FiedlerKelly_2020_fremanezumab

library(nlmixr2lib)
library(rxode2)
#> rxode2 5.0.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)

Model and source

Citation: Fiedler-Kelly JB, Passarell J, Ludwig E, Levi M, Cohen-Barak O. Effect of Fremanezumab Monthly and Quarterly Doses on Efficacy Responses. Headache. 2020 Jul;60(7):1376-1391. doi:10.1111/head.13855. PMID: 32445498.
Description: Population PD exposure-response model relating fremanezumab average plasma concentration (Cav) to monthly moderate-to-severe headache days in adults with chronic migraine. Placebo time-course is a Hill (sigmoid) function in months and the drug effect is a power function of Cav centered on the population median Cav. Fitted to 5312 monthly observations from 1361 chronic-migraine patients pooled across the LBR-101-021 phase 2b and TV48125-CNS-30049 phase 3 studies (Fiedler-Kelly 2020).
Article: https://doi.org/10.1111/head.13855

This vignette covers the chronic-migraine (CM) exposure-response model from Fiedler-Kelly 2020. The companion EM model is FiedlerKelly_2020_fremanezumab_em. The fremanezumab population PK is not fitted in this paper; per-subject Cav values are taken from the Fiedler-Kelly 2019 popPK model (Fiedler-Kelly_2019_fremanezumab in this library).

The CM model relates monthly moderate-to-severe (M/S) headache days to fremanezumab Cav and time-on-treatment via a Hill-in-time placebo and a power-of-Cav drug effect, both centered on individual baseline:

$\text{msHeadacheDays}(t, C_{av}) = \text{BL}_i + \text{Max}_{P,i}\,\frac{t^{H_i}}{T_{50}^{H_i} + t^{H_i}} - \text{BL}_i \cdot \theta_{D,i}\,\left(\frac{C_{av}}{\text{Cav}_{\text{med}}}\right)^{\theta_{E,i}}$

with the individual baseline a piecewise-linear function of baseline acute-medication days,

$\text{BL}_i = \theta_{BL} + \theta_{S}\,\max(0,\,\text{ACUTE\_MED\_DAYS} - 5) + \eta_{\text{BL},i}$

(breakpoint at 5 d/mo). t is in months (28-day periods). The placebo Hill function and power-of-Cav drug effect were operator-confirmed from Figure 2B; parameter values come from Supplementary Table S4.

Population

The model was fitted to 5,312 monthly M/S-headache-day observations from 1,361 chronic-migraine patients pooled across two studies — the LBR-101-021 phase 2b study (n = 251) and the TV48125-CNS-30049 phase 3 study (n = 1,110). Patients met ICHD-3 criteria for chronic migraine: headache on at least 15 days/month with at least 8 migraine days/month. Pooled demographics (Supplementary Table S2): mean age 41.3 years (range 18–71); mean baseline weight 72.66 kg (range 43.5–131.8); 87.2% female; 79.8% White, 9.0% Black, 9.0% Asian; 9.1% Hispanic ethnicity; mean years since onset 19.73 (range 0–61); mean baseline M/S headache days 13.2 (range 0–28); mean baseline acute-medication days 5.73 d/mo (range 0–28). Concomitant analgesic use 10.5% and concomitant migraine-preventive use 24.2%. Patients received fremanezumab 225 mg q1m with a 675 mg starting dose, 675 mg quarterly, 900 mg monthly (phase 2b only), or placebo SC for 3 months; observation unit is one 28-day month.

str(rxode2::rxode2(readModelDb("FiedlerKelly_2020_fremanezumab_cm"))$meta$population)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line
#> List of 14
#>  $ n_subjects            : int 1361
#>  $ n_observations        : int 5312
#>  $ n_studies             : int 2
#>  $ age_range             : chr "18-71 years"
#>  $ age_median            : chr "42 years"
#>  $ weight_range          : chr "43.5-131.8 kg"
#>  $ weight_median         : chr "70.80 kg"
#>  $ sex_female_pct        : num 87.2
#>  $ race_ethnicity        : Named num [1:6] 79.8 9 9 0.4 0.2 1.5
#>   ..- attr(*, "names")= chr [1:6] "White" "Black" "Asian" "AmIndAlaskaNative" ...
#>  $ ethnicity_hispanic_pct: num 9.1
#>  $ disease_state         : chr "Adults with chronic migraine (headaches on at least 15 days/month with at least 8 migraine days/month per ICHD-3 criteria)."
#>  $ dose_range            : chr "Fremanezumab 225 mg monthly with a 675 mg starting dose, 675 mg quarterly, 900 mg monthly (phase 2b only), or p"| __truncated__
#>  $ regions               : chr "Multinational (LBR-101-021 phase 2b and TV48125-CNS-30049 phase 3 chronic-migraine studies)."
#>  $ notes                 : chr "Demographics from Supplementary Table S2 of Fiedler-Kelly 2020. Concomitant analgesic-medication use 10.5% and "| __truncated__

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/FiedlerKelly_2020_fremanezumab_cm.R. The table below collects the equations and parameters in one place for review.

Equation / parameter	Value	Source location
Composite endpoint equation `msHeadacheDays = BL + maxPLCt^H/(T50^H+t^H) - BL drugInt * (Cav/CavMedian)^drugExp`	n/a	Figure 2B; Methods — E-R Analysis Methodology
Piecewise-linear baseline `BL = bl_cm + slope_AM * max(0, ACUTE_MED_DAYS - 5)`	n/a	Results — Monthly Headache Days of at Least Moderate Severity in Patients With CM
`bl_cm` (typical baseline at AM ≤ 5 d/mo)	10.2 d/mo	Table S4
`slope_AM` (slope on AM days > 5)	0.460 d/d	Table S4
`maxPLC_cm` (max placebo response, FIXED)	-6.24 d	Table S4
`T50_PLC` (FIXED, no IIV)	1.76 months	Table S4
`lhill_PLC` (Hill, FIXED, log-transformed in `ini()`)	0.486 (unitless)	Table S4
`drugInt` typical (logit-transformed in `ini()`)	0.157 (fractional reduction at median Cav)	Table S4
`ldrugExp` (Cav exponent, log-transformed in `ini()`)	0.328 (unitless)	Table S4
`CavMedian` (centering value used inside `model()`)	69 µg/mL	Visually inferred from Figure 2B (operator); not numerically listed in S4. See Assumptions and deviations.
IIV `bl_cm` / `slope_AM` (shared additive eta)	SD 4.69 (variance 21.99)	Table S4
IIV `maxPLC_cm` (additive eta)	SD 6.66 (variance 44.36)	Table S4
IIV `lhill_PLC` (log-normal eta)	omega² = 1.69 (130 %CV per footnote a)	Table S4
IIV `logitDrugInt` (logit-normal eta)	omega² = 1.21 (92.6 %CV per footnote b)	Table S4
IIV `ldrugExp` (log-normal eta)	omega² = 0.945 (97.2 %CV per footnote a)	Table S4
Additive residual SD on monthly M/S headache days	SD 2.66 (variance 7.09)	Table S4

Sanity check at typical-value baseline with AM = 0 d/mo and Cav = 0 (placebo), at months 0, 1, 2, 3:

mod <- readModelDb("FiedlerKelly_2020_fremanezumab_cm")
ev_check <- data.frame(
  id   = 1L,
  time = 0:3,
  CAV  = 0,
  ACUTE_MED_DAYS = 0
)
sim_check <- rxode2::rxSolve(mod |> rxode2::zeroRe(), events = ev_check, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etabl_cm', 'etamaxPLC_cm', 'etalhill_PLC', 'etalogitDrugInt', 'etaldrugExp'
sim_check[, c("time", "msHeadacheDays")]
#>   time msHeadacheDays
#> 1    0      10.200000
#> 2    1       7.505923
#> 3    2       6.983113
#> 4    3       6.677923

The month-3 placebo M/S-headache-day count is 6.68, a reduction of 3.52 days from the typical baseline (paper narrative: “approximately 3.5 days with placebo”). The asymptotic placebo reduction (Max_PLC = -6.24 d) matches the paper’s “typical maximal reduction from baseline of approximately 6 days with placebo treatment”.

Virtual cohort

The original M/S-headache-day diary data are not publicly available. For validation we construct a virtual CM cohort whose covariate distributions match Supplementary Table S2, and we simulate the three Phase 3 regimens (placebo; 225 mg q1m + 675 mg starting dose; 675 mg quarterly) using a fixed schedule of period-mean Cav values.

set.seed(20260427)

n_per_arm <- 250L

# Per-period Cav values per the regimen-specific median Cavs reported in
# the Results — CM section.
regimen_cav <- list(
  placebo            = c(0, 0, 0),
  q3m_675            = c(70, 28, 28),     # Single 675 mg q3m: high mo 1, declining
  q1m_225_with_LD    = c(70, 70, 70)      # 225 mg q1m + 675 mg LD: ~steady-state high
)

make_arm <- function(arm_name, cav_per_month, n, id_offset) {
  expand.grid(
    id    = id_offset + seq_len(n),
    time  = 1:3
  ) |>
    arrange(id, time) |>
    mutate(
      regimen        = arm_name,
      ACUTE_MED_DAYS = pmax(0, rnorm(n(), mean = 5.73, sd = 7.01)),
      CAV            = cav_per_month[time]
    )
}

events <- bind_rows(
  make_arm("placebo",         regimen_cav$placebo,         n_per_arm, id_offset =      0L),
  make_arm("q3m_675",         regimen_cav$q3m_675,         n_per_arm, id_offset =   1000L),
  make_arm("q1m_225_with_LD", regimen_cav$q1m_225_with_LD, n_per_arm, id_offset =   2000L)
) |>
  mutate(evid = 0)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation

mod <- readModelDb("FiedlerKelly_2020_fremanezumab_cm")

sim_typ <- rxode2::rxSolve(
  mod |> rxode2::zeroRe(),
  events     = events,
  keep       = c("regimen"),
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etabl_cm', 'etamaxPLC_cm', 'etalhill_PLC', 'etalogitDrugInt', 'etaldrugExp'
#> Warning: multi-subject simulation without without 'omega'

sim_iiv <- rxode2::rxSolve(
  mod,
  events     = events,
  keep       = c("regimen"),
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalogitDrugInt
#> as a work-around try putting the mu-referenced expression on a simple line

Replicate published figures

Figures 3c-d and 4b-5b of Fiedler-Kelly 2020 plot the simulated mean monthly M/S headache days and percent of CM responders.

# Replicates Figure 3C of Fiedler-Kelly 2020: mean monthly M/S headache days by regimen.
sim_iiv |>
  group_by(regimen, time) |>
  summarise(
    mean_md = mean(msHeadacheDays),
    sd_md   = sd(msHeadacheDays),
    .groups = "drop"
  ) |>
  ggplot(aes(time, mean_md, colour = regimen, fill = regimen)) +
  geom_ribbon(aes(ymin = mean_md - sd_md, ymax = mean_md + sd_md), alpha = 0.15, colour = NA) +
  geom_line(linewidth = 0.8) +
  geom_point(size = 1.5) +
  labs(
    x        = "Time (months)",
    y        = "Mean monthly M/S headache days",
    title    = "Figure 3C — mean (±1 SD) monthly M/S headache days, virtual CM cohort",
    caption  = "Replicates Figure 3C of Fiedler-Kelly 2020 in the virtual cohort."
  ) +
  theme_minimal()

# Replicates Figure 4B: percent responders (>= 50% reduction in M/S headache days).
baseline_per_id <- events |>
  group_by(id, regimen) |>
  summarise(BL = first(10.2 + 0.460 * pmax(0, ACUTE_MED_DAYS - 5)), .groups = "drop")

responders <- sim_iiv |>
  left_join(baseline_per_id, by = c("id", "regimen")) |>
  mutate(reduction_pct = 100 * (BL - msHeadacheDays) / BL,
         responder     = reduction_pct >= 50)

responder_summary <- responders |>
  group_by(regimen, time) |>
  summarise(pct_responders = mean(responder) * 100, .groups = "drop")

ggplot(responder_summary, aes(time, pct_responders, colour = regimen)) +
  geom_line(linewidth = 0.8) +
  geom_point(size = 2) +
  labs(
    x       = "Time (months)",
    y       = "Percent responders (≥ 50% reduction)",
    title   = "Figure 4B — simulated percent CM responders by month",
    caption = "Replicates Figure 4B of Fiedler-Kelly 2020."
  ) +
  theme_minimal()

Comparison against published narrative

Fiedler-Kelly 2020 Results — CM section reports specific quantitative checks that should reproduce in the typical-value simulation:

narrative_compare <- sim_typ |>
  filter(time == 3) |>
  group_by(regimen) |>
  summarise(
    typical_md_month3 = round(mean(msHeadacheDays), 2),
    typical_reduction = round(10.2 - mean(msHeadacheDays), 2),
    .groups = "drop"
  )

knitr::kable(
  narrative_compare,
  caption = "Typical-value month-3 M/S headache days and reduction from baseline by regimen."
)

Typical-value month-3 M/S headache days and reduction from baseline by regimen.
regimen	typical_md_month3	typical_reduction
placebo	8.30	1.90
q1m_225_with_LD	6.22	3.98
q3m_675	6.79	3.41

The placebo arm produces a 1.9-day month-3 reduction (paper: “approximately 3.5 days with placebo”). At a typical Cav of 70 µg/mL (q1m + LD), the model gives a 3.98-day reduction, of which the drug-only contribution at typical baseline 10.2 d is 10.2 × 0.157 × (70/69)^0.328 ≈ 1.61 days (paper narrative: 2.7 to 3.6 days).

PKNCA validation

PKNCA is the wrong validation target here for the same reasons as in the EM vignette: there is no concentration profile to integrate (Cav is a covariate), and the response is a count of days per month. The validation strategy is therefore the narrative-comparison table above, mirroring the operator-confirmed Figure 2B interpretation.

Assumptions and deviations

Time unit is months (28-day periods). As in the EM vignette.
Placebo time-course form is operator-confirmed from Figure 2B. Supplementary Table S4 lists Maximum response (placebo), T50 placebo, and Hill coefficient for placebo, all FIXED. The Hill-in-time form placebo_eff(t) = MaxPLC * t^Hill / (T50^Hill + t^Hill) was visually read from Figure 2B by the operator during sidecar request 3 of this extraction.
CavMedian = 69 µg/mL is visually inferred from Figure 2B. The drug-effect intercept drugInt = 0.157 is described in S4 as the “fractional reduction from baseline at median fremanezumab Cav”, but the median Cav itself is not listed numerically in S4 nor in the trimmed text. The value 69 µg/mL was read from the x-axis position of the per-regimen median markers in Figure 2B (operator decision in sidecar request 3, answer cm_cavmed = USER) and reproduces the paper’s narrative drug-effect ranges (12-16% across Cav 28-70 µg/mL; 18-19% at Cav 120 µg/mL). Users who can recover the exact published Cav_median from the analysis dataset should override CavMedian accordingly when the model is consumed.
Cav as a per-period covariate, not a model output. The CAV column must be supplied per row by the user, derived externally from the Fiedler-Kelly 2019 popPK model (Fiedler-Kelly_2019_fremanezumab).
Cav values in the virtual cohort. Hand-tuned from the Results section’s regimen medians; for exact reproduction of the paper’s full simulation, drive the model with EB Cav from the Fiedler-Kelly 2019 popPK simulator.
ACUTE_MED_DAYS distribution. The virtual cohort draws from N(5.73, 7.01) truncated at 0 (Supplementary Table S2 mean and SD across the pooled CM cohort). The actual data is right-skewed with median 1.75 d/mo.
Observation variable is msHeadacheDays, not Cc. Convention waiver as in the EM vignette.
units$dosing carries an explanatory string to satisfy the checkModelConventions() requirement; this PD-only model does not consume dose events.
MU-referencing warning. As in the EM vignette: etalogitDrugInt’s link goes through inverse-logit. Affects refitting, not simulation.