Frequentist approaches to correct prevalence under misclassification with a known test

Funtions that implement the Rogen Gladen Estimator (1978)

correct_sero_misclass(num_pos, num_neg, sens = 0.806, spec = 0.83)

correct_sero_misclass_p(p_A, sens = 0.891, spec = 0.792)

rogan_gladen_estimator(prev.obs, Se, Sp)

Arguments

num_pos

number of positives
num_neg

number of negatives
sens

senstivitity
spec

specifcity
p_A

  • proportion of positives by imperfect test
prev.obs

observed prevalence
Se

sensitivity
Sp

specificity
N

  • number tested

Value

numeric vector

Functions

  • correct_sero_misclass: corrects num positive by sens and spec. source: here

  • correct_sero_misclass_p: takes known sensitivity and specificity of test and returns proportion of sample that 'true' positive

  • rogan_gladen_estimator: Function to adjust the observed prevalence for a single Se & Sp. limitation: this allows values out of 0-1 range. source: here

References

Rogan, W. J., & Gladen, B. (1978). Estimating prevalence from the results of a screening test. American journal of epidemiology, 107(1), 71-76. https://doi.org/10.1093/oxfordjournals.aje.a112510

Azman, A. S., Lauer, S., Bhuiyan, M. T. R., Luquero, F. J., Leung, D. T., Hegde, S., ... & Lessler, J. (2020). Vibrio cholerae O1 transmission in Bangladesh: insights from a nationally-representative serosurvey. medRxiv. doi: https://doi.org/10.1101/2020.03.13.20035352

Takahashi, S., Greenhouse, B., & Rodríguez-Barraquer, I. (2020). Are SARS-CoV-2 seroprevalence estimates biased?. doi: https://doi.org/10.1093/infdis/jiaa523

Examples


if (FALSE) {

library(tidyverse)
library(skimr)

sensitivity = 0.93
specificity = 0.975
positive_pop <- c(321, 123, 100, 10)
negative_pop <- c(1234, 500, 375, 30)

# HopkinsIDD/Bangladesh-Cholera-Serosurvey ------------------------------

correct_sero_misclass_p(p_A = 0.74)
correct_sero_misclass(num_pos = positive_pop,
                      num_neg = negative_pop,
                      sens = 0.999,spec = 0.960)
correct_sero_misclass_p(p_A = positive_pop/negative_pop,
                        sens = 0.999,spec = 0.960)

# sakitakahashi/COVID-sensitivity -------------------------------------

tibble(
  g=1:2,
  p=seq(10L,20L,10L),
  n=seq(200L,100L,-100L),
  se=seq(0.9,0.8,-0.1),
  sp=seq(0.8,0.9,0.1)) %>%
  mutate(raw=p/n) %>%
  mutate(adjust=pmap_dbl(.l = select(.,prev.obs=raw, Se=se, Sp=sp),
                         .f = rogan_gladen_estimator))

}