Modeling directly from antibody levels
In serosv: Model Infectious Disease Parameters from Serosurveys

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(serosv)

Mixture model

Proposed model

Two-component mixture model for test result $Z$ with $Z_j (j = {I, S})$ being the latent mixing component having density $f_j(z_j|\theta_j)$ and with $\pi_{\text{TRUE}}(a)$ being the age-dependent mixing probability can be represented as

$$ f(z|z_I, z_S,a) = (1-\pi_{\text{TRUE}}(a))f_S(z_S|\theta_S)+\pi_{\text{TRUE}}(a)f_I(z_I|\theta_I) $$

The mean $E(Z|a)$ thus equals

$$ \mu(a) = (1-\pi_{\text{TRUE}}(a))\mu_S+\pi_{\text{TRUE}}(a)\mu_I$$

From which the true prevalence can be calculated by

$$ \pi_{\text{TRUE}}(a) = \frac{\mu(a) - \mu_S}{\mu_I - \mu_S} $$

Force of infection can then be calculated by

$$ \lambda_{TRUE} = \frac{\mu'(a)}{\mu_I - \mu(a)} $$

Fitting data

To fit the mixture data, use mixture_model function

df <- vzv_be_2001_2003[vzv_be_2001_2003$age < 40.5,]
df <- df[order(df$age),]
data <- df$VZVmIUml
model <- mixture_model(antibody_level = data)
model$info

plot(model)

sero-prevalence and FOI can then be esimated using function estimate_from_mixture

est_mixture <- estimate_from_mixture(df$age, data, mixture_model = model, threshold_status = df$seropositive, sp=83, monotonize = FALSE)
plot(est_mixture)