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Pediatric HIV/HCV CD4 z-score recovery on ART (Majekodunmi 2017)

Source: vignettes/articles/Majekodunmi_2017_HIV_HCV_CD4_recovery.Rmd
Majekodunmi_2017_HIV_HCV_CD4_recovery.Rmd

Model and source

  • Citation: Majekodunmi AO, Thorne C, Malyuta R, Volokha A, Callard RE, Klein NJ, Lewis J; on behalf of The European Paediatric HIV/HCV Co-infection Study group in the European Pregnancy and Paediatric HIV Cohort Collaboration and the Ukraine Paediatric HIV Cohort Study in EuroCoord. Modelling CD4 T Cell Recovery in Hepatitis C and HIV Co-infected Children Receiving Antiretroviral Therapy. Pediatr Infect Dis J. 2017 May;36(5):e123-e129. doi:10.1097/INF.0000000000001478.
  • Article: https://doi.org/10.1097/INF.0000000000001478
  • Description: Longitudinal disease-progression / immune-reconstitution model for age-standardised CD4 T-cell counts (z-scores) in HIV-infected children receiving antiretroviral therapy (ART), with HIV/HCV coinfection slowing the recovery rate (Majekodunmi 2017, fit to 401 children – 355 HIV monoinfected and 46 HIV/HCV coinfected – from the Ukraine Paediatric HIV Cohort Study and the EPPICC HIV/HCV coinfection study across 8 European countries). The age-standardised CD4 z score is modelled as an asymptotic recovery curve z(t) = asy + (int - asy) * exp(-krec * t), where t is duration on ART, int is the pre-ART z score, asy is the long-term z score, and krec (the paper’s symbol c) is the per-subject recovery rate (1/year; ln(2)/krec is the time to half the total recovery from int to asy; renamed from the paper’s c to avoid shadowing R’s built-in c() combine function). Age at start of ART (centred at 4.3 years – the all-cohort median per Table 2 footnote) shifts both asy and int (younger children start higher and reach higher long-term levels). EPPICC enrollment country shifts int with Ukraine as the implicit reference. HCV coinfection is a multiplicative fractional reduction on krec: krec_coinf = krec_mono * (1 + e_hcv_pos_krec * HCV_POS) with e_hcv_pos_krec = -0.77, so coinfected children recover at krec = 1.55 * 0.23 = 0.357 /year (half-time ~2 years) versus 1.55 /year for monoinfected (half-time ~0.45 year). Disease-progression model with no drug dosing – the population were on combination ART (most commonly lamivudine + zidovudine + lopinavir/ritonavir) and the model’s t = 0 is the time of ART initiation.

Population

Majekodunmi 2017 pooled two pediatric HIV cohorts: the Ukraine Paediatric HIV Cohort Study (HIV monoinfected children, n = 355, all from Ukraine) and the EPPICC HIV/HCV coinfection sub-study (n = 46 across 8 European countries – Russia 17, Ukraine 18, Switzerland 3, Spain 2, UK 2, Italy 2, Germany 1, Poland 1). The pooled analytic cohort is 401 children with longitudinal CD4 measurements after ART initiation. Median age at ART start was 4.40 years (IQR 1.73-7.07) for monoinfected and 3.12 years (IQR 1.31-5.65) for coinfected; the all-cohort reference age used in the model is 4.3 years (Table 2 footnote). Median follow-up on ART was 4.2 years overall (IQR 2.7-5.3), with a median of 5 CD4 measurements per child (IQR 3-7). Sex was approximately balanced (monoinfected 48.2% male / 51.8% female; coinfected 43.5% male / 54.3% female / 2.2% unknown). The most common ART regimen across both cohorts was lamivudine + zidovudine + kaletra (lopinavir/ritonavir); 33% of monoinfected and 49% of coinfected children received a 3-drug ART regimen.

The same demographic detail is available programmatically via readModelDb("Majekodunmi_2017_HIV_HCV_CD4_recovery")$population.

Source trace

The recovery model (Majekodunmi 2017 Equation 1, schematic in Figure 1) is

zij=asyi+(inti−asyi)exp⁡(−citij)+εij z_{ij} \;=\; \mathrm{asy}_{i} + (\mathrm{int}_{i} - \mathrm{asy}_{i})\, \exp(-c_{i}\,t_{ij}) + \varepsilon_{ij}

with tijt_{ij} the duration on ART for child ii, inti\mathrm{int}_{i} the pre-ART z score, asyi\mathrm{asy}_{i} the long-term z score, cic_{i} the per-subject recovery-rate constant, and εij\varepsilon_{ij} an additive residual error. The half-recovery time from inti\mathrm{int}_{i} to asyi\mathrm{asy}_{i} is ln⁡(2)/ci\ln(2)/c_{i}. In the packaged model the symbol cc is renamed krec to avoid shadowing R’s built-in c() combine function; the symbol int\mathrm{int} is renamed intercept to avoid the C reserved word int (rxode2 transpiles to C).

The per-parameter origin is recorded as an in-file comment next to each ini() entry. The table below collects them in one place.

Equation / parameter Value (SE) Source location
asy (typical long-term z score, Ukraine ref, AGE = 4.3 y) -1.07 (0.08) Table 2 row Asy
e_age_asy -0.11 (0.03) Table 2 row Asy:age
intercept (typical pre-ART z score, Ukraine ref, AGE = 4.3 y) -2.42 (0.28) Table 2 row Int
e_age_intercept -0.29 (0.09) Table 2 row Int:age
e_region_poland_intercept +0.44 (0.29) Table 2 row Int:Poland
e_region_russia_intercept +0.69 (0.57) Table 2 row Int:Russia
e_region_switzerland_intercept +0.02 (0.77) Table 2 row Int:Switzerland
e_region_uk_intercept -17.5 (0.93) Table 2 row Int: United Kingdom
e_region_spain_intercept +2.89 (0.71) Table 2 row Int:Spain
e_region_germany_intercept +0.34 (0.29) Table 2 row Int:Germany
e_region_italy_intercept -3.63 (1.50) Table 2 row Int:Italy
krec (typical recovery rate, 1/y; paper’s c) 1.55 (0.63) Table 2 row c
e_hcv_pos_krec -0.77 (0.09) Table 2 row C:Coinf
addSd (residual SD on z-score) 1.43 (0.16) Table 2 row ‘Residual error’
Variance of REs: asy 1.83 Table 2 column ‘Variance of REs’, Asy row
Variance of REs: intercept 4.78 Table 2 column ‘Variance of REs’, Int row
Variance of REs: krec 0.39 Table 2 column ‘Variance of REs’, c row
Reference age (centring) 4.3 y Table 2 footnote
Reference cohort Ukraine Table 2 footnote
Asymptotic-recovery functional form n/a Methods ‘Mixed-effects Modeling’ and Equation 1

Variances of random effects are encoded as additive normal on the natural (z-score) scale for asy and intercept, and additive normal on the linear (1/year) scale for krec, matching the source paper’s “Variance of REs” column (which reports raw variances, not %CV).

Errata

No published erratum or corrigendum was located for this paper as of the model extraction date (2026-05-22). The paper itself notes two limitations the consumer should keep in mind. First, the HIV monoinfected cohort was drawn entirely from Ukraine while the HCV coinfected cohort spans 8 European countries; the model carries 7 EPPICC enrollment-country indicator covariates on the pre-ART intercept to absorb the resulting laboratory / clinical-practice differences, with Ukraine as the implicit reference. Second, two of the country-effect estimates rest on very small subgroups (UK n = 2, Italy n = 2) and the UK estimate of -17.5 z-score units is implausibly large for a CD4 z score effect, almost certainly a small-sample artifact – see Assumptions and deviations.

Verify the model and parameters are loaded correctly

The model loads via readModelDb(). Quick sanity check on the parameter values is done by reading the fixed-effect typical-value parameters back from the model.

mod     <- readModelDb("Majekodunmi_2017_HIV_HCV_CD4_recovery")
mod_typ <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

typical_theta <- mod_typ$theta
knitr::kable(data.frame(parameter = names(typical_theta),
                        value     = unname(typical_theta)),
             digits = 4,
             caption = "Typical-value (fixed-effect) parameters as packaged.")
Typical-value (fixed-effect) parameters as packaged.
parameter value
asy -1.07
e_age_asy -0.11
intercept -2.42
e_age_intercept -0.29
e_region_poland_intercept 0.44
e_region_russia_intercept 0.69
e_region_switzerland_intercept 0.02
e_region_uk_intercept -17.50
e_region_spain_intercept 2.89
e_region_germany_intercept 0.34
e_region_italy_intercept -3.63
krec 1.55
e_hcv_pos_krec -0.77
addSd 0.00

Reproducing Figure 3A: monoinfected children at ages 2, 4, and 8 years

Majekodunmi 2017 Figure 3A shows the typical-value (fixed-effect) CD4 z-score recovery trajectory for monoinfected children starting ART at ages 2, 4, and 8 years (all from the Ukraine reference cohort, HCV_POS = 0). Younger children start ART at higher pre-ART z scores and reach higher long-term z scores than older children – Asy:age and Int:age are both negative (-0.11 and -0.29 per year of age above 4.3 y respectively).

ukraine_ref_cov <- function(age, hcv_pos = 0L) {
  data.frame(
    AGE                = age,
    HCV_POS            = hcv_pos,
    REGION_POLAND      = 0L,
    REGION_RUSSIA      = 0L,
    REGION_SWITZERLAND = 0L,
    REGION_UK          = 0L,
    REGION_SPAIN       = 0L,
    REGION_GERMANY     = 0L,
    REGION_ITALY       = 0L
  )
}

# Per-figure observation grid: 0 to 11 years on ART (matches Figure 3A x-axis)
t_grid <- seq(0, 11, by = 0.05)

build_events <- function(id, age, hcv_pos) {
  cov <- ukraine_ref_cov(age = age, hcv_pos = hcv_pos)
  cbind(
    data.frame(id = id, time = t_grid, amt = 0, evid = 0L),
    cov[rep(1L, length(t_grid)), , drop = FALSE]
  )
}

ev_3a <- bind_rows(
  build_events(id = 1L, age = 2, hcv_pos = 0L) |> mutate(age_label = "2 y old (mono)"),
  build_events(id = 2L, age = 4, hcv_pos = 0L) |> mutate(age_label = "4 y old (mono)"),
  build_events(id = 3L, age = 8, hcv_pos = 0L) |> mutate(age_label = "8 y old (mono)")
)

sim_3a <- as.data.frame(rxode2::rxSolve(mod_typ, events = ev_3a, keep = "age_label"))
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_3a, aes(x = time, y = Cc, colour = age_label, linetype = age_label)) +
  geom_line(linewidth = 0.9) +
  scale_colour_manual(values = c(
    "2 y old (mono)" = "steelblue",
    "4 y old (mono)" = "darkorange",
    "8 y old (mono)" = "firebrick"
  )) +
  scale_linetype_manual(values = c(
    "2 y old (mono)" = "longdash",
    "4 y old (mono)" = "dashed",
    "8 y old (mono)" = "solid"
  )) +
  scale_x_continuous(breaks = seq(0, 11, by = 2)) +
  scale_y_continuous(limits = c(-4, -1)) +
  labs(
    x = "Duration on ART (years)",
    y = "CD4 z-score",
    colour = NULL, linetype = NULL,
    title = "Majekodunmi 2017 Figure 3A: monoinfected children at ages 2, 4, and 8 years"
  ) +
  theme_bw() +
  theme(legend.position = "bottom")
#> Warning: Removed 199 rows containing missing values or values outside the scale range
#> (`geom_line()`).
Typical-value CD4 z-score recovery trajectories for monoinfected children starting ART at ages 2, 4, and 8 years (reproducing Majekodunmi 2017 Figure 3A).

Typical-value CD4 z-score recovery trajectories for monoinfected children starting ART at ages 2, 4, and 8 years (reproducing Majekodunmi 2017 Figure 3A).

Reproducing Figure 3B: monoinfected vs HCV-coinfected 8-year-old

Figure 3B compares the typical-value trajectories for an 8-year-old monoinfected child (solid line) versus an 8-year-old HIV/HCV coinfected child (long-dashed line). Both share the same intercept and asymptote (HCV coinfection does not affect intercept or asy), but coinfection slows the recovery rate by a factor of 1 + e_hcv_pos_krec = 0.23, taking ~2 years to reach half-recovery instead of ~5 months.

ev_3b <- bind_rows(
  build_events(id = 1L, age = 8, hcv_pos = 0L) |> mutate(group = "Monoinfected (8 y)"),
  build_events(id = 2L, age = 8, hcv_pos = 1L) |> mutate(group = "HIV/HCV coinfected (8 y)")
)

sim_3b <- as.data.frame(rxode2::rxSolve(mod_typ, events = ev_3b, keep = "group"))
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_3b, aes(x = time, y = Cc, colour = group, linetype = group)) +
  geom_line(linewidth = 0.9) +
  scale_colour_manual(values = c(
    "Monoinfected (8 y)"       = "steelblue",
    "HIV/HCV coinfected (8 y)" = "firebrick"
  )) +
  scale_linetype_manual(values = c(
    "Monoinfected (8 y)"       = "solid",
    "HIV/HCV coinfected (8 y)" = "longdash"
  )) +
  scale_x_continuous(breaks = seq(0, 11, by = 2)) +
  scale_y_continuous(limits = c(-4, -1)) +
  labs(
    x = "Duration on ART (years)",
    y = "CD4 z-score",
    colour = NULL, linetype = NULL,
    title = "Majekodunmi 2017 Figure 3B: monoinfected vs HIV/HCV coinfected 8-year-old"
  ) +
  theme_bw() +
  theme(legend.position = "bottom")
Typical-value CD4 z-score recovery trajectories for an 8-year-old child: HIV monoinfected vs HIV/HCV coinfected (reproducing Majekodunmi 2017 Figure 3B).

Typical-value CD4 z-score recovery trajectories for an 8-year-old child: HIV monoinfected vs HIV/HCV coinfected (reproducing Majekodunmi 2017 Figure 3B).

Sanity checks against closed-form algebra

Because the model is purely algebraic (no ODE state, no dose events), the rxode2-simulated trajectory must agree with the closed-form expression at every time point. We spot-check the typical-value output at four canonical times for both monoinfected and coinfected 8-year-olds.

asy_pop  <- -1.07
int_pop  <- -2.42
krec_pop <- 1.55
ref_age  <- 4.3
e_age_asy       <- -0.11
e_age_intercept <- -0.29
e_hcv_pos_krec  <- -0.77

closed_form <- function(t, age, hcv) {
  asy_i <- asy_pop + e_age_asy       * (age - ref_age)
  int_i <- int_pop + e_age_intercept * (age - ref_age)
  k_i   <- krec_pop * (1 + e_hcv_pos_krec * hcv)
  asy_i + (int_i - asy_i) * exp(-k_i * t)
}

checkpoints <- expand.grid(
  age  = c(2, 4, 8),
  hcv  = c(0L, 1L),
  time = c(0, 0.5, 2, 11)
) |>
  mutate(
    expected = closed_form(time, age, hcv)
  )

ev_chk <- checkpoints |>
  mutate(
    id   = seq_len(dplyr::n()),
    amt  = 0,
    evid = 0L,
    AGE = age, HCV_POS = hcv,
    REGION_POLAND = 0L, REGION_RUSSIA = 0L, REGION_SWITZERLAND = 0L,
    REGION_UK = 0L,     REGION_SPAIN = 0L,   REGION_GERMANY = 0L,
    REGION_ITALY = 0L
  )

sim_chk <- as.data.frame(rxode2::rxSolve(mod_typ, events = ev_chk,
                                         keep = c("age", "hcv", "expected")))
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> Warning: multi-subject simulation without without 'omega'
#> Warning: Cannot keep missing columns:

sim_chk$diff <- sim_chk$Cc - sim_chk$expected

knitr::kable(
  sim_chk |> select(age, hcv, time, expected, actual = Cc, diff) |>
    arrange(age, hcv, time),
  digits = 4,
  caption = "rxode2 typical-value output vs closed-form Equation 1."
)
rxode2 typical-value output vs closed-form Equation 1.
age hcv time expected actual diff
2 0 0.0 -1.7530 -1.7530 0
2 0 0.5 -1.2482 -1.2482 0
2 0 2.0 -0.8592 -0.8592 0
2 0 11.0 -0.8170 -0.8170 0
2 1 0.0 -1.7530 -1.7530 0
2 1 0.5 -1.6002 -1.6002 0
2 1 2.0 -1.2758 -1.2758 0
2 1 11.0 -0.8355 -0.8355 0
4 0 0.0 -2.3330 -2.3330 0
4 0 0.5 -1.6341 -1.6341 0
4 0 2.0 -1.0954 -1.0954 0
4 0 11.0 -1.0370 -1.0370 0
4 1 0.0 -2.3330 -2.3330 0
4 1 0.5 -2.1214 -2.1214 0
4 1 2.0 -1.6723 -1.6723 0
4 1 11.0 -1.0627 -1.0627 0
8 0 0.0 -3.4930 -3.4930 0
8 0 0.5 -2.4058 -2.4058 0
8 0 2.0 -1.5678 -1.5678 0
8 0 11.0 -1.4770 -1.4770 0
8 1 0.0 -3.4930 -3.4930 0
8 1 0.5 -3.1639 -3.1639 0
8 1 2.0 -2.4652 -2.4652 0
8 1 11.0 -1.5169 -1.5169 0 

stopifnot(max(abs(sim_chk$diff)) < 1e-6)

Half-recovery time check

The paper text states “coinfected children had a significantly reduced recovery rate of 0.357 per year compared to 1.55 per year in monoinfected children. This difference corresponds to a time for half the long-term recovery to occur of 2 years in coinfected children, compared with 5 months (0.45 years) in monoinfected children.” The half-recovery time is ln⁡(2)/c\ln(2)/c. The packaged model reproduces both numbers.

half_time <- function(hcv) log(2) / (krec_pop * (1 + e_hcv_pos_krec * hcv))
cat(sprintf("Mono  krec   = %.3f /year, half-recovery = %.3f years (%.2f months)\n",
            krec_pop, half_time(0L), half_time(0L) * 12))
#> Mono  krec   = 1.550 /year, half-recovery = 0.447 years (5.37 months)
cat(sprintf("Coinf krec   = %.3f /year, half-recovery = %.3f years (%.2f months)\n",
            krec_pop * (1 + e_hcv_pos_krec), half_time(1L), half_time(1L) * 12))
#> Coinf krec   = 0.356 /year, half-recovery = 1.944 years (23.33 months)
cat(sprintf("Ratio (coinf / mono half-time) = %.2f (paper text: 'more than 4 times')\n",
            half_time(1L) / half_time(0L)))
#> Ratio (coinf / mono half-time) = 4.35 (paper text: 'more than 4 times')

Side-by-side comparison against the paper text

Source claim Source value Packaged-model value
Reference-case pre-ART z (Ukraine, 4.3 y) -2.42 (Table 2 Int) -2.42
Reference-case long-term z (Ukraine, 4.3 y) -1.07 (Table 2 Asy) -1.07
Mono recovery rate c 1.55 /year (paper text) 1.55
Coinf recovery rate c 0.357 /year (paper text) 0.356
Mono half-recovery time ~0.45 year (5 months) 0.447
Coinf half-recovery time ~2 years 1.944
Ratio coinf/mono half-time “more than 4 times” 4.35
Long-term z drop per year of age -0.11 per year -0.11
Pre-ART z drop per year of age -0.29 per year (Table 2) -0.29

Stochastic simulation with full IIV

Although the paper does not show a VPC, we generate a 200-subject stochastic VPC for an 8-year-old monoinfected cohort to confirm the random-effect magnitudes encoded in the model produce a realistic spread around the typical-value trajectory.

set.seed(20260522)

n_vpc <- 200L
vpc_cov <- ukraine_ref_cov(age = 8, hcv_pos = 0L)

vpc_obs_times <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 8, 10)
ev_vpc <- expand.grid(id = seq_len(n_vpc), time = vpc_obs_times) |>
  mutate(amt = 0, evid = 0L) |>
  bind_cols(vpc_cov[rep(1L, n_vpc * length(vpc_obs_times)), , drop = FALSE])

sim_vpc <- as.data.frame(rxode2::rxSolve(mod, events = ev_vpc))
#> ℹ parameter labels from comments will be replaced by 'label()'

vpc_summary <- sim_vpc |>
  group_by(time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_summary, aes(x = time)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), fill = "steelblue", alpha = 0.25) +
  geom_line(aes(y = Q50), colour = "steelblue", linewidth = 0.8) +
  geom_line(data = sim_3a |> filter(age_label == "8 y old (mono)"),
            aes(x = time, y = Cc), colour = "black", linewidth = 0.5, linetype = "dashed") +
  scale_x_continuous(breaks = seq(0, 10, by = 2)) +
  labs(
    x = "Duration on ART (years)", y = "CD4 z-score",
    title = "Stochastic 5/50/95 envelope for 8-year-old monoinfected cohort",
    caption = paste("n =", n_vpc,
                    "virtual subjects with full IIV + additive residual error.",
                    "Dashed black line: typical-value 8-y-old trajectory from Figure 3A reproduction.")
  ) +
  theme_bw()

Stratified simulation for the 8 EPPICC cohorts (Figure 3A logic, extended)

The model carries 7 EPPICC enrollment-country indicators on the pre-ART intercept. Switching them on one at a time (with Ukraine as the reference) shows the country-stratified typical-value pre-ART z scores reported in Table 2; the long-term z score and recovery rate are unaffected because the country effects act only on intercept.

country_specs <- list(
  Ukraine     = c(),
  Poland      = "REGION_POLAND",
  Russia      = "REGION_RUSSIA",
  Switzerland = "REGION_SWITZERLAND",
  UK          = "REGION_UK",
  Spain       = "REGION_SPAIN",
  Germany     = "REGION_GERMANY",
  Italy       = "REGION_ITALY"
)

country_t0 <- function(label, on_indicator) {
  cov <- ukraine_ref_cov(age = 4.3, hcv_pos = 0L)
  if (length(on_indicator) > 0) cov[[on_indicator]] <- 1L
  ev <- cbind(data.frame(id = 1L, time = c(0, 6), amt = 0, evid = 0L),
              cov[c(1L, 1L), , drop = FALSE])
  sim <- as.data.frame(rxode2::rxSolve(mod_typ, events = ev))
  tibble::tibble(country = label,
                 t0      = sim$Cc[sim$time == 0],
                 t6      = sim$Cc[sim$time == 6])
}

country_table <- bind_rows(lapply(names(country_specs), function(nm) {
  country_t0(nm, country_specs[[nm]])
})) |>
  mutate(shift_from_ukraine_at_t0 = t0 - t0[country == "Ukraine"])
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'
#> ℹ omega/sigma items treated as zero: 'etaasy', 'etaintercept', 'etakrec'

knitr::kable(country_table, digits = 3,
             caption = "Typical-value pre-ART (t = 0) and 6-year-on-ART (t = 6) CD4 z-score for a 4.3-y-old monoinfected child, by EPPICC enrollment country.")
Typical-value pre-ART (t = 0) and 6-year-on-ART (t = 6) CD4 z-score for a 4.3-y-old monoinfected child, by EPPICC enrollment country.
country t0 t6 shift_from_ukraine_at_t0
Ukraine -2.42 -1.070 0.00
Poland -1.98 -1.070 0.44
Russia -1.73 -1.070 0.69
Switzerland -2.40 -1.070 0.02
UK -19.92 -1.072 -17.50
Spain 0.47 -1.070 2.89
Germany -2.08 -1.070 0.34
Italy -6.05 -1.070 -3.63

The UK row shows the small-sample artifact discussed in Errata: at t = 0 the model predicts a z-score around -19.9 – biologically implausible – because the UK indicator carries a -17.5 shift fit to only 2 subjects. By t = 6 the trajectory has converged toward the long-term asymptote (about -1.1), so the artifact is concentrated in the pre-ART intercept; the recovery rate and the asymptote are unaffected by country.

Assumptions and deviations

  • Implausibly large UK and Italy intercept shifts. Majekodunmi 2017 Table 2 reports Int: United Kingdom = -17.5 and Int:Italy = -3.63, both with very small subgroup sizes (UK n = 2, Italy n = 2 of 46 coinfected). A z-score effect of -17.5 implies a UK pre-ART z-score around -20, which is far below any observed z-score in Figure 2 (range -11.9 to 3.9) and is biologically implausible. The packaged model reproduces both values verbatim per the published table. Users simulating UK or Italian children should interpret pre-ART predictions cautiously and consider down-weighting these effects (or rebuilding the model with the country effect pooled into a single small-sample-Europe indicator) for any population-level application.

  • All HIV monoinfected children come from Ukraine. The Ukrainian reference therefore conflates “monoinfected” with “Ukraine cohort” in the original fit. The seven EPPICC enrollment-country indicators absorb the laboratory and clinical-practice differences but only for coinfected children; the model has no way to express, e.g., a Spanish HIV-monoinfected child. This is a known limitation of the source data and is preserved in the packaged model.

  • Additive normal IIV on krec (the recovery-rate constant). Table 2’s “Variance of REs” column reports raw variances (not %CV), so the random effects on asy, intercept, and krec are encoded as additive normal etas on the natural (z-score) scale for asy and intercept, and additive normal on the linear (1/year) scale for krec. The latter is unusual for a positive rate constant – with SD = 0.62 around a typical value of 1.55 (mono) or 0.357 (coinf), occasional simulated subjects will have krec < 0, which is biologically meaningless (CD4 going backwards). The typical-value trajectory is unaffected; consumers wanting purely positive simulated rates should truncate krec at a small positive value (e.g., 0.05 /year) after rxSolve, or rederive the model with a log-normal IIV on krec. The packaged encoding reproduces the paper’s reported variance scale faithfully.

  • Recovery-rate parameter renamed c to krec. The paper uses the symbol cc for the recovery-rate constant. In R, c is the built-in combine function; shadowing it inside ini() and model() is technically permitted but risks confusion for any downstream code that uses c() in proximity to the model block. The packaged model renames the parameter to krec (recovery rate constant), consistent with the endogenous-model rate-constant convention (kpro, kdeg, kcat, etc.). The covariate effect symbol is renamed accordingly to e_hcv_pos_krec; the eta is etakrec.

  • Intercept parameter renamed int to intercept. rxode2 transpiles the model() block to C, and int is a C reserved word. The packaged model renames the typical-value intercept to intercept (matching the existing Hamuro_2017_DMD_6MWT.R intercept naming). The eta and covariate-effect names follow: etaintercept, e_age_intercept, e_region_<country>_intercept.

  • Observation variable Cc denotes a CD4 z-score, not a drug concentration. The single observation endpoint is named Cc per the nlmixr2lib convention for single-output models; the variable holds the modelled CD4 z score (no units), not a drug concentration. The units$concentration string explicitly says so. checkModelConventions() warns about the missing “/” in the concentration unit string (it heuristically expects mg/L or similar for a single-output Cc); the warning is a justified deviation for this non-PK model (the same deviation appears in Hamuro_2017_DMD_6MWT.R, Sherer_2012_AAA.R, Harun_2019_cysticFibrosis.R, and Tortorici_2017_a1pi.R).

  • No PKNCA validation. This is a disease-progression / immune-reconstitution model with no dosing events and no concentration-time data, so PKNCA non-compartmental analysis is not applicable. Validation is via closed-form-algebra spot checks (at canonical ages and times) and direct reproduction of the typical-value trajectories in Figures 3A and 3B.

  • Age covariate is time-fixed at ART initiation. Although a child ages during the follow-up window, the source model uses the age at ART initiation as a time-fixed baseline covariate on intercept and asy. The packaged model expects the same AGE column on every observation row for a given subject; the rxode2 time column carries duration on ART (in years).

  • Pre-ART HIV viral load, AIDS status, and sex were tested but not retained in the final multivariate model (Methods ‘Covariate Analysis’ and Results ‘Pre-ART HIV Viral Load Had No Impact’). The packaged model carries only the retained covariates (AGE, HCV_POS, and 7 EPPICC enrollment-country indicators). HCV genotype, anti-HCV therapy, and ART regimen detail (3-drug vs other) were also not used as covariates in the source.

  • No HCV-coinfected children from Ukraine in the model intercepts. The 18 HCV-coinfected Ukrainian children contribute to the Ukrainian reference (REGION_* = 0). All 7 non-Ukraine country indicators were fit only from EPPICC coinfected children (n = 1 to 17 per country); Ukraine therefore pools 355 monoinfected + 18 coinfected for the reference intercept and asymptote.