# Imperfect serological test

    library(serosv)

## 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)

  - Users can specifiy the name for these columns in the input data frame using arguments `age_col`, `pos_col`, `tot_col`or `age_col`, `status_col` respectively

- `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 5.2e-05 seconds
    #> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.52 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)
    #> Chain 1: Iteration:  800 / 4000 [ 20%]  (Warmup)
    #> Chain 1: Iteration: 1001 / 4000 [ 25%]  (Sampling)
    #> Chain 1: Iteration: 1400 / 4000 [ 35%]  (Sampling)
    #> Chain 1: Iteration: 1800 / 4000 [ 45%]  (Sampling)
    #> Chain 1: Iteration: 2200 / 4000 [ 55%]  (Sampling)
    #> Chain 1: Iteration: 2600 / 4000 [ 65%]  (Sampling)
    #> Chain 1: Iteration: 3000 / 4000 [ 75%]  (Sampling)
    #> Chain 1: Iteration: 3400 / 4000 [ 85%]  (Sampling)
    #> Chain 1: Iteration: 3800 / 4000 [ 95%]  (Sampling)
    #> Chain 1: Iteration: 4000 / 4000 [100%]  (Sampling)
    #> Chain 1:
    #> Chain 1:  Elapsed Time: 0.161 seconds (Warm-up)
    #> Chain 1:                0.323 seconds (Sampling)
    #> Chain 1:                0.484 seconds (Total)
    #> Chain 1:

    # check fitted value
    output$info[1:2, ]
    #>             mean      se_mean          sd      2.5%       25%       50%
    #> est_se 0.9279110 1.030783e-04 0.006108971 0.9156867 0.9238106 0.9280891
    #> est_sp 0.8028227 9.624223e-05 0.006862949 0.7894737 0.7981445 0.8029028
    #>              75%     97.5%    n_eff      Rhat
    #> est_se 0.9321756 0.9391947 3512.383 1.0000643
    #> est_sp 0.8074229 0.8163628 5084.991 0.9996717

    # ---- 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 = (observed_sero + sp - 1) / (se + sp -1)"

User can then visualize the output using `plot_corrected_prev()` function

    # Plot output of the frequentist approach
    plot_corrected_prev(freq_output)

    # Plot output of the bayesian approach
    plot_corrected_prev(output)

To compare both correction methods in a single plot, provide the output from the second method as the optional `y` argument in `plot_corrected_prev()`

    plot_corrected_prev(output, freq_output)

    # set facet = TRUE to display the confidence or credible intervals for each method
    plot_corrected_prev(output, freq_output, facet = TRUE)

### 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.