pempi Overview

The proportion estimation with marginal proxy information (pempi) package, allows to estimate and build confidence intervals for proportions, from random or stratified samples and census data with participation bias. Measurement errors in the form of false positive and false negative are also included in the inferential procedure. The pempi package also contains code for simulation studies and sensitivity analysis reported in the companion paper Guerrier et al. (2024), as well as the Austrian dataset on COVID-19 prevalence in November 2020.

Remark on notation

The notation and conventions used in Guerrier et al. (2024) are slightly amended for convenience in this package. In particular, we use R1 instead R11, R2 instead of R10, R3 instead of R01 and R4 instead of R00.

Package installation

The pempi package is available on both CRAN and GitHub. The CRAN version is considered stable, whereas the GitHub version is subject to modifications/updates which may lead to installation problems or broken functions. You can install the stable version of the pempi package with:

The latest version can install from GitHub as follows:

# Install devtools
install.packages("devtools")

# Install the package from GitHub
devtools::install_github("stephaneguerrier/pempi")

Note that Windows users are assumed that have Rtools installed (if this is not the case, please visit this link).

Example: Austrian COVID-19 survey

In November 2020, a survey sample of n = 2, 287 was collected in Statistics Austria (2020) to test for COVID-19 using PCR-tests. In this study, seventy-two participants were tested positive (i.e., R1 + R3 = 72)), and among these ones, thirty-five (R1 = 35) had reported being tested positive with the official procedure, during the same month. In November, there were 93, 914 declared cases among the official (approximately) 7, 166, 167 inhabitants in Austria (above 16 years old), so that π0 ≈ 1.3105%. For simplicity, we consider a random (unweighted) sampling and assume that the PCR false positive and negative rate as well as the false case positive rate are equal to 0. The data from this study can be obtained as follows:

# Load pempi
library(pempi)

# Austrian data (November 2020)
pi0 = 93914/7166167

# Load data
data("covid19_austria")

# Random sampling
n = nrow(covid19_austria)
R1 = sum(covid19_austria$Y == 1 & covid19_austria$Z == 1)
R2 = sum(covid19_austria$Y == 0 & covid19_austria$Z == 1)
R3 = sum(covid19_austria$Y == 1 & covid19_austria$Z == 0)
R4 = sum(covid19_austria$Y == 0 & covid19_austria$Z == 0)

# Print table
data_mat =c(R1, R2, R3, R4)
names(data_mat) = c("R1", "R2", "R3", "R4")
data_mat
#>   R1   R2   R3   R4 
#>   35    0   37 2218

The survey MLE as well as the conditional MLE and moment estimator proposed in Guerrier et al. (2024) can be computed as follows:

survey_mle(R = R1 + R3, n = n)
#> Method: Survey MLE
#> 
#> Estimated proportion: 3.1441%
#> Standard error      : 0.3647%
#> 
#> Confidence intervals at the 95% level:
#> Asymptotic Approach: 2.4294% - 3.8588%
#> Clopper-Pearson    : 2.4680% - 3.9433%
#> 
#> Assumed measurement error: alpha = 0%, beta = 0% 
#> Sampling: Random

conditional_mle(R1 = R1, R2 = R2, R3 = R3, R4 = R4, pi0 = pi0)
#> Method: Conditional MLE
#> 
#> Estimated proportion: 2.9317%
#> Standard error      : 0.2639%
#> 
#> Confidence interval at the 95% level:
#> Asymptotic Approach: 2.4145% - 3.4489%
#> 
#> Assumed measurement error: alpha  = 0%, beta = 0%,
#>                            alpha0 = 0% 
#> 
#> Estimated false negative rate of the
#> official procedure: beta0 = 55.30%
#> CI at the 95% level: 47.41% - 63.18%
#> 
#> Estimated ascertainment rate: 
#> pi0/pi = 44.70%
#> CI at the 95% level: 36.82% - 52.59%
#> 
#> Sampling: Random

moment_estimator(R3 = R3, n = n, pi0 = pi0)
#> Method: Moment Estimator
#> 
#> Estimated proportion: 2.9262%
#> Standard error      : 0.2635%
#> 
#> Confidence intervals at the 95% level:
#> Asymptotic Approach: 2.4099% - 3.4426%
#> Clopper-Pearson    : 2.4506% - 3.5308%
#> 
#> Assumed measurement error: alpha  = 0%, beta = 0%,
#>                            alpha0 = 0% 
#> 
#> Estimated false negative rate of the
#> official procedure: beta0 = 55.21%
#> CI at the 95% level: 47.31% - 63.12%
#> 
#> Estimated ascertainment rate: 
#> pi0/pi = 44.79%
#> CI at the 95% level: 36.88% - 52.69%
#> 
#> Sampling: Random

Reproducibility

All results, including figures, tables, real data analysis, and simulations from Guerrier et al. (2024), can be reproduced as detailed here: https://stephaneguerrier.github.io/pempi/articles/reproducibility.html.

How to cite 

@Manual{guerrier2024cape,
    title = {{pempi}: Proportion estimation with marginal proxy information},
    author = {Guerrier, S and Kuzmics, C and Victoria-Feser, M.-P.},
    year = {2024},
    note = {R package},
    url = {https://github.com/stephaneguerrier/pempi}
}

License

The license this source code is released under is the GNU AFFERO GENERAL PUBLIC LICENSE (AGPL) v3.0. Please see the LICENSE file for full text. Otherwise, please consult GNU which will provide a synopsis of the restrictions placed upon the code.

References

Guerrier, Stéphane, Christoph Kuzmics, and Maria-Pia Victoria-Feser, “Assessing COVID-19 Prevalence in Austria with Infection Surveys and Case Count Data as Auxiliary Information”, Journal of the American Statistical Association, in press, 2024.

Statistics Austria, “Pravalenz von SARS-CoV-2-Infektionen liegt bei 3,1%”, 2020.