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Imperfect serological test

Source: vignettes/imperfect_test.Rmd
imperfect_test.Rmd

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 0.000106 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.06 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: 4000 / 4000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 2.134 seconds (Warm-up)
#> Chain 1:                3.991 seconds (Sampling)
#> Chain 1:                6.125 seconds (Total)
#> Chain 1:

# check fitted value 
output$info[1:2, ]
#>             mean      se_mean          sd      2.5%       25%       50%
#> est_se 0.9277289 9.789702e-05 0.005943015 0.9158427 0.9239500 0.9277263
#> est_sp 0.8027427 9.223906e-05 0.006921599 0.7887524 0.7980911 0.8027793
#>              75%     97.5%    n_eff      Rhat
#> est_se 0.9318139 0.9390842 3685.315 0.9997749
#> est_sp 0.8075447 0.8158433 5630.969 0.9999903

# ---- 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.