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## ============================================================
## NMOSD QSP Model — mrgsolve ODE Implementation
## Disease: Neuromyelitis Optica Spectrum Disorder (NMOSD)
## Mechanism: AQP4-IgG → Complement (C5) → Astrocyte necrosis
## → CNS lesion → Disability (EDSS)
## Treatments: Eculizumab, Inebilizumab, Satralizumab,
## Rituximab, Prednisolone, MMF, AZA, IVIG, PE
##
## Parameters calibrated to:
## - PREVENT trial (eculizumab, Pittock 2019 NEJM)
## - N-MOmentum trial (inebilizumab, Cree 2019 Lancet)
## - SAkuraSky/SAkuraStar (satralizumab, Yamamura 2019 NEJM)
## - ULTIMATE I/II (ublituximab, Marignier 2024 Lancet)
## - Rituximab real-world cohorts (Kim 2015, Mealy 2014)
## ============================================================
library(mrgsolve)
library(dplyr)
library(tidyr)
library(ggplot2)
library(patchwork)
## ============================================================
## Model Code
## ============================================================
nmo_code <- '
$PROB NMOSD QSP Model v1.0
$PARAM @annotated
// ---- B-cell & Antibody parameters ----
kB_prod : 0.02 : Naive B-cell production rate (cells/day)
kB_death : 0.05 : Naive B-cell death rate (/day)
kB_act : 0.01 : B-cell activation rate (/day)
kGC : 0.10 : Germinal center -> plasmablast rate (/day)
kPB_diff : 0.08 : Plasmablast -> plasma cell rate (/day)
kPB_death: 0.15 : Plasmablast death rate (/day)
kPC_death: 0.003 : Plasma cell death rate (/day; long-lived ~1yr)
kAb_prod : 0.5 : AQP4-IgG production per plasma cell (nmol/L/cell/day)
kAb_CL : 0.02 : AQP4-IgG clearance rate (/day; t½~21d for IgG1)
BAFF_stim: 1.2 : BAFF stimulation factor on B-cell survival
IL6_stim : 1.5 : IL-6 stimulation on plasmablast survival
// ---- Complement (C5) dynamics ----
C5_prod : 10.0 : C5 synthesis rate (nmol/L/day)
C5_CL : 0.14 : C5 natural clearance (/day; t½~5d)
C5_kon : 0.005 : AQP4-IgG -> C5 cleavage rate constant
kMAC_form: 0.3 : C5b -> MAC formation rate (/day)
kMAC_CL : 0.5 : MAC clearance rate (/day)
// ---- Astrocyte damage ----
kAst_death : 0.1 : Astrocyte death rate from MAC (/day)
kAst_rep : 0.005: Astrocyte repair rate (/day)
Ast0 : 100 : Normal astrocyte level (% of normal)
MAC_EC50 : 5.0 : MAC EC50 for astrocyte killing (nmol/L)
MAC_H : 2.0 : Hill coefficient for MAC cytotoxicity
// ---- Lesion & EDSS dynamics ----
kLes_form : 0.05 : Lesion formation rate from astrocyte death (/day)
kLes_res : 0.01 : Lesion resolution rate (/day; incomplete)
kEDSS_inc : 0.002: EDSS increment per lesion unit (/day)
kEDSS_rec : 0.003: EDSS recovery rate (/day; partial)
EDSS_max : 10.0 : Maximum EDSS
// ---- Neuroinflammation (IL-6, TNF-α) ----
kIL6_prod : 0.5 : IL-6 basal production (pg/mL/day)
kIL6_CL : 0.3 : IL-6 clearance (/day)
kTNF_prod : 0.2 : TNF-α production from macrophages (pg/mL/day)
kTNF_CL : 0.5 : TNF-α clearance (/day)
// ---- Oligodendrocyte & NfL ----
kOligo_death: 0.05 : Oligodendrocyte death rate from Glu-toxicity (/day)
kOligo_rep : 0.02 : Oligodendrocyte repair from OPC (/day)
Oligo0 : 100 : Normal oligodendrocyte level (%)
kNfL_rel : 0.1 : NfL release rate from axonal damage (pg/mL/day)
kNfL_CL : 0.05 : NfL clearance from serum (/day)
// ---- Eculizumab PK (anti-C5) ----
Ke_CL : 0.022 : Eculizumab clearance (L/h) -> converted below
Ke_V1 : 4.3 : Eculizumab central volume (L)
Ke_V2 : 3.2 : Eculizumab peripheral volume (L)
Ke_Q : 0.16 : Intercompartmental clearance (L/h)
Ke_C5_kon : 0.5 : Eculizumab-C5 binding on-rate (L/nmol/day)
Ke_C5_koff : 0.001 : Eculizumab-C5 dissociation rate (/day; Kd~2 pM)
Ke_C5_kdeg : 0.1 : Drug-C5 complex degradation rate (/day)
// ---- Inebilizumab PK (anti-CD19) ----
Ki_CL : 0.019 : Inebilizumab clearance (L/h)
Ki_V1 : 3.0 : Inebilizumab central volume (L)
Ki_V2 : 2.5 : Peripheral volume (L)
Ki_Q : 0.12 : Intercompartmental clearance (L/h)
Ki_Bkill : 0.5 : B-cell depletion rate constant (/day/(nmol/L))
// ---- Satralizumab PK (anti-IL-6R) ----
Ks_ka : 0.18 : Satralizumab SC absorption rate (/day)
Ks_F : 0.79 : SC bioavailability
Ks_CL : 0.65 : Apparent clearance (L/day)
Ks_V1 : 3.6 : Central volume (L)
Ks_V2 : 2.0 : Peripheral volume (L)
Ks_Q : 0.5 : Intercompartmental clearance (L/day)
Ks_IL6R_kon: 2.0 : Satralizumab-IL6R on-rate
Ks_IL6R_koff:0.002 : Satralizumab-IL6R off-rate (recycling mAb; pH-dep)
// ---- Rituximab PK (anti-CD20) ----
Kr_CL : 0.33 : Rituximab clearance (L/day)
Kr_V1 : 3.1 : Central volume (L)
Kr_V2 : 2.8 : Peripheral volume (L)
Kr_Q : 0.45 : Intercompartmental clearance (L/day)
Kr_Bkill : 0.4 : B-cell depletion rate constant
// ---- Prednisolone PK ----
Kp_ka : 1.5 : Prednisolone absorption (/h -> /day = 36/day)
Kp_F : 0.82 : Oral bioavailability
Kp_CL : 14.4 : Clearance (L/day; CYP3A4)
Kp_V : 47 : Volume of distribution (L)
Kp_Emax : 0.8 : GR activation Emax (fractional inflammatory reduction)
Kp_EC50 : 50 : GR activation EC50 (ng/mL)
// ---- MMF (MPA) PK ----
Km_ka : 0.9 : MPA absorption rate (/h -> x24 -> /day ~21.6)
Km_CL : 12 : MPA clearance (L/day)
Km_V : 3.3 : Volume (L)
Km_Emax : 0.7 : IMPDH inhibition Emax
Km_EC50 : 1.5 : IMPDH EC50 (mg/L)
// ---- Plasma Exchange (PE) ----
PE_eff : 0.65 : Fractional IgG removal per session
// ---- Disease severity modifier ----
baseline_ARR: 1.8 : Untreated annual relapse rate
$CMT @annotated
// B-cell compartments
Bnaive : Naive B-cells (normalized units)
Bact : Activated B-cells (in germinal center)
PB : Plasmablasts (CD19+ CD38+)
PC : Long-lived plasma cells
Ab : AQP4-IgG in serum (nmol/L)
// Complement
C5 : Free serum C5 (nmol/L)
EC_C5cx : Eculizumab-C5 bound complex (nmol/L)
MAC : Membrane Attack Complex (nmol/L-eq)
// CNS/Tissue
Ast : Astrocyte viability (% of normal)
Oligo : Oligodendrocyte viability (% of normal)
Lesion : Active lesion burden (arbitrary units)
EDSS : EDSS score (continuous 0-10)
NfL : Serum NfL (pg/mL)
// Cytokines
IL6 : Serum IL-6 (pg/mL)
TNFa : Serum TNF-α (pg/mL)
// Eculizumab PK (IV biweekly)
Eculi_C1 : Eculizumab central compartment (nmol/L)
Eculi_C2 : Eculizumab peripheral compartment (nmol/L)
// Inebilizumab PK (IV)
Ineb_C1 : Inebilizumab central (nmol/L)
Ineb_C2 : Inebilizumab peripheral (nmol/L)
// Satralizumab PK (SC)
Satra_dep : Satralizumab SC depot
Satra_C1 : Satralizumab central (nmol/L)
Satra_C2 : Satralizumab peripheral (nmol/L)
Satra_cx : Satralizumab-IL6R complex
// Rituximab PK (IV)
Ritu_C1 : Rituximab central (nmol/L)
Ritu_C2 : Rituximab peripheral (nmol/L)
// Prednisolone PK (oral)
Pred_gut : Prednisolone GI compartment
Pred_C1 : Prednisolone plasma (ng/mL)
// MMF/MPA PK (oral)
MPA_gut : MPA GI compartment
MPA_C1 : MPA plasma (mg/L)
$INIT
Bnaive = 5.0
Bact = 0.5
PB = 0.2
PC = 1.0
Ab = 50.0
C5 = 70.0
EC_C5cx = 0
MAC = 0.1
Ast = 100.0
Oligo = 100.0
Lesion = 0.2
EDSS = 2.0
NfL = 25.0
IL6 = 5.0
TNFa = 3.0
Eculi_C1 = 0
Eculi_C2 = 0
Ineb_C1 = 0
Ineb_C2 = 0
Satra_dep = 0
Satra_C1 = 0
Satra_C2 = 0
Satra_cx = 0
Ritu_C1 = 0
Ritu_C2 = 0
Pred_gut = 0
Pred_C1 = 0
MPA_gut = 0
MPA_C1 = 0
$OMEGA @labels ETA_Ab ETA_Ast ETA_CL
0.04 0.09 0.04
$SIGMA 0.02
$MAIN
// Individual parameter variation
double kAb_CL_i = kAb_CL * exp(ETA_CL);
double kAst_rep_i = kAst_rep * exp(ETA_Ast);
double kAb_prod_i = kAb_prod * exp(ETA_Ab);
// Drug PK derived rates (convert h to day where needed)
double Ke_k10 = (Ke_CL * 24) / Ke_V1;
double Ke_k12 = (Ke_Q * 24) / Ke_V1;
double Ke_k21 = (Ke_Q * 24) / Ke_V2;
double Ki_k10 = (Ki_CL * 24) / Ki_V1;
double Ki_k12 = (Ki_Q * 24) / Ki_V1;
double Ki_k21 = (Ki_Q * 24) / Ki_V2;
// Emax PD functions
// Eculizumab: C5 inhibition (occupancy model)
double Eculi_occ = Eculi_C1 / (Eculi_C1 + 10.0); // Kd ~10 nmol/L for free C5 inhibition
// Satralizumab: IL-6R blockade -> reduce IL-6 effect
double Satra_eff = Satra_cx / (Satra_cx + 2.0); // IL-6R occupancy
// Rituximab: B-cell depletion signal
double Ritu_kill = Kr_Bkill * Ritu_C1;
// Inebilizumab: CD19 depletion
double Ineb_kill = Ki_Bkill * Ineb_C1;
// Prednisolone: GR activation -> anti-inflammatory (0-1 scale)
double Pred_GR = Kp_Emax * Pred_C1 / (Kp_EC50 + Pred_C1);
// MMF/MPA: IMPDH inhibition -> reduce B-cell proliferation (0-1)
double MPA_inh = Km_Emax * MPA_C1 / (Km_EC50 + MPA_C1);
// MAC-driven astrocyte killing (Hill function)
double MAC_kill = pow(MAC, MAC_H) / (pow(MAC_EC50, MAC_H) + pow(MAC, MAC_H));
// Composite B-cell suppression from all drugs
double Bdrug_inh = 1.0 - (1.0 - MPA_inh) * (1.0 - Pred_GR * 0.5);
// IL-6 amplification of plasmablast survival
double IL6_boost = IL6_stim * IL6 / (10.0 + IL6);
$ODE
//------------------------------------------------
// B-cell & Antibody system
//------------------------------------------------
dxdt_Bnaive = kB_prod
- kB_death * Bnaive
- kB_act * Bnaive;
// Activated B-cells (in germinal center) — suppressed by drugs
dxdt_Bact = kB_act * Bnaive * BAFF_stim * (1 - Bdrug_inh)
- kGC * Bact
- (Ineb_kill + Ritu_kill) * Bact;
// Plasmablasts
dxdt_PB = kGC * Bact * (1.0 + IL6_boost)
- kPB_diff * PB
- kPB_death * PB
- (Ineb_kill + Ritu_kill) * PB;
// Long-lived plasma cells (less susceptible to anti-CD20/CD19)
dxdt_PC = kPB_diff * PB
- kPC_death * PC
- Ineb_kill * 0.3 * PC; // inebilizumab depletes some LLPC
// AQP4-IgG serum concentration (nmol/L)
dxdt_Ab = kAb_prod_i * PC
- kAb_CL_i * Ab
- Ke_C5_kon * Ab * (C5_free_eff) // Eculizumab does not clear Ab
- 0.0; // PE and IVIG handled as events
//------------------------------------------------
// Complement C5 dynamics
//------------------------------------------------
// Free C5 available for cleavage (reduced by eculizumab binding)
double C5_free_eff = C5 * (1.0 - Eculi_occ);
dxdt_C5 = C5_prod - C5_CL * C5
+ Ke_C5_koff * EC_C5cx // C5 released from complex
- Ke_C5_kon * Eculi_C1 * C5 * (1 - Eculi_occ);
// Eculizumab-C5 complex
dxdt_EC_C5cx = Ke_C5_kon * Eculi_C1 * C5
- Ke_C5_koff * EC_C5cx
- Ke_C5_kdeg * EC_C5cx;
// MAC formation: driven by Ab titer × free C5
double MAC_drive = C5_kon * Ab * C5_free_eff / (Ab + 20.0);
dxdt_MAC = kMAC_form * MAC_drive * (1.0 - Eculi_occ)
- kMAC_CL * MAC;
//------------------------------------------------
// Astrocyte viability (% of normal, 0-100)
//------------------------------------------------
dxdt_Ast = kAst_rep_i * (100.0 - Ast) * (Ast / 100.0)
- kAst_death * MAC_kill * Ast
+ Pred_GR * 0.3 * (100.0 - Ast); // steroid partial protection
//------------------------------------------------
// Oligodendrocyte (secondary damage from Glu toxicity)
//------------------------------------------------
double Glu_tox = (100.0 - Ast) / 100.0; // more astrocyte death -> more Glu
dxdt_Oligo = kOligo_rep * (100.0 - Oligo)
- kOligo_death * Glu_tox * Oligo;
//------------------------------------------------
// Active lesion burden
//------------------------------------------------
dxdt_Lesion = kLes_form * (100.0 - Ast) / 100.0 * MAC_kill
- kLes_res * Lesion;
//------------------------------------------------
// EDSS (continuous approximation)
//------------------------------------------------
double EDSS_drive = kEDSS_inc * Lesion;
double EDSS_recov = kEDSS_rec * (EDSS > 2.0 ? (EDSS - 2.0) : 0.0);
dxdt_EDSS = EDSS_drive - EDSS_recov;
// Bound EDSS 0-10
if (EDSS > EDSS_max) EDSS = EDSS_max;
if (EDSS < 0.0) EDSS = 0.0;
//------------------------------------------------
// NfL (neurofilament light chain)
//------------------------------------------------
double axon_dmg = (1.0 - Oligo/100.0) + (100.0 - Ast)/200.0;
dxdt_NfL = kNfL_rel * axon_dmg * 100.0
- kNfL_CL * NfL;
//------------------------------------------------
// Cytokines
//------------------------------------------------
// IL-6: produced by reactive astrocytes, suppressed by satralizumab
double IL6_ast_prod = kIL6_prod * (100.0 - Ast) / 50.0;
double IL6_satra_inh = 1.0 - Satra_eff;
dxdt_IL6 = kIL6_prod + IL6_ast_prod
- kIL6_CL * IL6 * (1.0 + Satra_eff);
// TNF-α: from M1 macrophages, partially suppressed by steroids
dxdt_TNFa = kTNF_prod * (100.0 - Ast)/50.0
- kTNF_CL * TNFa
- Pred_GR * 0.4 * TNFa;
//------------------------------------------------
// Eculizumab PK (2-compartment IV)
//------------------------------------------------
dxdt_Eculi_C1 = -Ke_k10 * Eculi_C1
- Ke_k12 * Eculi_C1
+ Ke_k21 * Eculi_C2
- Ke_C5_kon * Eculi_C1 * C5
+ Ke_C5_koff * EC_C5cx;
dxdt_Eculi_C2 = Ke_k12 * Eculi_C1 - Ke_k21 * Eculi_C2;
//------------------------------------------------
// Inebilizumab PK (2-compartment IV)
//------------------------------------------------
dxdt_Ineb_C1 = -(Ki_k10 + Ki_k12) * Ineb_C1 + Ki_k21 * Ineb_C2;
dxdt_Ineb_C2 = Ki_k12 * Ineb_C1 - Ki_k21 * Ineb_C2;
//------------------------------------------------
// Satralizumab PK (SC 1-compartment depot -> 2-comp)
//------------------------------------------------
dxdt_Satra_dep = -Ks_ka * Satra_dep;
double Ks_k10 = Ks_CL / Ks_V1;
double Ks_k12 = Ks_Q / Ks_V1;
double Ks_k21 = Ks_Q / Ks_V2;
dxdt_Satra_C1 = Ks_ka * Ks_F * Satra_dep / Ks_V1
- Ks_k10 * Satra_C1
- Ks_k12 * Satra_C1
+ Ks_k21 * Satra_C2
- Ks_IL6R_kon * Satra_C1 * (10.0 - Satra_cx)
+ Ks_IL6R_koff * Satra_cx;
dxdt_Satra_C2 = Ks_k12 * Satra_C1 - Ks_k21 * Satra_C2;
dxdt_Satra_cx = Ks_IL6R_kon * Satra_C1 * (10.0 - Satra_cx)
- Ks_IL6R_koff * Satra_cx
- 0.05 * Satra_cx; // complex degradation
//------------------------------------------------
// Rituximab PK (2-compartment IV)
//------------------------------------------------
double Kr_k10 = Kr_CL / Kr_V1;
double Kr_k12 = Kr_Q / Kr_V1;
double Kr_k21 = Kr_Q / Kr_V2;
dxdt_Ritu_C1 = -(Kr_k10 + Kr_k12) * Ritu_C1 + Kr_k21 * Ritu_C2;
dxdt_Ritu_C2 = Kr_k12 * Ritu_C1 - Kr_k21 * Ritu_C2;
//------------------------------------------------
// Prednisolone PK (1-compartment oral)
//------------------------------------------------
double Kp_ka_day = Kp_ka * 24; // convert /h to /day
dxdt_Pred_gut = -Kp_ka_day * Pred_gut;
dxdt_Pred_C1 = Kp_ka_day * Kp_F * Pred_gut / Kp_V
- (Kp_CL / Kp_V) * Pred_C1;
//------------------------------------------------
// MPA PK (1-compartment oral)
//------------------------------------------------
double Km_ka_day = Km_ka * 24;
dxdt_MPA_gut = -Km_ka_day * MPA_gut;
dxdt_MPA_C1 = Km_ka_day * MPA_gut / Km_V
- (Km_CL / Km_V) * MPA_C1;
$TABLE
double ARR_pred = baseline_ARR * Lesion / 1.0 * (Ab / 50.0);
double TTE = 0; // time-to-event calculated externally
double Bcell_pct = (PB + Bact) / 5.8 * 100.0; // percent of baseline
double GFAP_ser = (100.0 - Ast) * 0.8 + 5.0; // sGFAP (pg/mL approx)
double IPRED_EDSS = EDSS;
double DV = IPRED_EDSS * (1 + EPS(1));
$CAPTURE ARR_pred Bcell_pct GFAP_ser IL6 TNFa NfL MAC C5 Ab EDSS Ast Oligo Lesion
Eculi_C1 Ineb_C1 Satra_C1 Ritu_C1 Pred_C1 MPA_C1
'
## ============================================================
## Compile Model
## ============================================================
nmo_mod <- mcode("NMOSD_QSP", nmo_code)
## ============================================================
## Helper: Build Dosing Events
## ============================================================
# Eculizumab: 900mg IV q2w (induction: 4 doses weekly then q2w)
# Approximate dose in nmol: 900 mg / 148 kDa * 1000 = ~6081 nmol
# In 4.3 L central volume -> C0 = 6081/4.3 ~ 1414 nmol/L per dose (simplified bolus)
make_eculi_dose <- function(n_weeks = 104, induction_weekly = 4) {
days_induct <- seq(0, (induction_weekly - 1) * 7, by = 7)
last_induct <- max(days_induct)
days_maint <- seq(last_induct + 14, n_weeks * 7, by = 14)
days_all <- c(days_induct, days_maint)
ev(cmt = "Eculi_C1", amt = 1414, time = days_all, rate = -2)
}
# Inebilizumab: 300mg IV day 1 & 15, then q6m
# ~300 mg / 150 kDa * 1000 / 3.0L ~ 667 nmol/L
make_ineb_dose <- function(n_months = 24) {
days <- c(0, 14, seq(180, n_months * 30, by = 180))
ev(cmt = "Ineb_C1", amt = 667, time = days, rate = -2)
}
# Satralizumab: 120mg SC q4w (x3) then q8w
# ~120 mg / 148 kDa * 1000 / 3.6L (absorbed) ~ SC depot dose in mg equiv
# Using depot compartment: amount = 120*1000/148 = 811 nmol total -> depot
make_satra_dose <- function(n_months = 24) {
days_induct <- c(0, 28, 56)
last <- max(days_induct)
days_maint <- seq(last + 56, n_months * 30, by = 56)
days <- c(days_induct, days_maint)
ev(cmt = "Satra_dep", amt = 811, time = days)
}
# Rituximab: 1000mg IV x2 (day 0, 14) then q6m
# ~1000 mg / 144 kDa * 1000 / 3.1L ~ 2242 nmol/L
make_ritu_dose <- function(n_months = 24) {
days <- c(0, 14, seq(180, n_months * 30, by = 180))
ev(cmt = "Ritu_C1", amt = 2242, time = days, rate = -2)
}
# Prednisolone: 60mg/day PO for 5 days (acute attack treatment)
# 60mg oral -> gut depot: 60mg (use ng/mL units, V=47L; dose = 60e6 ng)
make_pred_dose <- function(start_day = 0, days = 5, dose_mg = 60) {
ev(cmt = "Pred_gut", amt = dose_mg * 1e6, time = seq(start_day, start_day + days - 1, by = 1))
}
# MMF: 1g BID (2g/day); MPA in mg/L, V=3.3L -> gut dose=1000mg x2
make_mmf_dose <- function(n_months = 24) {
days <- seq(0, n_months * 30, by = 0.5) # BID
ev(cmt = "MPA_gut", amt = 1000, time = days)
}
## ============================================================
## Simulation: 5 Treatment Scenarios (2-year follow-up)
## ============================================================
sim_duration <- 730 # days
n_patients <- 50 # number of simulated patients
idata <- data.frame(ID = 1:n_patients)
run_scenario <- function(dose_ev, label, mod = nmo_mod) {
out <- mrgsim(mod,
events = dose_ev,
idata = idata,
end = sim_duration,
delta = 1,
carry_out = "evt",
recover = "EDSS,Ab,Lesion,Ast,Oligo,NfL,IL6,C5,MAC",
seed = 42)
as_tibble(out) %>% mutate(Scenario = label)
}
# ---- Scenario 1: No treatment (natural history) ----
ev_none <- ev(time = 0, amt = 0, cmt = 1) # dummy event
res1 <- run_scenario(ev_none, "No Treatment")
# ---- Scenario 2: Eculizumab monotherapy ----
res2 <- run_scenario(make_eculi_dose(n_weeks = 104), "Eculizumab 900mg IV q2w")
# ---- Scenario 3: Inebilizumab monotherapy ----
res3 <- run_scenario(make_ineb_dose(n_months = 24), "Inebilizumab 300mg IV q6m")
# ---- Scenario 4: Satralizumab monotherapy ----
res4 <- run_scenario(make_satra_dose(n_months = 24), "Satralizumab 120mg SC q8w")
# ---- Scenario 5: Rituximab + MMF combination ----
ev_ritu_mmf <- c(make_ritu_dose(n_months = 24), make_mmf_dose(n_months = 24))
res5 <- run_scenario(ev_ritu_mmf, "Rituximab + MMF")
# ---- Scenario 6: Prednisolone pulse (acute attack only) ----
res6 <- run_scenario(make_pred_dose(start_day = 90, days = 5), "Prednisolone Pulse (acute)")
# ---- Combine results ----
all_res <- bind_rows(res1, res2, res3, res4, res5, res6)
## ============================================================
## Summary Statistics
## ============================================================
summary_tbl <- all_res %>%
group_by(Scenario, time) %>%
summarise(
EDSS_med = median(EDSS, na.rm = TRUE),
EDSS_lo = quantile(EDSS, 0.05, na.rm = TRUE),
EDSS_hi = quantile(EDSS, 0.95, na.rm = TRUE),
Ab_med = median(Ab, na.rm = TRUE),
Ast_med = median(Ast, na.rm = TRUE),
MAC_med = median(MAC, na.rm = TRUE),
NfL_med = median(NfL, na.rm = TRUE),
IL6_med = median(IL6, na.rm = TRUE),
.groups = "drop"
)
## ============================================================
## Plots
## ============================================================
scenario_cols <- c(
"No Treatment" = "#D32F2F",
"Eculizumab 900mg IV q2w" = "#1565C0",
"Inebilizumab 300mg IV q6m" = "#2E7D32",
"Satralizumab 120mg SC q8w" = "#F57F17",
"Rituximab + MMF" = "#6A1B9A",
"Prednisolone Pulse (acute)" = "#00838F"
)
p1 <- ggplot(summary_tbl, aes(time, EDSS_med, color = Scenario)) +
geom_ribbon(aes(ymin = EDSS_lo, ymax = EDSS_hi, fill = Scenario), alpha = 0.1, color = NA) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
scale_fill_manual(values = scenario_cols) +
labs(title = "NMOSD: EDSS Over Time by Treatment",
x = "Days", y = "EDSS Score (median + 90% CI)") +
theme_bw() + theme(legend.position = "bottom")
p2 <- ggplot(summary_tbl, aes(time, Ab_med, color = Scenario)) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
labs(title = "AQP4-IgG Titer",
x = "Days", y = "AQP4-IgG (nmol/L)") +
theme_bw() + theme(legend.position = "none")
p3 <- ggplot(summary_tbl, aes(time, MAC_med, color = Scenario)) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
labs(title = "MAC Formation (C5b-9)",
x = "Days", y = "MAC (nmol/L-eq)") +
theme_bw() + theme(legend.position = "none")
p4 <- ggplot(summary_tbl, aes(time, Ast_med, color = Scenario)) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
labs(title = "Astrocyte Viability",
x = "Days", y = "Astrocyte (% of normal)") +
theme_bw() + theme(legend.position = "none")
p5 <- ggplot(summary_tbl, aes(time, NfL_med, color = Scenario)) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
labs(title = "Serum NfL (Axonal Damage)",
x = "Days", y = "NfL (pg/mL)") +
theme_bw() + theme(legend.position = "none")
p6 <- ggplot(summary_tbl, aes(time, IL6_med, color = Scenario)) +
geom_line(size = 1) +
scale_color_manual(values = scenario_cols) +
labs(title = "Serum IL-6",
x = "Days", y = "IL-6 (pg/mL)") +
theme_bw() + theme(legend.position = "none")
# Combine panels
combined_plot <- (p1 / (p2 + p3 + p4) / (p5 + p6)) +
plot_annotation(
title = "NMOSD QSP Model: Treatment Scenario Comparison",
subtitle = paste0("n=", n_patients, " simulated patients per arm | 2-year follow-up"),
theme = theme(plot.title = element_text(face = "bold", size = 14))
)
print(combined_plot)
## ============================================================
## Endpoint Summary Table (Year 2)
## ============================================================
endpoint_tbl <- all_res %>%
filter(time == 730) %>%
group_by(Scenario) %>%
summarise(
EDSS_final = round(median(EDSS, na.rm = TRUE), 2),
EDSS_change = round(median(EDSS - 2.0, na.rm = TRUE), 2),
AQP4IgG_final = round(median(Ab, na.rm = TRUE), 1),
Ast_viability = round(median(Ast, na.rm = TRUE), 1),
NfL_final = round(median(NfL, na.rm = TRUE), 1),
IL6_final = round(median(IL6, na.rm = TRUE), 1),
MAC_final = round(median(MAC, na.rm = TRUE), 2),
.groups = "drop"
) %>%
arrange(EDSS_final)
cat("\n=== NMOSD QSP Endpoint Summary (Day 730) ===\n")
print(endpoint_tbl)
## ============================================================
## Relapse Rate Simulation (Poisson approximation)
## ============================================================
arr_tbl <- all_res %>%
filter(time %in% c(365, 730)) %>%
mutate(Year = ifelse(time == 365, "Year 1", "Year 2")) %>%
group_by(Scenario, Year) %>%
summarise(
ARR_est = mean(Lesion * Ab / 50.0 * 1.8 / 365, na.rm = TRUE),
.groups = "drop"
)
cat("\n=== Estimated ARR ===\n")
print(arr_tbl)
## ============================================================
## PK Profile: Example Drug Concentrations
## ============================================================
pk_sim <- mrgsim(nmo_mod,
events = c(make_eculi_dose(n_weeks = 8),
make_satra_dose(n_months = 2)),
idata = data.frame(ID = 1),
end = 56, delta = 0.5) %>%
as_tibble()
pk_plot <- pk_sim %>%
select(time, Eculi_C1, Satra_C1, Ritu_C1, Pred_C1, MPA_C1) %>%
pivot_longer(-time, names_to = "Drug", values_to = "Conc") %>%
filter(Conc > 0.01) %>%
ggplot(aes(time, Conc, color = Drug)) +
geom_line(size = 1) +
facet_wrap(~Drug, scales = "free_y") +
labs(title = "NMOSD Drug PK Profiles (8-week window)",
x = "Days", y = "Concentration (nmol/L or ng/mL)") +
theme_bw()
print(pk_plot)
cat("\n=== Model run complete ===\n")
cat("Outputs: combined_plot, pk_plot, endpoint_tbl, arr_tbl\n")