Imperfect serological test

library(serosv)
library(ggplot2)

Imperfect test

Function correct_prevalence() is used for estimating the true prevalence if the serological test used is imperfect

Arguments:

data the input data frame, must either have:
- age, pos, tot columns (for aggregated data)
- OR age, status columns for (linelisting data)
bayesian whether to adjust sero-prevalence using the Bayesian or frequentist approach. If set to TRUE, true sero-prevalence is estimated using MCMC.
init_se sensitivity of the serological test (default value 0.95)
init_sp specificity of the serological test (default value 0.8)
study_size_se (applicable when bayesian=TRUE) sample size for sensitivity validation study (default value 1000)
study_size_sp (applicable when bayesian=TRUE) sample size for specificity validation study (default value 1000)
chains (applicable when bayesian=TRUE) number of Markov chains (default to 1)
warmup (applicable when bayesian=TRUE) number of warm up runs (default value 1000)
iter (applicable when bayesian=TRUE) number of iterations (default value 2000)

The function will return a list of 2 items:

info
- if bayesian = TRUE contains estimated values for se, sp and corrected seroprevalence
- else return the formula for computing corrected seroprevalence
corrected_sero return a data.frame with age, sero (corrected sero) and pos, tot (adjusted based on corrected prevalence)

# ---- estimate real prevalence using Bayesian approach ----
data <- rubella_uk_1986_1987
output <- correct_prevalence(data, warmup = 1000, iter = 4000, init_se=0.9, init_sp = 0.8, study_size_se=1000, study_size_sp=3000)
#> 
#> SAMPLING FOR MODEL 'prevalence_correction' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 2.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 4000 [  0%]  (Warmup)
#> Chain 1: Iteration:  400 / 4000 [ 10%]  (Warmup)
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#> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling)
#> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.449 seconds (Warm-up)
#> Chain 1:                0.898 seconds (Sampling)
#> Chain 1:                1.347 seconds (Total)
#> Chain 1:

# check fitted value 
output$info[1:2, ]
#>             mean      se_mean          sd      2.5%       25%       50%
#> est_se 0.9275947 0.0001025618 0.005816939 0.9157572 0.9236543 0.9277112
#> est_sp 0.8028048 0.0001036128 0.007066057 0.7887178 0.7979157 0.8027604
#>              75%     97.5%    n_eff      Rhat
#> est_se 0.9316509 0.9389357 3216.752 0.9998059
#> est_sp 0.8077617 0.8162707 4650.795 0.9996685

# ---- estimate real prevalence using frequentist approach ----
freq_output <- correct_prevalence(data, bayesian = FALSE, init_se=0.9, init_sp = 0.8)

# check info
freq_output$info
#> [1] "Formula: real_sero = (apparent_sero + sp - 1) / (se + sp -1)"

# compare original prevalence and corrected prevalence
ggplot()+
  geom_point(aes(x = data$age, y = data$pos/data$tot, color="apparent prevalence")) + 
  geom_point(aes(x = output$corrected_se$age, y = output$corrected_se$sero, color="estimated prevalence (bayesian)" )) +
  geom_point(aes(x = freq_output$corrected_se$age, y = freq_output$corrected_se$sero, color="estimated prevalence (frequentist)" )) +
  scale_color_manual(
    values = c(
      "apparent prevalence" = "red", 
      "estimated prevalence (bayesian)" = "blueviolet",
      "estimated prevalence (frequentist)" = "royalblue")
  )+ 
  labs(x = "Age", y = "Prevalence")

Fitting corrected data

Data after seroprevalence correction

Bayesian approach

suppressWarnings(
  corrected_data <- farrington_model(
  output$corrected_se,
  start=list(alpha=0.07,beta=0.1,gamma=0.03))
)

plot(corrected_data)
#> Warning: No shared levels found between `names(values)` of the manual scale and the
#> data's fill values.

Frequentist approach

suppressWarnings(
  corrected_data <- farrington_model(
  freq_output$corrected_se,
  start=list(alpha=0.07,beta=0.1,gamma=0.03))
)

plot(corrected_data)
#> Warning: No shared levels found between `names(values)` of the manual scale and the
#> data's fill values.

Original data

suppressWarnings(
  original_data <- farrington_model(
  data,
  start=list(alpha=0.07,beta=0.1,gamma=0.03))
)
plot(original_data)
#> Warning: No shared levels found between `names(values)` of the manual scale and the
#> data's fill values.

- Imperfect test