Estimate seroprevalence and FOI from a fixed mixture model

Estimate age-specific seroprevalence and FOI given a fitted mixture model (generated by [serosv::mixture_model()])

Usage

estimate_from_mixture(
  age,
  antibody_level,
  threshold_status = NULL,
  mixture_model,
  s = "ps",
  sp = 83,
  monotonize = TRUE
)

Arguments

age: vector of age
antibody_level: vector of the corresponding raw antibody level
threshold_status: sero status using threshold approach in line listing (optional, for visualization and comparison only)
mixture_model: mixture_model object generated by serosv::mixture_model()
s: smoothing basis used to fit antibody level
sp: smoothing parameter
monotonize: whether to monotonize seroprevalence (default to TRUE)

Value

a list of class estimated_from_mixture with the following items

df: the dataframe used for fitting the model
info: a fitted "gam" model for mu(a)
sp: seroprevalence
foi: force of infection
threshold_status: serostatus using threshold method only if provided

Details

Antibody level (denoted $Z$) is modeled using a 2-component Gaussian mixture model. Each component $Z_j$ ($j \in \{I, S\}$) represents the antibody level of the latent Infected and Susceptible sub-populations, following density $f_j(z_j|\theta_j)$

Let $\pi_{\text{TRUE}}(a)$ denotes the age-dependent mixing probability (i.e., the true prevalence), the density of the mixture is formulated 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 true prevalence can be computed as $$\pi_{\text{TRUE}}(a) = \frac{\mu(a) - \mu_S}{\mu_I - \mu_S}$$

And FOI can then be inferred as $$\lambda_{TRUE} = \frac{\mu'(a)}{\mu_I - \mu(a)}$$

Function [serosv::mixture_model()] fits antibody level data to $f_S(z_S|\theta_S)$ and $f_I(z_I|\theta_I)$

Function [serosv::estimate_mixture()] will then estimate age-specific antibody level $\mu(a)$ and infer the estimation for $\pi_{\text{TRUE}}(a)$ and $\lambda_{TRUE}$

Refer to section 11.3. of the the book by Hens et al. (2012) for further details.

References