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pempi — Proportion Estimation with Marginal Proxy Information

Install 

# CRAN (stable)
install.packages("pempi")

# GitHub (development)
# install.packages("devtools")
devtools::install_github("stephaneguerrier/pempi")

Windows users will need Rtools installed.

A Quick Taste — Austrian COVID-19 survey

In November 2020, Statistics Austria collected a survey sample of n = 2,287 to test for COVID-19 by PCR. 72 participants tested positive in the survey (R1 + R3 = 72); 35 of them (R1 = 35) had also been recorded positive by the official procedure that month. With 93,914 declared cases among ~7,166,167 inhabitants over 16, the official rate is π₀ ≈ 1.31%.

# Load pempi
library(pempi)

# Austrian official rate (November 2020)
pi0 = 93914/7166167

# Bundled real-world dataset
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 alongside the conditional MLE and moment estimator from Guerrier et al. (2024):

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

The conditional MLE and moment estimators correct the survey-only estimate downward (from 3.14% to ~2.93%) by leveraging the auxiliary case-count information — and shrink the standard error by roughly 30%.

Where to Next

📐 Get Started — Methodology The mathematical setup, the four R-counts, and how each estimator corrects the survey-only baseline.
🔬 Reproducibility Reproduce every table, figure, and simulation from the award-winning paper.
🇦🇹 Austrian COVID-19 Survey The bundled real-world dataset (n = 2,287, November 2020) used throughout the package.
📑 How to Cite BibTeX, JASA citation, and DOI for the package and the underlying paper.

Notation note

The notation in Guerrier, Kuzmics & Victoria-Feser (2024) is slightly amended for convenience here. The package uses R1, R2, R3, R4 for the paper’s R11R_{11}, R10R_{10}, R01R_{01}, R00R_{00} respectively.

Citation

If you use this package, please cite both the paper and the package.

Paper

@article{guerrier2024prevalence,
  title   = {Assessing {COVID-19} Prevalence in {Austria} with Infection
             Surveys and Case Count Data as Auxiliary Information},
  author  = {Guerrier, St\'ephane and Kuzmics, Christoph and
             Victoria-Feser, Maria-Pia},
  journal = {Journal of the American Statistical Association},
  volume  = {119},
  number  = {547},
  pages   = {1722--1735},
  year    = {2024},
  doi     = {10.1080/01621459.2024.2313790}
}

Package

@Manual{guerrier2024pempi,
  title  = {{pempi}: Proportion Estimation with Marginal Proxy Information},
  author = {Guerrier, St\'ephane and Kuzmics, Christoph and
            Victoria-Feser, Maria-Pia},
  year   = {2024},
  note   = {R package},
  url    = {https://github.com/stephaneguerrier/pempi}
}

License

This source code is released under the GNU Affero General Public License (AGPL) v3.0. See the LICENSE file or the GNU summary.

References

Guerrier, S., Kuzmics, C., Victoria-Feser, M.-P. (2024). Assessing COVID-19 Prevalence in Austria with Infection Surveys and Case Count Data as Auxiliary Information. Journal of the American Statistical Association, 119(547), 1722–1735. doi:10.1080/01621459.2024.2313790

Statistics Austria. (2020). Prävalenz von SARS-CoV-2-Infektionen liegt bei 3,1%.