Symbol Units Note
CSS_CVC ng/mL total (not unbound) plasma cenicriviroc
ic50 ng/mL same basis as CSS_CVC, so the ratio is dimensionless
CSS_CVC / (ic50 + CSS_CVC) dimensionless fraction of maximal effect, in [0, 1)
emax (hiv1rna) log10 copies/mL signed; negative = viral suppression
emax (mcp1) log10 pg/mL signed; positive = MCP-1 accumulation
dviralLoad log10 copies/mL change from baseline; add baseline to get an absolute level
dmcp1 log10 pg/mL change from baseline, i.e. a log10 fold-change

The product of a dimensionless fraction with emax therefore carries emax’s units, which is what each model’s units$concentration declares. Note that neither model carries a baseline, so neither can produce an absolute HIV-1 RNA or MCP-1 concentration on its own.

Structural verification

Three exact identities are checked first. They are algebraic consequences of the encoding, so they are asserted at machine precision.

chk_hiv  <- solve_static(mod_hiv,  c(0, 13.1))
chk_mcp1 <- solve_static(mod_mcp1, c(0, 29.8))

stopifnot(
  # 1. No intercept: at zero exposure (placebo) both models return exactly 0.
  #    This is the property Figure 3 and Figure 4 show graphically, with the
  #    placebo subjects sitting on the origin.
  chk_hiv$dviralLoad[1]  == 0,
  chk_mcp1$dmcp1[1]      == 0,

  # 2. The reported IC50 really is the half-maximal concentration: at
  #    Css = IC50 each model returns exactly emax / 2.
  isTRUE(all.equal(chk_hiv$dviralLoad[2], -1.43 / 2, tolerance = 1e-12)),
  isTRUE(all.equal(chk_mcp1$dmcp1[2],      2.63 / 2, tolerance = 1e-12)),

  # 3. Residual error really is switched off: the simulated observation
  #    equals the individual prediction exactly, confirming addSd = fixed(0).
  isTRUE(all.equal(chk_hiv$sim,  chk_hiv$dviralLoad,  tolerance = 1e-12)),
  isTRUE(all.equal(chk_mcp1$sim, chk_mcp1$dmcp1,      tolerance = 1e-12))
)

# The signs are opposite and that is the point: CCR5 blockade suppresses virus,
# CCR2 blockade lets the receptor's own ligand accumulate.
stopifnot(chk_hiv$dviralLoad[2] < 0, chk_mcp1$dmcp1[2] > 0)

The exposure metric: Css = AUC0-24 / 24 h

The models consume an NCA-derived quantity, so the first validation is of that quantity rather than of the model. Marier 2011 defines Css as the average concentration under steady-state conditions and computes AUC0-24 by the linear trapezoidal rule (Methods, p. 2769). Table 2 reports both, which makes the definition checkable against the paper’s own numbers.

This is why the vignette carries no PKNCA section. PKNCA validates a simulated concentration-time profile against a published NCA table; here the published NCA table is the model’s input, and there is no PK model to generate a profile from. The identity below is the corresponding check that is actually meaningful.

tab2 <- tibble::tribble(
  ~dose_mg, ~auc0_24, ~css_reported, ~cmax,  ~cmin,  ~tmax, ~thalf, ~cl_f,
        25,    382.0,         15.92,  35.11,  6.883,  2.98,  22.50,  81.31,
        50,   1245.0,         51.89, 102.40, 21.470,  4.00,  47.62,  49.26,
        75,   1916.0,         79.82, 157.00, 30.060,  3.50,  29.78,  42.17,
       100,   2659.0,        110.80, 196.50, 30.000,  4.00,  32.06,  48.06,
       150,   7272.0,        303.00, 508.10, 128.000, 4.00,  41.26,  22.95
) |>
  dplyr::mutate(
    css_derived = auc0_24 / 24,
    pct_diff    = 100 * (css_derived - css_reported) / css_reported
  )

# Deterministic arithmetic on transcribed table values -- no simulation, no RNG.
# The residue is pure rounding of the 4-significant-figure printed AUC and Css,
# so the bound is tight on purpose: anything larger means a mis-transcription.
stopifnot(max(abs(tab2$pct_diff)) < 0.05)

tab2 |>
  dplyr::select(dose_mg, auc0_24, css_reported, css_derived, pct_diff) |>
  dplyr::rename(
    "Dose (mg QD)"          = dose_mg,
    "AUC0-24 (ng*h/mL)"     = auc0_24,
    "Css reported (ng/mL)"  = css_reported,
    "AUC0-24 / 24 (ng/mL)"  = css_derived,
    "Difference (%)"        = pct_diff
  ) |>
  knitr::kable(
    digits  = c(0, 1, 2, 3, 4),
    caption = "Table 2 of Marier 2011: the reported Css is exactly AUC0-24 / 24 h."
  )
Table 2 of Marier 2011: the reported Css is exactly AUC0-24 / 24 h.
Dose (mg QD) AUC0-24 (ng*h/mL) Css reported (ng/mL) AUC0-24 / 24 (ng/mL) Difference (%)
25 382 15.92 15.917 -0.0209
50 1245 51.89 51.875 -0.0289
75 1916 79.82 79.833 0.0167
100 2659 110.80 110.792 -0.0075
150 7272 303.00 303.000 0.0000

Reproducing the paper’s published percentages of Emax

This is the sharpest available check on the HIV-1 RNA model, and it is worth spelling out why. Results (p. 2772) states:

Based on the PK/PD model, the average steady-state concentration levels of TBR-652 for the 25-, 50-, 75-, 100-, and 150-mg doses are expected to result in 54.5%, 79.6%, 85.7%, 89.3%, and 95.8% of the maximum inhibitory effect (Emax) of TBR-652, respectively.

That single row simultaneously pins down four things that would otherwise be assumptions: the driver (Css, not AUC0-24 and not Cmax, both of which the Methods say were tested), the IC50 (13.1 ng/mL), the absence of a Hill coefficient, and the absence of an intercept. No other combination reproduces it.

emax_hiv <- -1.43

pct <- tab2 |>
  dplyr::transmute(
    dose_mg,
    css        = css_reported,
    paper_pct  = c(54.5, 79.6, 85.7, 89.3, 95.8),
    model_pct  = 100 * solve_static(mod_hiv, css_reported)$dviralLoad / emax_hiv,
    diff_pp    = model_pct - paper_pct
  )

# Deterministic: a fixed curve evaluated at five transcribed concentrations.
# The residue is 0.06-0.36 percentage points and is explained by the paper
# averaging PER-SUBJECT percentages while this evaluates at the cohort MEAN
# Css -- Jensen's inequality on a concave function, which must bias the
# per-subject average DOWNWARD, and does, at every one of the five doses.
# A wrong IC50, a wrong driver or a stray Hill term moves these by whole
# percentage points, so 0.5 still goes red on any of those.
stopifnot(max(abs(pct$diff_pp)) < 0.5)

# Direction of the residue is itself informative and is deterministic here
# (no cohort, no RNG), so it can be asserted exactly.
stopifnot(all(pct$diff_pp > 0))

pct |>
  dplyr::rename(
    "Dose (mg QD)"        = dose_mg,
    "Css (ng/mL)"         = css,
    "Paper % of Emax"     = paper_pct,
    "Model % of Emax"     = model_pct,
    "Difference (pp)"     = diff_pp
  ) |>
  knitr::kable(
    digits  = c(0, 2, 1, 2, 3),
    caption = "Marier 2011 Results p. 2772, reproduced from the packaged model."
  )
Marier 2011 Results p. 2772, reproduced from the packaged model.
Dose (mg QD) Css (ng/mL) Paper % of Emax Model % of Emax Difference (pp)
25 15.92 54.5 54.86 0.359
50 51.89 79.6 79.84 0.243
75 79.82 85.7 85.90 0.202
100 110.80 89.3 89.43 0.127
150 303.00 95.8 95.86 0.056

Replicate published figures 

# Replicates Figure 3 of Marier 2011: fitted Emax curve of the day-11 change
# from baseline in HIV-1 RNA against average steady-state concentration.
# The published figure spans 0-500 ng/mL on the x-axis and +1.0 to -2.5 on the
# y-axis; the individual patient data it overlays are not publicly available,
# so only the fitted curve is reproduced, with the cohort mean Css marked.
css_grid <- seq(0, 500, length.out = 200)

curve_hiv <- solve_static(mod_hiv, css_grid)

cohort_hiv <- solve_static(mod_hiv, tab2$css_reported) |>
  dplyr::mutate(dose = paste0(tab2$dose_mg, " mg"))

ggplot(curve_hiv, aes(CSS_CVC, dviralLoad)) +
  geom_hline(yintercept = emax_hiv, linetype = "dotted") +
  geom_line(linewidth = 0.7) +
  geom_point(data = cohort_hiv, size = 2.4) +
  geom_text(
    data = cohort_hiv, aes(label = dose),
    vjust = 1.9, size = 3
  ) +
  scale_y_continuous(limits = c(-2.5, 1.0)) +
  labs(
    x       = "Average concentration of cenicriviroc (ng/mL)",
    y       = expression(Delta*"log HIV-1 RNA (log"[10]*" copies/mL)"),
    title   = "Figure 3 - exposure vs. day-11 change in HIV-1 RNA",
    caption = paste(
      "Replicates Figure 3 of Marier 2011 (fitted curve only).",
      "Points mark each cohort's mean Css; dotted line is Emax = -1.43."
    )
  )

# Replicates Figure 4 of Marier 2011: fitted Emax curve of the change from
# baseline in plasma MCP-1 against average steady-state concentration.
# Published axes: 0-500 ng/mL and 0.0-3.0.
curve_mcp1 <- solve_static(mod_mcp1, css_grid)

cohort_mcp1 <- solve_static(mod_mcp1, tab2$css_reported) |>
  dplyr::mutate(dose = paste0(tab2$dose_mg, " mg"))

ggplot(curve_mcp1, aes(CSS_CVC, dmcp1)) +
  geom_hline(yintercept = 2.63, linetype = "dotted") +
  geom_line(linewidth = 0.7) +
  geom_point(data = cohort_mcp1, size = 2.4) +
  geom_text(
    data = cohort_mcp1, aes(label = dose),
    vjust = -1.1, size = 3
  ) +
  scale_y_continuous(limits = c(0, 3.0)) +
  labs(
    x       = "Average concentration of cenicriviroc (ng/mL)",
    y       = expression(Delta*"log plasma MCP-1 (log"[10]*" pg/mL)"),
    title   = "Figure 4 - exposure vs. change in plasma MCP-1",
    caption = paste(
      "Replicates Figure 4 of Marier 2011 (fitted curve only).",
      "Points mark each cohort's mean Css; dotted line is Emax = +2.63."
    )
  )

The published Figure 4 curve reaches roughly 2.47 at the right-hand edge of the plotted concentration range. That is a readable feature of the figure rather than a printed number, so it is checked loosely, as a shape check on the plateau:

plateau <- solve_static(mod_mcp1, 490)$dmcp1

# Deterministic curve evaluation. 2.479 is the exact value; the window admits
# the imprecision of reading an asymptote off a printed figure, while still
# failing if Emax or IC50 were mis-transcribed (which would move it by >0.3).
stopifnot(plateau > 2.35, plateau < 2.60)
round(plateau, 3)
#> [1] 2.479

Comparison against the published observed medians

Table 3 (p. 2772) reports the observed median day-11 change from baseline in each cohort. The model was fit to individual patients rather than to these medians, and the medians carry the placebo response (+0.1 log10 copies/mL) and the 100 mg cohort’s distinct F2 tablet formulation, neither of which the model represents. This comparison is therefore a plausibility check, not an identity.

obs_cmp <- tibble::tibble(
  dose_mg       = tab2$dose_mg,
  css           = tab2$css_reported,
  observed      = c(-0.5, -1.3, -1.6, -1.2, -1.5),
  predicted     = solve_static(mod_hiv, tab2$css_reported)$dviralLoad
) |>
  dplyr::mutate(residual = predicted - observed)

# Deterministic (transcribed medians vs a fixed curve), but the two sides
# differ by a real mechanism -- cohort median vs individual-level fit, plus an
# unmodelled placebo response and formulation effect -- so this is bounded on
# the CENTRE and on magnitude, not on any single cohort's extreme.
stopifnot(
  abs(mean(obs_cmp$residual)) < 0.25,
  max(abs(obs_cmp$residual))  < 0.60
)

obs_cmp |>
  dplyr::rename(
    "Dose (mg QD)"                        = dose_mg,
    "Css (ng/mL)"                         = css,
    "Observed median (log10 copies/mL)"   = observed,
    "Model prediction (log10 copies/mL)"  = predicted,
    "Residual"                            = residual
  ) |>
  knitr::kable(
    digits  = c(0, 2, 2, 3, 3),
    caption = "Marier 2011 Table 3 day-11 medians vs. the packaged model at each cohort's mean Css."
  )
Marier 2011 Table 3 day-11 medians vs. the packaged model at each cohort’s mean Css.
Dose (mg QD) Css (ng/mL) Observed median (log10 copies/mL) Model prediction (log10 copies/mL) Residual
25 15.92 -0.5 -0.784 -0.284
50 51.89 -1.3 -1.142 0.158
75 79.82 -1.6 -1.228 0.372
100 110.80 -1.2 -1.279 -0.079
150 303.00 -1.5 -1.371 0.129

The largest residual is at 75 mg, where the observed median (-1.6) is the deepest of any cohort while its mean Css sits mid-range. The model, being monotone in exposure, cannot reproduce a non-monotone dose-median sequence (-0.5, -1.3, -1.6, -1.2, -1.5); the authors attribute the 100 mg dip to the F2 formulation, and the 75 mg and 150 mg cohorts differ by only 0.1 log10 in observed median despite a nearly 4-fold difference in exposure, which is exactly the saturation the Emax model encodes.

Parameter precision

The standard errors reported alongside the point estimates are worth carrying into the vignette, because they differ sharply between the two parameters and that difference is interpretable.

prec <- tibble::tribble(
  ~model,     ~parameter, ~estimate, ~se,
  "hiv1rna",  "Emax",         -1.43, 0.138,
  "hiv1rna",  "IC50",         13.10, 6.530,
  "mcp1",     "Emax",          2.63, 0.233,
  "mcp1",     "IC50",         29.80, 9.450
) |>
  dplyr::mutate(
    rse_pct = 100 * se / abs(estimate),
    ci_lo   = estimate - 1.96 * se,
    ci_hi   = estimate + 1.96 * se
  )

# A Wald interval must bracket its own point estimate -- a cheap guard against
# a transposed SE or a sign-mangled estimate (the PDF-glyph hazard noted in the
# model files). Deterministic arithmetic, so exact.
stopifnot(all(prec$ci_lo < prec$estimate), all(prec$estimate < prec$ci_hi))

# Both Emax parameters are well determined; both IC50s are not. Assert the
# ordering that the paper's own numbers imply.
stopifnot(
  prec$rse_pct[prec$parameter == "Emax"] < 15,
  prec$rse_pct[prec$parameter == "IC50"] > 25
)

prec |>
  dplyr::rename(
    "Model"           = model,
    "Parameter"       = parameter,
    "Estimate"        = estimate,
    "SE"              = se,
    "RSE (%)"         = rse_pct,
    "Wald 95% lower"  = ci_lo,
    "Wald 95% upper"  = ci_hi
  ) |>
  knitr::kable(
    digits  = c(0, 0, 2, 3, 1, 3, 3),
    caption = "Point estimates and standard errors as reported in Marier 2011 Results."
  )
Point estimates and standard errors as reported in Marier 2011 Results.
Model Parameter Estimate SE RSE (%) Wald 95% lower Wald 95% upper
hiv1rna Emax -1.43 0.138 9.7 -1.700 -1.160
hiv1rna IC50 13.10 6.530 49.8 0.301 25.899
mcp1 Emax 2.63 0.233 8.9 2.173 3.087
mcp1 IC50 29.80 9.450 31.7 11.278 48.322

The HIV-1 RNA IC50 has an RSE of 49.8% and a Wald lower bound of 0.30 ng/mL – positive, but only just. This is a structural consequence of the study design rather than a transcription problem: only the 25 mg cohort (mean Css 15.92 ng/mL) sits anywhere near 13.1 ng/mL, and every other cohort is on the plateau. The data constrain the maximum effect far better than the potency. Any use of this model to extrapolate to sub-25 mg doses should carry that caveat.

Cross-model comparison 

ic50_hiv  <- 13.1
ic50_mcp1 <- 29.8

# Deterministic ratio of two printed constants.
stopifnot(isTRUE(all.equal(ic50_mcp1 / ic50_hiv, 2.275, tolerance = 1e-3)))

tibble::tibble(
  `Dose (mg QD)`             = tab2$dose_mg,
  `Css (ng/mL)`              = tab2$css_reported,
  `% of antiviral Emax`      = 100 * tab2$css_reported / (ic50_hiv  + tab2$css_reported),
  `% of MCP-1 Emax`          = 100 * tab2$css_reported / (ic50_mcp1 + tab2$css_reported)
) |>
  knitr::kable(
    digits  = c(0, 2, 1, 1),
    caption = "CCR5-mediated antiviral effect saturates at lower exposure than CCR2-mediated MCP-1 accumulation."
  )
CCR5-mediated antiviral effect saturates at lower exposure than CCR2-mediated MCP-1 accumulation.
Dose (mg QD) Css (ng/mL) % of antiviral Emax % of MCP-1 Emax
25 15.92 54.9 34.8
50 51.89 79.8 63.5
75 79.82 85.9 72.8
100 110.80 89.4 78.8
150 303.00 95.9 91.0

The MCP-1 IC50 is 2.3-fold higher than the antiviral IC50, i.e. more cenicriviroc exposure is needed for half-maximal CCR2 blockade than for half-maximal CCR5-mediated viral suppression. That ordering is consistent with the in-vitro potencies the paper quotes in its Introduction (p. 2768) and with the authors’ reading that the MCP-1 plateau is reached only at the exposures associated with the 150 mg dose.

For orientation, the Discussion (p. 2773) compares the antiviral parameters against maraviroc, the first approved CCR5 antagonist, for which 10 days of 100-300 mg dosing gave Emax values of -1.13 to -1.45 log10 copies/mL and an IC50 of 8 ng/mL. Cenicriviroc’s -1.43 log10 copies/mL and 13.1 ng/mL sit inside and just above those, respectively. That comparator model is packaged separately as Davis_2008_maraviroc – note, however, that the Davis model is a concentration-QT analysis, not the antiviral exposure-response the Discussion cites (which is reference 13 of Marier 2011, not on disk here), so the two are not directly comparable and no cross-check is attempted.

Assumptions and deviations

  • No pharmacokinetic model exists in the source. Marier 2011 analysed cenicriviroc PK by noncompartmental methods only. The models therefore consume CSS_CVC as a covariate and cannot be driven from a dose. To simulate a dose, supply Css externally, or approximate it as Dose / (CL/F * 24 h) using the cohort mean CL/F values in Table 2 – but note that CL/F is not constant over the studied range (81.31, 49.26, 42.17, 48.06 and 22.95 L/h at 25 to 150 mg QD), exposure rose more than dose-proportionally at 150 mg, and two patients dosed in Argentina showed more than 2-fold higher exposure than the rest of their cohort, which the authors attribute to a possible high-fat food effect. A single clearance value will misstate Css outside 50-100 mg.

  • No inter-individual variability and no residual error are reported, for either endpoint. The source publishes two point estimates and two standard errors per model and nothing else. Figures 3 and 4 show clear residual scatter (roughly +/- 0.5 log10 units about each curve), but no estimate of it is given, so none is invented: addSd is fixed(0) in both files and each model returns the deterministic curve. Re-fitting either model to new data requires supplying a residual-error estimate.

  • Neither model carries a baseline. Both outputs are changes from baseline. dviralLoad must be added to a subject’s baseline log10 HIV-1 RNA to obtain an absolute day-11 level; dmcp1 is a log10 fold-change, so an absolute MCP-1 concentration is baseline * 10^dmcp1. The paper reports baseline HIV-1 RNA by cohort (Table 3 medians 4.0-4.6 log10 copies/mL) but reports no baseline MCP-1 concentration at all, so the MCP-1 model cannot be converted to absolute concentrations from on-disk information.

  • Drug naming. The source names the compound only as TBR-652 (also TAK-652). The files use the INN cenicriviroc per the library’s generic-name-over- development-code policy, with the development code retained in each description and in this vignette so the paper remains findable.

  • The model form is inferred from prose plus a numeric check, not from a printed equation. Marier 2011 never writes the Emax equation out. Methods (p. 2770) says a maximum-inhibitory-effect model “with and without sigmoidal factor (gamma)” and linear models were tested against AUC0-24, Cmax and Css, and Results (p. 2772) says the simple Emax model was selected by AIC. The specific form encoded here – hyperbolic, no Hill term, no intercept, driven by Css – is fixed by three independent confirmations: it reproduces the paper’s own published percentages of Emax to within 0.36 percentage points at all five doses (checked above), the fitted curves in Figures 3 and 4 both pass through the origin, and the observed placebo change was +0.1 log10 copies/mL, leaving no placebo effect to model. No alternative form reproduces the percentage row.

  • Sign of the MCP-1 Emax. The MCP-1 Emax is printed without a sign (2.63 log10) immediately adjacent to a sibling parameter that is negative, which is precisely the situation in which a dropped minus sign hides. It is confirmed positive three ways: the raw PDF text layer preserves minus-sign glyphs on every occurrence of the -1.43 antiviral Emax and shows none before 2.63; Figure 4’s y-axis runs 0.0 to 3.0 with no negative region and its curve rises; and the mechanism requires it, since blocking CCR2 blocks the clearance route of its own ligand.

  • Two new canonical PD-output names were registered for this extraction, both as members of the existing change-from-baseline PD-output family documented at ddbp / dsbp / tmccfb in inst/references/compartment-names.md: dviralLoad (the change-from-baseline sibling of the existing absolute viralLoad state, on the same pattern as ddbp / dbp) and dmcp1. A new covariate canonical CSS_CVC was registered as a member of the documented CSS_<DRUG> family alongside CSS_RBV, CSS_ALBIFN and CSS_DFO; it differs from those three in being noncompartmental in origin rather than derived from an upstream population PK fit.

  • No PKNCA section. There is no simulated concentration-time profile to integrate, because there is no PK model. The paper’s NCA table is this model’s input rather than something it can reproduce; the corresponding meaningful check – that the reported Css really is AUC0-24 / 24 h – is done above instead.

  • n_subjects differs between the two files. The HIV-1 RNA file records 52 (42 treated per the day-11 row of Table 3, plus 10 placebo). The MCP-1 file records NA: the paper states no analysis-set size for that endpoint, and counting points off Figure 4 would be a guess.

  • Covariates are documented but unused. Weight, age and sex are tabulated in Table 1 but never entered into either PK/PD model, and the paper reports no covariate screen on the Emax parameters. They are recorded in covariatesDataExcluded in both files so the provenance is preserved without implying an effect that was never estimated.