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Snake venom (Sanhajariya 2018)

Source: vignettes/articles/Sanhajariya_2018_snake_venom.Rmd
Sanhajariya_2018_snake_venom.Rmd

Model and source

  • Citation: Sanhajariya S, Duffull SB, Isbister GK. Pharmacokinetics of snake venom. Toxins (Basel). 2018;10(2):73.
  • Article: https://doi.org/10.3390/toxins10020073
  • Description: Exploratory one-compartment population PK meta-analysis of snake venom in humans, with zero-order input over a fixed 1 h duration and first-order elimination. The model was fit in NONMEM 7.2 to 218 timed venom concentrations pooled from 145 snakebite patients across 24 published case reports / case series (9 elapid-bite studies, 16 viper-bite studies). Snake family (Elapidae vs Viperidae) modifies F1; Viperidae is the reference (F1 = 1, fixed). The authors describe the model as a preliminary prior for future, richer snake-envenoming PK datasets.

Population

The structural model was developed on data pooled from 145 snakebite patients across 24 primary publications (Sanhajariya 2018 Table 6). Most patients contributed a single pre-antivenom venom concentration; only five primary studies reported serial samples. Snakebite patients were drawn from Australia, Brazil, France, Slovenia, Thailand, Taiwan, Sri Lanka, Myanmar, the UK, Switzerland, Martinique, and Papua New Guinea. Patient-level demographics (age, weight, sex, race / ethnicity) are not aggregated in the paper; the underlying primary studies are individual case reports or small series.

Pre-antivenom venom concentrations were measured by ELISA (assay limit of detection 0.1 to 20 mcg/L per the included primary studies; inter-laboratory CV 4 to 20 % per the paper’s Section 1 prose).

The model partitions the cohort by the snake family that delivered the bite: 9 of the 24 primary studies reported elapid envenomation (Pseudonaja, Naja, Acanthophis, Denisonia, Pseudechis, Bungarus, Ophiophagus, Micropechis) and 16 reported viperid envenomation (Vipera, Crotalus, Daboia, Bothrops, Bitis, Cerastes). The model encodes this via the binary covariate SNAKEFAMILY_ELAPID (1 = elapid bite, 0 = viperid bite).

The same information is available programmatically via readModelDb("Sanhajariya_2018_snake_venom")$population.

Source trace

Per-parameter origin comments live next to each ini() entry in inst/modeldb/specificDrugs/Sanhajariya_2018_snake_venom.R. The table below is the collected audit trail.

Equation / parameter Value Source location
Structural form (1-cmt, zero-order input, first-order elimination) – Section 2.2.3 prose; Appendix A heading
CL 13.3 L/h Table A1 ‘Covariate Model’ column, row CL (RSE 14 %)
V 184 L Table A1 ‘Covariate Model’ column, row V (RSE 10 %)
D1 (duration of zero-order input) 1 h, FIXED Table A1 ‘Covariate Model’ column, row D1 (1 FIX)
F1 (Viperidae, reference) 1, FIXED Table A1 ‘Covariate Model’ column, row F1(Viperidae)
F1 (Elapidae, relative) 0.569 Table A1 ‘Covariate Model’ column, row F1(Elapidae) (RSE 43 %)
BSV on CL (CV %) 43.7 % Table A1 ‘Between subject variability’ row CL (RSE 52 %)
BSV on V (CV %) 29.8 % Table A1 ‘Between subject variability’ row V (RSE 101 %)
BSV on D1 (CV %) 44.1 % Table A1 ‘Between subject variability’ row D1 (RSE 17 %)
BSV on F1 (CV %) 275.4 % Table A1 ‘Between subject variability’ row F1 (RSE 7 %)
Proportional residual error 0.047 (variance) Table A1 ‘Residual error’ row Proportional error (RSE 25 %)
Reported elimination half-life 9.71 +/- 1.29 h Section 2.2.3 prose; ln(2) * V / CL = 9.59 h matches

Virtual cohort

The original observed concentration data are not publicly available as an individual-level dataset; the paper provides plots (Figures 3 and 4) of the pooled extracted observations. The simulation below builds a virtual cohort of 200 snakebite patients (100 elapid, 100 viperid) and uses the published parameter values to generate prediction-corrected concentration ribbons that can be visually compared with Figure 3 of the source paper.

Per-bite venom mass is unknown in the source dataset; F1 absorbs that variability (CV 275 %) on top of the typical-value elapid-vs-viperid scaling (0.569 vs 1). For simulation we supply a single nominal venom-mass dose so that the typical-value concentration scale is comparable to Figures 3 to 5 of the paper (observed snake venom concentrations ranged roughly 1 to 300 mcg/L in the first 24 h post-bite).

set.seed(20180207L)  # paper publication date 2018-02-07

n_per_family <- 100L

make_cohort <- function(n, snakefamily_elapid, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  nominal_dose_mcg <- 10000  # 10 mg nominal venom load per bite

  obs_times <- c(
    seq(0.25, 4,  by = 0.25),
    seq(4.5,  12, by = 0.5),
    seq(13,   24, by = 1)
  )

  dose_df <- tibble::tibble(
    id   = ids,
    time = 0,
    amt  = nominal_dose_mcg,
    cmt  = "central",
    evid = 1L,
    rate = -2,                  # modeled duration -> dur(central) <- d1 applies
    SNAKEFAMILY_ELAPID = snakefamily_elapid,
    family = ifelse(snakefamily_elapid == 1L, "Elapidae", "Viperidae")
  )

  obs_df <- tidyr::expand_grid(
    id   = ids,
    time = obs_times
  ) |>
    dplyr::mutate(
      amt  = 0,
      cmt  = "central",
      evid = 0L,
      rate = 0,
      SNAKEFAMILY_ELAPID = snakefamily_elapid,
      family = ifelse(snakefamily_elapid == 1L, "Elapidae", "Viperidae")
    )

  dplyr::bind_rows(dose_df, obs_df) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_cohort(n_per_family, snakefamily_elapid = 0L, id_offset =          0L),
  make_cohort(n_per_family, snakefamily_elapid = 1L, id_offset = n_per_family)
)

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

Simulation 

mod <- readModelDb("Sanhajariya_2018_snake_venom")

sim <- rxode2::rxSolve(
  mod,
  events = as.data.frame(events),
  keep   = c("family", "SNAKEFAMILY_ELAPID")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication (no between-subject variability):

mod_typ <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typ <- rxode2::rxSolve(
  mod_typ,
  events = as.data.frame(events),
  keep   = c("family", "SNAKEFAMILY_ELAPID")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etald1', 'etalfdepot'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Typical-value concentration-time profiles (Figure 4 of Sanhajariya 2018)

Figure 4 of the source paper plots the pooled observed concentration-time data by snake family (panel a: Elapidae; panel b: Viperidae). The deterministic typical-value simulation below shows the model-predicted mean concentration trajectory in each family after a 10 mg nominal venom bite.

sim_typ |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(family, time) |>
  dplyr::summarise(Cc_typ = mean(Cc), .groups = "drop") |>
  ggplot(aes(time, Cc_typ, colour = family)) +
  geom_line(size = 0.8) +
  scale_y_log10() +
  labs(
    x = "Time post-bite (h)",
    y = "Venom concentration (mcg/L)",
    colour = NULL,
    title = "Typical-value snake venom concentration vs time post-bite",
    caption = "Reproduces the qualitative pattern of Figure 4 of Sanhajariya 2018."
  ) +
  theme_minimal()
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

Stochastic prediction ribbons (Figure 3 of Sanhajariya 2018)

Figure 3 of the source paper overlays the pooled observed concentrations (closed triangles = elapid bites, closed circles = viperid bites). The simulated 5th / 50th / 95th percentile ribbons below cover the same observation window and concentration range, including the very large between-bite F1 variability.

sim |>
  dplyr::filter(time > 0, Cc > 0) |>
  dplyr::group_by(family, time) |>
  dplyr::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(aes(time, Q50, colour = family, fill = family)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line(size = 0.8) +
  scale_y_log10() +
  labs(
    x = "Time post-bite (h)",
    y = "Venom concentration (mcg/L)",
    colour = NULL,
    fill = NULL,
    title = "Simulated 5th / 50th / 95th percentile venom concentrations",
    caption = "Compare with Figure 3 of Sanhajariya 2018 (pooled observed concentrations)."
  ) +
  theme_minimal()

PKNCA validation

A formal NCA-based half-life check is the appropriate validation here because the paper reports a derived elimination half-life (9.71 +/- 1.29 h, Section 2.2.3) computed from the population CL and V estimates. The PKNCA configuration below stratifies by snake family and computes per-family typical-value half-life and AUC0-Inf.

sim_typ_nca <- sim_typ |>
  dplyr::filter(time > 0, !is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, family)

conc_obj <- PKNCA::PKNCAconc(sim_typ_nca, Cc ~ time | family + id)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, family) |>
  as.data.frame()

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | family + id)

intervals <- data.frame(
  start      = 0,
  end        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed

nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  caption = "Simulated NCA parameters from the typical-value model, stratified by snake family."
)
Simulated NCA parameters from the typical-value model, stratified by snake family.
start end family N cmax tmax half.life aucinf.obs
0 Inf Elapidae 100 29.8 [0.000] 1.00 [1.00, 1.00] 9.59 [0.000] NC
0 Inf Viperidae 100 52.4 [0.000] 1.00 [1.00, 1.00] 9.59 [0.000] NC

Comparison against the published half-life

The paper reports a single elimination half-life of 9.71 +/- 1.29 h (Section 2.2.3) derived from the typical-value CL = 13.3 L/h and V = 184 L. The analytic value is log(2) * V / CL = log(2) * 184 / 13.3, which gives:

analytic_t_half <- log(2) * 184 / 13.3
analytic_t_half
#> [1] 9.589405

The simulated NCA half-life from the typical-value virtual cohort above should match this value to within the numerical accuracy of the terminal-phase fit (PKNCA defaults). Both families share the same CL and V (only F1 differs); the per-family half-life therefore agrees with the population value.

Assumptions and deviations

  • Snake-family covariate naming. The Sanhajariya 2018 NONMEM control stream is not included with the paper, so the source column name for the snake-family indicator is not disclosed in Appendix Table A1. We registered the canonical column SNAKEFAMILY_ELAPID (binary; 1 = elapid bite, 0 = viperid reference) following the paper’s Section 2.2.3 prose. See inst/references/covariate-columns.md for the full entry.
  • lfdepot used without a depot compartment (semantic stretch). The structural model has only a central compartment; the dose enters via zero-order input over D1 = 1 h. The canonical parameter name lfdepot is normally paired with a depot compartment that drains to central. Here we reuse lfdepot (and the matching IIV / covariate-effect names etalfdepot / e_snakefamily_elapid_fdepot) as the log of F1, with f(central) <- exp(lfdepot + e_snakefamily_elapid_fdepot * SNAKEFAMILY_ELAPID + etalfdepot). This stretch was approved at the pre-flight sidecar stage to avoid introducing a new canonical parameter for a borderline case; the source paper’s F1 is the bioavailability of the single input compartment regardless of whether that compartment is named depot or central.
  • Residual-error interpretation. Table A1 reports Proportional error 0.047 (25 %). The label does not carry an explicit CV % suffix, and the surrounding Between subject variability rows do carry explicit (CV %) formatting. We interpret 0.047 as the NONMEM $SIGMA variance and encode the proportional residual SD as propSd = sqrt(0.047) = 0.2168 (~21.7 % CV). The 25 % RSE applies to the variance estimate. This interpretation was confirmed at the pre-flight sidecar stage.
  • Unknown per-bite venom mass. The actual venom mass injected by each bite is not measured in the source dataset; the model assigns each subject a nominal unit dose and absorbs the per-bite mass variability into the F1 BSV (CV 275 %). For simulation, the vignette supplies a nominal 10 mg venom dose so that the typical-value concentration trajectory is on the observed-range scale (1 to 300 mcg/L over 24 h post-bite); a user simulating a specific snake species can substitute a species-typical venom yield.
  • Animal-data section not extracted. Section 2.1 and Tables 3 to 5 of Sanhajariya 2018 are a pure systematic review of 12 animal popPK studies from other authors; no original animal popPK model is fit. The extraction here covers only the original human meta-analysis popPK model (Section 2.2 and Appendix Table A1). The 12 cited primary animal studies were not queued for separate extraction at the operator’s direction in the pre-flight sidecar.
  • No errata identified. A search of the journal’s article landing page and PubMed for Sanhajariya 2018 snake venom erratum returned no corrigendum.