Using diagcounts

Motivation

Diagnostic accuracy studies frequently report summary measures such as sensitivity, specificity, predictive values, and prevalence, but omit the underlying 2×2 table counts (true positives, false negatives, false positives, and true negatives). These counts are often required for downstream analyses, including meta-analysis, decision modeling, and health economic evaluation.

The diagcounts package implements a system of linear equations to recover these unreported counts when a sufficient set of accuracy measures is available.

Basic usage

The primary function is derive_counts(). Users supply the total sample size and any combination of reported diagnostic accuracy measures that uniquely identify the underlying 2×2 table.

library(diagcounts)

res <- derive_counts(
  n = 105,
  sensitivity = 0.6,
  specificity = 0.893,
  prevalence = 0.733
)

res

The function returns integer-valued counts:

as.table(res)

Alternative combinations of inputs

Any identifiable combination of accuracy measures may be used. For example, counts can also be recovered using predictive values:

derive_counts(
  n = 200,
  sensitivity = 0.75,
  ppv = 0.82,
  npv = 0.70
)

Internally, the package constructs and solves a system of linear equations corresponding to the supplied measures.

Infeasible systems

If the supplied measures do not uniquely identify a valid 2×2 table, or if the resulting system is mathematically inconsistent, derive_counts() will stop with an error:

# Not enough information
# derive_counts(n = 100, sensitivity = 0.8)

This behavior is intentional and ensures that returned counts are both mathematically and epidemiologically valid.

Discussion

The methods implemented in diagcounts focus on settings in which the system of equations is exactly identified and yields a unique integer solution. Extensions to partially identified systems and bound-based solutions, as discussed in the accompanying paper, may be considered in future versions of the package.

References

Xie X, Wang M, Antony J, Vandersluis S, Kabali CB (2025). System of Linear Equations to Derive Unreported Test Accuracy Counts. Statistics in Medicine. https://doi.org/10.1002/sim.70336