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Estimate Prior Distribution for Asymptomatic Shedding Rate (zeta_2)

Source: R/est_zeta_2_prior.R
est_zeta_2_prior.Rd

Compiles a meta-analysis of published Vibrio cholerae asymptomatic shedding anchors (stool concentration x normal daily stool mass) and fits a lognormal prior on the per-person-per-day asymptomatic shedding rate used in the MOSAIC environmental reservoir update: $$W(t+1) \mathrel{+}= (1 - \theta_j) \cdot \mathrm{Poisson}(\zeta_2 \cdot I_{\mathrm{asym}})$$ so \(\zeta_2\) is the expected total V. cholerae cells shed per asymptomatic infected person per day during the shedding phase.

Usage

est_zeta_2_prior(PATHS)

Arguments

PATHS

A list of paths generated by get_paths(). Must include:

  • MODEL_INPUT: directory where parameter CSVs are saved.

  • DOCS_FIGURES: directory where the summary figure is saved.

Value

Invisibly returns a list with elements:

  • data: the source meta-analysis table.

  • fit: fitted lognormal parameters (meanlog, sdlog, median, mode, mean, ci_lower, ci_upper, n_sources, mu_log10, sd_log10).

  • param_df: long-format parameter data frame (as saved to disk).

  • prediction: density grid on linear and log10-x scales.

  • sensitivity: a leave_nelson_out sub-fit that uses only the Kaper review rows (n_primary_sources = 0, published as a warning).

Details

The function assembles a small literature table of per-person-per-day asymptomatic shedding anchors. The evidence base is thin: Nelson 2009 gives the only verbatim primary-source anchor ("approximately 10^3 vibrios per gram of stool") and Kaper 1995 provides an expert-review range (10^3 to 10^5 cells per gram). Given this single primary source, the fit applies a hard floor sdlog >= 2.0 to honestly reflect that \(n_{\mathrm{independent}} = 1\).

Assembly equation. Each entry contributes \(\zeta_{2,i} = c_i \times V_i\) with V = 150 g/day taken from normal adult physiology (100-250 g/day); no cholera-specific asymptomatic stool-volume measurement exists.

Single-source caveat and sdlog floor. The central anchor rests on a single primary source (Nelson 2009). The fit applies a hard floor sdlog >= 2.0 (raised from 1.5 in rev 1 per modeller review). The floor preserves the lognormal median (meanlog is unchanged); the mode shifts left as a consequence. With the weights 1.0 / 0.1 / 0.1 (v0.29.1) the weighted log10 mean is ~5.34, so the median is ~2.2e5; with sdlog = 2.0 the 95 percent CI spans roughly 4.4e3 to 1.1e7 - factor ~50 on each side - which is the correct spread to cover a +/- 1 order-of-magnitude error in the single primary source.

King 2008 caveat (documentation only). King, Ionides, Pascual & Bouma (2008) describe "a negligible quantity of vibrio" shed by asymptomatic hosts in their natural-vaccination model. This is qualitative and directionally supports a small zeta_2 / large zeta_ratio, but it does not give a quantitative value. It is therefore NOT included as a fitted row - treating a qualitative claim as quantitative data would masquerade ignorance as evidence. See claude/zeta_priors_update/zeta_sources/12_King_2008_Nature_inapparent.md.

Leave-Nelson-out sensitivity. $sensitivity$leave_nelson_out returns the fit using only the Kaper review rows. This fit has effective n_primary_sources = 0 (Kaper is a review that cites Nelson-era primary data) and is published as a warning, not a usable prior.

n_sources caveat. The returned $fit$n_sources equals nrow(fit_df) = 3 (Nelson, Kaper-lower, Kaper-upper). The effective number of independent primary sources is 1 (Nelson 2009); Kaper 1995 is a review that does not contribute independent primary data. The sdlog-floor mechanism encodes this single-source risk regardless of the n_sources count.

Per-day vs per-infection. zeta_2 is a per-day shedding rate during asymptomatic infection; \(\gamma_2^{-1}\) (~2 d) governs the duration. Nelson's verbatim claim is that asymptomatic shedding lasts "only one day" – close to the current gamma_2 prior. Cumulative cells per asymptomatic infection is zeta_2 / gamma_2.

Relation to documented priors. Earlier MOSAIC-docs narrative states zeta_2 ~ Uniform(0.01, 10^3). That range derives from the Frame-B calibration rescaling and is superseded by this lognormal literature-derived prior, whose 95% CI extends to ~10^7.

References

  • Nelson EJ, Harris JB, Morris JG, Calderwood SB, Camilli A (2009). Cholera transmission: the host, pathogen and bacteriophage dynamic. Nat Rev Microbiol 7(10):693-702. ("Asymptomatic patients typically shed vibrios for only one day at approximately 10^3 vibrios per gram of stool.")

  • Kaper JB, Morris JG, Levine MM (1995). Cholera. Clin Microbiol Rev 8(1):48-86. (expert review range 10^3 to 10^5 cells per gram)

  • King AA, Ionides EL, Pascual M, Bouma MJ (2008). Inapparent infections and cholera dynamics. Nature 454(7206):877-80. (qualitative only; not a fitted row)

Examples

if (FALSE) { # \dontrun{
PATHS <- get_paths()
est_zeta_2_prior(PATHS)
} # }