Processing math: 100%

Modeling directly from antibody levels

library(serosv)

Mixture model

Proposed model

Two-component mixture model for test result Z with Zj(j={I,S}) being the latent mixing component having density fj(zj|θj) and with πTRUE(a) being the age-dependent mixing probability can be represented as

f(z|zI,zS,a)=(1πTRUE(a))fS(zS|θS)+πTRUE(a)fI(zI|θI)

The mean E(Z|a) thus equals

μ(a)=(1πTRUE(a))μS+πTRUE(a)μI

From which the true prevalence can be calculated by

πTRUE(a)=μ(a)μSμIμS

Force of infection can then be calculated by

λTRUE=μ(a)μIμ(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
#> 
#> Parameters:
#>       pi    mu  sigma
#> 1 0.1088 2.349 0.6804
#> 2 0.8912 6.439 0.9437
#> 
#> Distribution:
#> [1] "norm"
#> 
#> Constraints:
#>    conpi    conmu consigma 
#>   "NONE"   "NONE"   "NONE"
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)
#> Warning: No shared levels found between `names(values)` of the manual scale and the
#> data's fill values.