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Alzheimer CDR-SOB (Delor 2013)

Source: vignettes/articles/Delor_2013_alzheimer.Rmd
Delor_2013_alzheimer.Rmd

Model and source

  • Citation: Delor I, Charoin J-E, Gieschke R, Retout S, Jacqmin P; for the Alzheimer’s Disease Neuroimaging Initiative. (2013). Modeling Alzheimer’s Disease Progression Using Disease Onset Time and Disease Trajectory Concepts Applied to CDR-SOB Scores From ADNI. CPT Pharmacometrics Syst Pharmacol 2(10):e78.
  • Article: https://doi.org/10.1038/psp.2013.54

This is a disease-progression model for the Clinical Dementia Rating scale - Sum of Boxes (CDR-SOB, 0-18 score) score over time, fit to 2,700 longitudinal CDR-SOB observations from 380 mild cognitive impairment (MCI) plus 180 Alzheimer’s disease (AD) subjects in the ADNI database with up to 4 years of follow-up. There is no drug input – the model captures the natural history of CDR-SOB change in untreated (or placebo-arm) patients, with a study-entry transient (“placebo”) term to capture an early drop / delay frequently seen at enrollment.

Key features:

  1. Individual disease-onset time (DOT). Each subject has a DOT estimated from their baseline cognitive scores (CDR-SOB and ADAS-cog). DOT positions the subject on a common disease-time axis, allowing back- and forward-extrapolation across MCI and AD patients.
  2. Logit-domain disease trajectory. The hidden disease state A(1) evolves in the logit domain to handle the floor and ceiling of the 0-18 CDR-SOB score; the observed CDR-SOB is the back-transformation 18 / (1 + exp(BLC - A(1))).
  3. Smooth-step disease activation. Disease progression is triggered when global model time crosses DOT via the smooth-step T^30 / (DOT^30 + T^30) (~0 before DOT, ~1 after DOT).
  4. Two-component mixture. A NONMEM $MIX divides patients into a slow-progression branch (rate alone, alpha = 0) and a fast-progression branch (rate plus accelerating term alpha * A(1)). The per-subject mixture probability depends on baseline CDR-SOB, FAQ, and normalised hippocampal volume (RHPNM).
  5. Study-entry placebo term. PL * (1 - exp(-KPL * (t - T_ENTRY))) is subtracted from the predicted CDR-SOB to capture the empirically observed early drop / delay after enrollment.

Population

  • 560 subjects (380 MCI + 180 AD) with 2,700 CDR-SOB observations over up to 4 years of follow-up, drawn from the ADNI database downloaded 1 August 2011. Control subjects (normal cognition) had CDR-SOB scores at or near zero and were excluded from the modelled dataset. Subjects with a single CDR-SOB record were also removed.
  • Age at enrollment: 55-91 years (full ADNI cohort range, prior to MCI / AD selection).
  • Regions: United States and Canada (over 50 ADNI sites).
  • MCI / AD conversion: 166 MCI converted to AD during the observation period in the wider ADNI download; the mixture model identifies a “fast-progressing” subpopulation (~56% of MCI patients and ~97% of AD patients) and a “slow-progressing” subpopulation (~44% of MCI and ~3% of AD).
  • Detailed demographic distributions (sex split, ethnicity / race breakdown, median age) are not tabulated in the source paper and are recorded as NA in population.

The same metadata is available programmatically via readModelDb("Delor_2013_alzheimer").

Source trace

Per-parameter origins are recorded as in-file comments next to each ini() entry in inst/modeldb/therapeuticArea/Delor_2013_alzheimer.R. The table below collects them in one place.

nlmixr2 parameter Value Source location
lrate_fast log(0.373) (0.373 / year) Table 2 final ‘Fast disease progression rate, 1/year’ = 0.373
lrate_slow log(0.260) (0.260 / year) Table 2 final ‘Slow disease progression rate, 1/year’ = 0.26
ldot log(16.1) (16.1 years) Table 2 final ‘DOT, year’ = 16.1
e_cdr_sob_dot -0.072 Table 2 final ‘COV CDR-SOB on DOT’
e_adas_cog_dot -0.0439 Table 2 final ‘COV ADAS on DOT’
lalpha log(0.0499) Table 2 final ‘Multiplicative term (alpha)’ = 0.0499
e_mmse_alpha -2.01 Table 2 final ‘COV MMSE on alpha’
blc 4.48 Table 2 final ‘Baseline correction (BLC)’ = 4.48
lpl log(0.434) Table 2 final ‘Placebo magnitude (PL)’ = 0.434
lkpl fixed(log(1)) Table 2 final ‘Placebo rate (KPL), 1/year’ = 1 (FIXED)
logit_p_slow log(0.44/0.56) imputed from Table 2 ‘MCI/AD slow’ = 44/3 (see Errata)
e_cdr_sob_slow -1.27 Table 2 final ‘COV CDR-SOB on $MIX’
e_faq_slow -0.341 Table 2 final ‘COV FAQ on $MIX’
e_rhpnm_slow 7.5 Table 2 final ‘COV RHPNM on $MIX’
etaldot omega^2 = 0.000225 Table 2 final IIV(DOT) = 1.5%
etalalpha omega^2 = 0.3434 Table 2 final IIV(alpha) = 64%
etalpl omega^2 = 0.5535 Table 2 final IIV(PL) = 86%
addSd 0.377 Table 2 final ‘RES Error (SD)’ = 0.377 (applied to cdr_mix)
DOT power form n/a Table 1 Part I: DOT = theta1 * (CDR_bsl/2)^theta6 * (ADAS_bsl/12.67)^theta10
alpha power form n/a Table 1 Part III: alpha = theta3 * (MMSE_bsl/26)^theta14
Mixture-logit form n/a Table 1 Part II: P1 = exp(P1phi + COV)/(1 + exp(P1phi + COV))
Disease-progression ODE n/a Equation 1: dA(1)/dT = (RATE + A(1)*alpha) * T^30/(DOT^30+T^30)
Placebo term n/a Equation 2: CDR_SOB - PL*(1 - exp(-KPL*T))

Mechanistic structure

The hidden disease-state ODE on the logit-domain trajectory variable A(1) is

dA(1)dt=(RATE+A(1)⋅α)⋅t30DOT30+t30 \frac{dA(1)}{dt} \;=\; \bigl(\text{RATE} + A(1) \cdot \alpha \bigr) \cdot \frac{t^{30}}{\text{DOT}^{30} + t^{30}}

with the activation function approximating a smooth step at t = DOT (about 0 below, 0.5 at DOT, and about 1 above DOT). In the slow-progression branch, alpha is held to 0; in the fast-progression branch, the additive A(1) * alpha term accelerates progression once A(1) has grown.

The observed CDR-SOB is

CDR_SOBpred(t)=181+exp⁡(BLC−A(1)(t))−PL⋅(1−e−KPL(t−TENTRY))𝟙{t>TENTRY} \text{CDR\_SOB}_\text{pred}(t) \;=\; \frac{18}{1 + \exp(\text{BLC} - A(1)(t))} \;-\; \text{PL} \cdot \bigl(1 - e^{-\text{KPL}\,(t - T_\text{ENTRY})}\bigr)\,\mathbb{1}\{t > T_\text{ENTRY}\}

with BLC = 4.48 chosen so the floor of the score (A(1) = 0) maps to CDR_SOB ~= 0.2 and KPL = 1 / year (fixed) so the placebo term reaches its asymptote in about 4 years post-entry.

Per-subject covariate effects:

DOTi=exp⁡(lDOT+ηDOT)⋅(CDR_SOBi2)−0.072⋅(ADAS_COGi12.67)−0.0439 \text{DOT}_i = \exp(l_\text{DOT} + \eta_\text{DOT}) \cdot \left(\tfrac{\text{CDR\_SOB}_i}{2}\right)^{-0.072} \cdot \left(\tfrac{\text{ADAS\_COG}_i}{12.67}\right)^{-0.0439}

αi=exp⁡(lα+ηα)⋅(MMSEi26)−2.01 \alpha_i = \exp(l_\alpha + \eta_\alpha) \cdot \left(\tfrac{\text{MMSE}_i}{26}\right)^{-2.01}

logit(Pslowi)=logit(θ5)−1.27(CDR_SOBi−1)−0.341(FAQi−1)+7.5(RHPNMi−1) \text{logit}(P_\text{slow}^i) = \text{logit}(\theta_5) - 1.27\,(\text{CDR\_SOB}_i - 1) - 0.341\,(\text{FAQ}_i - 1) + 7.5\,(\text{RHPNM}_i - 1)

where theta_5 = 0.44 is imputed (see Errata).

Virtual cohort

We construct a small virtual cohort with five representative subjects spanning the MCI -> AD severity range, each with their own baseline cognitive / functional / imaging covariates and an integration window that starts at time = 0 (well before any subject’s DOT) and runs through the equivalent of 4 years of post-study-entry observations.

mod  <- readModelDb("Delor_2013_alzheimer")
mod0 <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

# Five reference scenarios: a more-advanced AD patient, a typical MCI patient,
# and three intermediate cases. The covariates are chosen to span the
# published baseline distributions; T_ENTRY is set to a few years past each
# subject's DOT so the patient is observed during active disease progression.
scenarios <- tibble::tribble(
  ~scenario,                             ~CDR_SOB, ~ADAS_COG, ~MMSE, ~FAQ, ~RHPNM,
  "Advanced AD (high CDR, severe ADAS)",    5.0,    25.0,    20.0,  15.0,  0.70,
  "Moderate AD (median AD baseline)",       4.0,    20.0,    23.0,  12.0,  0.80,
  "Intermediate MCI->AD",                   2.5,    15.0,    25.0,   6.0,  0.90,
  "Typical MCI (median MCI baseline)",      1.0,    12.0,    27.0,   2.0,  1.00,
  "Early MCI (low CDR, near-normal ADAS)",  0.5,     8.0,    29.0,   0.0,  1.05
)

# Compute the typical DOT for each scenario from the source paper covariate
# form, then set T_ENTRY to DOT + 4 years (well past the activation function)
# so the patient is observed during disease progression. Cap CDR_SOB at 0.5
# in the DOT formula to avoid divide-by-zero on the (CDR_SOB/2)^-0.072 form.
scenarios <- scenarios |>
  dplyr::mutate(
    dot_typ = 16.1 *
              (pmax(CDR_SOB, 0.5) / 2)^(-0.072) *
              (ADAS_COG / 12.67)^(-0.0439),
    T_ENTRY = dot_typ + 4.0
  )

knitr::kable(scenarios, digits = 3,
             caption = "Virtual-cohort covariates with the implied typical DOT and the study-entry time T_ENTRY used for plotting.")
Virtual-cohort covariates with the implied typical DOT and the study-entry time T_ENTRY used for plotting.
scenario CDR_SOB ADAS_COG MMSE FAQ RHPNM dot_typ T_ENTRY
Advanced AD (high CDR, severe ADAS) 5.0 25 20 15 0.70 14.629 18.629
Moderate AD (median AD baseline) 4.0 20 23 12 0.80 15.012 19.012
Intermediate MCI->AD 2.5 15 25 6 0.90 15.726 19.726
Typical MCI (median MCI baseline) 1.0 12 27 2 1.00 16.964 20.964
Early MCI (low CDR, near-normal ADAS) 0.5 8 29 0 1.05 18.153 22.153

Typical-value disease-progression trajectories

We solve the ODE on a fine time grid from time = 0 to time = T_ENTRY + 4 years and overlay both the fast-branch and slow-branch predicted CDR-SOB trajectories for each scenario. The mixture probability p_slow_indiv is included as a derived quantity; the user can compute a mixture-weighted prediction externally as p_slow_indiv * cdr_slow + p_fast_indiv * cdr_fast.

simulate_one <- function(s) {
  times <- seq(0, s$T_ENTRY + 4, by = 0.25)
  ev <- data.frame(
    id       = 1L,
    time     = times,
    evid     = 0L,
    amt      = 0,
    CDR_SOB  = s$CDR_SOB,
    ADAS_COG = s$ADAS_COG,
    MMSE     = s$MMSE,
    FAQ      = s$FAQ,
    RHPNM    = s$RHPNM,
    T_ENTRY  = s$T_ENTRY
  )
  sim <- rxode2::rxSolve(mod0, events = ev, returnType = "data.frame")
  sim$scenario   <- s$scenario
  sim$years      <- sim$time
  sim$years_post <- sim$time - s$T_ENTRY
  sim
}

sims <- lapply(seq_len(nrow(scenarios)), function(i) simulate_one(scenarios[i, ]))
#> ℹ omega/sigma items treated as zero: 'etaldot', 'etalalpha', 'etalpl'
#> ℹ omega/sigma items treated as zero: 'etaldot', 'etalalpha', 'etalpl'
#> ℹ omega/sigma items treated as zero: 'etaldot', 'etalalpha', 'etalpl'
#> ℹ omega/sigma items treated as zero: 'etaldot', 'etalalpha', 'etalpl'
#> ℹ omega/sigma items treated as zero: 'etaldot', 'etalalpha', 'etalpl'
sim_all <- dplyr::bind_rows(sims)

# Pivot to long form for plotting both branches.
sim_long <- sim_all |>
  dplyr::select(scenario, years_post, cdr_fast, cdr_slow, p_slow_indiv) |>
  tidyr::pivot_longer(c(cdr_fast, cdr_slow), names_to = "branch", values_to = "cdr_pred") |>
  dplyr::mutate(branch = ifelse(branch == "cdr_fast", "Fast branch", "Slow branch"))

ggplot(sim_long, aes(years_post, cdr_pred, colour = scenario, linetype = branch)) +
  geom_line(linewidth = 0.7) +
  scale_y_continuous(limits = c(0, 18), breaks = seq(0, 18, by = 3)) +
  labs(x = "Years since study entry",
       y = "Predicted CDR-SOB (0-18 score)",
       colour = "Scenario",
       linetype = "Mixture branch",
       title = "Typical-value CDR-SOB trajectories by mixture branch and baseline cohort",
       caption = "Solid: fast-progression branch. Dashed: slow-progression branch. Years since study entry on the x-axis (DOT shifted out per subject).") +
  theme_minimal()

The directions match the source paper:

  • Advanced AD subjects (high baseline CDR-SOB, severe baseline ADAS-cog) start at a more advanced CDR-SOB and progress rapidly under the fast branch. The implied DOT is earlier (smaller power-form multiplier), so by the time of study entry they are already well into the disease.
  • Early MCI subjects (low baseline CDR-SOB, near-normal ADAS-cog) have a later DOT, so at study entry the activation function is still gathering momentum; their slow-branch trajectory remains near the floor of the score for several years.
  • The fast vs slow gap widens with time as the alpha * A(1) acceleration term grows in the fast branch.

Replication of Figure 4 (visual predictive check style)

The published Figure 4 shows visual predictive checks (VPCs) for the base and final models grouped by diagnosed status. A full VPC requires the original ADNI dataset (not redistributable). The figure below produces a typical-value analogue: predicted CDR-SOB trajectories under the final model for representative MCI and AD patients, alongside a stochastic envelope from subject-level IIV.

# Two cohorts: a "typical AD" cohort and a "typical MCI" cohort.
make_cohort <- function(n, label, cdr, adas, mmse, faq, rhpnm, dot_offset = 4, id_offset = 0L) {
  tibble::tibble(
    id = id_offset + seq_len(n),
    scenario = label,
    CDR_SOB = cdr, ADAS_COG = adas, MMSE = mmse, FAQ = faq, RHPNM = rhpnm
  ) |>
    dplyr::mutate(
      dot_typ = 16.1 *
                (pmax(CDR_SOB, 0.5) / 2)^(-0.072) *
                (ADAS_COG / 12.67)^(-0.0439),
      T_ENTRY = dot_typ + dot_offset
    )
}

cohort_ad  <- make_cohort(50, "Typical AD",  4.0, 20.0, 23.0, 12.0, 0.80, id_offset = 0L)
cohort_mci <- make_cohort(50, "Typical MCI", 1.0, 12.0, 27.0,  2.0, 1.00, id_offset = 100L)
cohort     <- dplyr::bind_rows(cohort_ad, cohort_mci)

set.seed(13)
sim_vpc <- lapply(seq_len(nrow(cohort)), function(i) {
  s <- cohort[i, ]
  times <- seq(0, s$T_ENTRY + 4, by = 0.5)
  ev <- data.frame(
    id       = s$id,
    time     = times,
    evid     = 0L,
    amt      = 0,
    CDR_SOB  = s$CDR_SOB,
    ADAS_COG = s$ADAS_COG,
    MMSE     = s$MMSE,
    FAQ      = s$FAQ,
    RHPNM    = s$RHPNM,
    T_ENTRY  = s$T_ENTRY
  )
  out <- rxode2::rxSolve(mod, events = ev, returnType = "data.frame")
  out$scenario   <- s$scenario
  out$years_post <- out$time - s$T_ENTRY
  out
}) |> dplyr::bind_rows()

# Form per-subject expected (mixture-weighted) CDR-SOB and summarise by
# scenario across the 5-95% envelope at each post-entry time slice.
sim_vpc <- sim_vpc |>
  dplyr::mutate(
    cdr_mix = p_slow_indiv * cdr_slow + (1 - p_slow_indiv) * cdr_fast
  )

vpc_summary <- sim_vpc |>
  dplyr::filter(years_post >= 0, years_post <= 4) |>
  dplyr::mutate(years_post_round = round(years_post * 4) / 4) |>
  dplyr::group_by(scenario, years_post_round) |>
  dplyr::summarise(
    Q05 = quantile(cdr_mix, 0.05, na.rm = TRUE),
    Q50 = quantile(cdr_mix, 0.50, na.rm = TRUE),
    Q95 = quantile(cdr_mix, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_summary, aes(years_post_round, Q50, colour = scenario, fill = scenario)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, colour = NA) +
  geom_line(linewidth = 0.8) +
  scale_y_continuous(limits = c(0, 18), breaks = seq(0, 18, by = 3)) +
  labs(x = "Years since study entry",
       y = "Mixture-weighted predicted CDR-SOB (0-18 score)",
       colour = "Cohort", fill = "Cohort",
       title = "Mixture-weighted CDR-SOB envelope by diagnostic cohort (Figure 4 analogue)",
       caption = "5-95% envelope across 50 subjects per cohort under subject-level IIV (eta on DOT, alpha, PL).") +
  theme_minimal()

Sanity check: mixture-probability surface across baseline scores

The mixture-probability model P_slow = inv_logit(logit_p_slow - 1.27*(CDR-1) - 0.341*(FAQ-1) + 7.5*(RHPNM-1)) predicts that:

  • Higher baseline CDR-SOB -> lower slow-progression probability (more severe -> faster progression).
  • Higher baseline FAQ -> lower slow-progression probability.
  • Higher RHPNM (less atrophic hippocampus) -> higher slow-progression probability.
grid <- tidyr::expand_grid(
  CDR_SOB = seq(0, 6, by = 0.5),
  RHPNM   = c(0.7, 0.85, 1.0)
) |>
  dplyr::mutate(FAQ = 1) |>  # hold FAQ at the centring value
  dplyr::mutate(
    logit_p = log(0.44/(1-0.44)) +
              (-1.27) * (CDR_SOB - 1) +
              (-0.341) * (FAQ - 1) +
              ( 7.5  ) * (RHPNM - 1),
    p_slow = 1/(1 + exp(-logit_p))
  )

ggplot(grid, aes(CDR_SOB, p_slow, colour = factor(RHPNM))) +
  geom_line(linewidth = 0.7) +
  scale_y_continuous(limits = c(0, 1)) +
  labs(x = "Baseline CDR-SOB",
       y = "Probability of being in the slow-progression subpopulation",
       colour = "RHPNM",
       title = "Mixture probability of slow progression vs baseline CDR-SOB",
       caption = "FAQ held at median value 1. RHPNM = 1 = healthy reference hippocampal volume; 0.7 = ~30% atrophy.") +
  theme_minimal()

The figure replicates the qualitative finding in the source paper: subjects with low baseline CDR-SOB and a healthy-reference hippocampal volume are most likely to be slow progressors; subjects with high baseline CDR-SOB and significant atrophy are almost certain to be fast progressors. The cited paper reports about 44% of MCI and about 3% of AD subjects in the slow branch, which matches the right-hand vs left-hand tails of the curves above.

Assumptions and deviations (Errata)

The Delor 2013 supplement (NONMEM technical details) was not on disk at extraction time. The following choices were made:

  1. Typical mixture probability (theta_5). Table 2 of the source paper tabulates the three covariate coefficients on the mixture-logit (COV CDR-SOB on $MIX, COV FAQ on $MIX, COV RHPNM on $MIX) but not the typical / intercept value theta_5. The model file imputes theta_5 = 0.44 based on the source paper’s reported “MCI/AD slow (alpha = 0): 44/3” classification row in Table 2 – this corresponds to the MCI-cohort slow fraction (the typical patient at median CDR_SOB = 1, FAQ = 1, RHPNM = 1 is approximately an MCI patient). Alternative defaults the operator might prefer:

    • Overall slow fraction across MCI + AD cohorts: about 0.31 (computed as (0.44 * 380 + 0.03 * 180) / 560).
    • AD-cohort slow fraction: 0.03 (matches the AD cohort but mismatches the typical MCI patient at median covariate values). A downstream user re-fitting the model to ADNI data should free logit_p_slow and re-estimate from data; this typical-value imputation is purely for plotting / typical-value simulation.

  2. Residual-error domain. The source paper performs the fit with additive residual error on A(1) (the logit-domain disease state, paper Structural-base-model-development section: “modeling was performed in the logit domain and additive residual error was used”); the reported SD is 0.377 on the logit-domain scale. The nlmixr2lib model applies the additive error on the back-transformed CDR-SOB scale instead, because the natural output of the rxode2 / nlmixr2 model is the bounded 0-18 CDR-SOB rather than the unbounded logit. The typical-value trajectory is unaffected (the back-transformation is exact); the per-observation stochastic noise differs in scale-dependent fashion. A downstream user wanting to fit the source-paper residual structure exactly should add a logit-domain residual on the hidden a_fast / a_slow states; the current encoding is appropriate for typical-value simulation and for stochastic simulations where bounded-scale noise is acceptable.

  3. Mixture-weighted single observation endpoint. The source NONMEM $MIX mechanism makes the marginal likelihood for each subject a weighted sum across the two branches; nlmixr2lib does not yet expose $MIX natively. To keep the model usable with rxSolve() (which requires a single observation endpoint or a per-row CMT / DVID specifier on every observation row), the model declares a single observation endpoint cdr_mix that is the deterministic mixture-weighted expectation p_slow_indiv * cdr_slow + p_fast_indiv * cdr_fast. The per-branch trajectories cdr_fast and cdr_slow plus the per-subject mixture probability p_slow_indiv are all exposed as derived model variables and appear in the rxSolve data frame, so a downstream user can re-compose a true $MIX-style sampled-branch likelihood externally if needed. A single addSd = 0.377 applies to the mixture-weighted endpoint; this is a small approximation – the source paper would have a per-branch residual SD identically equal to 0.377 attached to the actually-realised branch, not to the mixture mean – but the typical-value trajectory and the per-branch curves are exactly the source-paper values.

  4. IIV conversion from %CV to omega^2. The source paper reports IIV as a percent CV (paper Table 2 column ‘IIV (%)’ with footnote b ‘Interindividual variability’). The model file uses omega^2 = log(1 + (CV/100)^2) (the log-normal-distribution back-conversion). For small IIV (DOT 1.5%) the difference between this and the simpler omega^2 = (CV/100)^2 is negligible; for larger IIVs (alpha 64%, PL 86%) the two conventions differ by ~10-20%. If the supplement clarifies the source paper’s exact convention, the values can be updated to match.

  5. No drug input / no dosing events. Disease-progression models are first-class members of nlmixr2lib but the package’s conventions favour PK / PK-PD models with a depot / central structure. This model has no depot compartment; the dataset’s TIME column carries global model time (years since some reference origin) and there are no evid = 1 rows. The pkgdown gate (devtools::check()) treats this as expected for a disease-progression model.

  6. Mixture model collapsed to a deterministic mixture-weighted prediction. The source NONMEM $MIX mechanism assigns each subject to either the slow or fast branch with a per-subject probability; the joint marginal likelihood is a true mixture sum across branches. In the nlmixr2lib port the model exposes a single observation endpoint cdr_mix = p_slow_indiv * cdr_slow + (1 - p_slow_indiv) * cdr_fast (the deterministic mixture-weighted expectation) and emits both per-branch trajectories (cdr_fast, cdr_slow) and the per-subject mixture probability (p_slow_indiv) as derived model variables in the rxSolve data frame. This single-endpoint encoding is what allows the model to plug into rxSolve() without per-row CMT / DVID assignments. The precedent for exposing both branches plus the mixture probability is Schoemaker_2018_levetiracetam in this package, but Schoemaker uses two Poisson endpoints because each branch has its own native likelihood; here a single Gaussian-additive endpoint on the mixture-weighted prediction is the natural analogue.

  7. Time variable handling and the per-subject covariate T_ENTRY. The source paper’s disease-progression equation (Equation 1) uses a single global disease-time variable T anchored to a hypothetical disease-onset reference; the placebo-term equation (Equation 2) uses time since study entry. To match the source mathematics exactly, the nlmixr2lib port carries both: the dataset’s time column is the global integration time (with time = 0 the integration origin and the activation function turning on around each subject’s individual DOT), and the per-subject covariate T_ENTRY records the global time at which the subject’s first observation falls. The placebo term then uses time - T_ENTRY as its clock. A reasonable virtual-cohort construction (used throughout this vignette) is T_ENTRY = DOT_individual + 4 years so the patient is observed during established disease progression.

  8. Compartment names. The hidden disease-state variables are named a_fast and a_slow (lowercase, matching the source paper’s A(1) notation with mixture-branch suffix), which are non-canonical in the nlmixr2lib compartment register (the canonical names are PK-flavoured: depot, central, effect, etc.). checkModelConventions() warns on these but does not error; the names are descriptive of the source paper’s notation and consistent with the precedent set by oncology TGI models in the same therapeuticArea / category (e.g., tumorSize, cyclingCells).

  9. Bridge to the related Conrado 2014 ADAS-Cog model. The Conrado_2014_alzheimer.R model in this package is a complementary AD progression model fit to ADAS-Cog scores (not CDR-SOB) on the CAMD database (not ADNI). Both models use the disease-progression-without-drug pattern but with different observation scales, residual-error families (Beta vs additive), and time-scale-adjustment mechanisms (Richards growth vs DOT activation). The two models can be used in tandem to interrogate the relationship between ADAS-Cog and CDR-SOB endpoints in a disease-modification simulation, but they are NOT fit jointly in either source paper.

  10. Source paper figures not reproduced verbatim. Figures 1-5 in Delor 2013 use the original ADNI dataset that is not redistributable through nlmixr2lib. The vignette therefore provides typical-value reproductions of the qualitative features (Figure-4 analogue: mixture-weighted CDR-SOB envelope by diagnostic cohort; mixture-probability surface) but not figure-by-figure visual-predictive-check overlays. A pkgdown user with their own ADNI extract can re-run the vignette with appropriate make_cohort() substitutions to generate the full VPC.