Capture-Recapture — STEP-T1D

Capture-Recapture Analysis Tool

Capture-recapture (CRC) methods estimate the true number of disease cases in a population when only partial registries are available. This technique, originally developed for wildlife population estimation, is now widely used in epidemiology and public health surveillance to assess underreporting and estimate disease burden.

Why Use Capture-Recapture?

Health information systems rarely capture every case. Hospital records, laboratory databases, pharmacy dispensation logs, and specialist registries each cover only a fraction of true cases. By comparing overlaps between these independent sources, CRC methods estimate how many cases were missed by all sources.

Lincoln-Petersen Chapman Estimator

For two independent sources, the Chapman estimator provides a nearly unbiased estimate of the total population size:

\[\hat{N} = \frac{(n_1 + 1)(n_2 + 1)}{m + 1} - 1\]

Where:

  • n₁ — number of individuals captured in source 1
  • n₂ — number of individuals captured in source 2
  • m — number of individuals captured in both sources (overlap)
  • N̂ — estimated total population size

The variance and 95% confidence interval are:

\[\text{Var}(\hat{N}) = \frac{(n_1+1)(n_2+1)(n_1-m)(n_2-m)}{(m+1)^2(m+2)}\] \[\text{CI}_{95\%} = \hat{N} \pm 1.96 \times \sqrt{\text{Var}(\hat{N})}\]

Three or More Sources

With three or more sources, log-linear models account for dependencies between sources. The tool fits six candidate models — M₀, Mt, Mh, Mth, Mb, and Mbh — and selects the best model by minimum BIC (Bayesian Information Criterion).

References

  • Lincoln-Petersen estimator: Petersen, C. G. J. (1896). The yearly immigration of young plaice into the Limfjord from the German Sea. Report of the Danish Biological Station, 6, 1–48. — Lincoln, F. C. (1930). Calculating waterfowl abundance on the basis of banding returns. USDA Circular, 118, 1–4.
  • Chapman estimator: Chapman, D. G. (1951). Some properties of the hypergeometric distribution with applications to zoological sample censuses. University of California Publications in Statistics, 1(7), 131–160.
  • Log-linear models for CRC: Fienberg, S. E. (1972). The multiple recapture census for closed populations and incomplete 2k contingency tables. Biometrika, 59(3), 591–603. — Cormack, R. M. (1989). Log-linear models for capture-recapture. Biometrics, 45(2), 395–413.
  • M0, Mt, Mh, Mth, Mb, Mbh models: Otis, D. L., Burnham, K. P., White, G. C., & Anderson, D. R. (1978). Statistical inference from capture data on closed animal populations. Wildlife Monographs, 62, 3–135. — Pollock, K. H. (1982). A capture-recapture design robust to unequal probability of capture. The Journal of Wildlife Management, 46(3), 752–757.
  • Rcapture R package: Baillargeon, S., & Rivest, L.-P. (2007). Rcapture: Loglinear models for capture-recapture in R. Journal of Statistical Software, 19(5), 1–31.
  • Epidemiological applications: Chao, A., Tsay, P. K., Lin, S. H., Shau, W. Y., & Chao, D. Y. (2001). The applications of capture-recapture models to epidemiological data. Statistics in Medicine, 20(20), 3123–3157.

Example Data

Download a sample dataset to explore the tool. The data format requires one row per individual with a unique id column. Each source column uses 1 if the individual was captured in that source and 0 if not. At least two source columns must be present.

Download Example XLSX

How to Cite

Pérez Bedoya, J. P., Pérez Aguirre, C. A., Barengo, N. C., Lacalle Remigio, J. R., & Diaz Valencia, P. A. (2026). Incidence of Type 1 Diabetes in the Metropolitan Area of the Aburrá Valley, Colombia, 2015–2024: Analysis of the STEP-T1D Study.

Disclaimer

No data collection: This tool runs entirely in your browser. No data is transmitted, stored, or collected by the tool — all computations are performed locally on your computer.

No responsibility: The authors are not responsible for any interpretations, decisions, or conclusions drawn from the results produced by this tool. Users should verify results independently and seek appropriate methodological guidance.

Contact

Juan Pablo Pérez Bedoya: juan.perez42@udea.edu.co
Carlos Andrés Pérez-Aguirre: caaperezag@unal.edu.co

Estimated N
—
Run analysis to see estimate
Observed
—
Unique individuals in data
Hidden
—
Est. unobserved cases
Prevalence / Incidence
—
Per 10,000 inhabitants (see Assumptions)
Source Overlap Visualization
Select 2 or more sources and run analysis to see the overlap diagram
Model Comparison
Select 3 or more sources to compare log-linear models
Intersection Frequency Table
Select 2 or more sources and run analysis to see intersection frequencies
Data PreviewFirst 15 rows
No data loaded

CRC Assumptions

All capture-recapture estimators rely on four key assumptions. Violations can bias estimates, so understanding them is essential for valid inference.

1. Closed Population

The population must remain constant during the study period — no births, deaths, immigration, or emigration. In epidemiological applications, this means the at-risk population should be stable and case definitions must be time-aligned across data sources.

2. Perfect Matching

Individuals captured in multiple sources must be correctly linked. This requires a reliable unique identifier (e.g., national ID number, medical record number) or high-quality probabilistic record linkage. Mismatches inflate the number of "unique" individuals and underestimate N.

3. Source Independence (for 2-source methods)

The Lincoln-Petersen estimator assumes the two sources are independent — capture in one source does not affect the probability of capture in the other. When sources are positively dependent (e.g., hospital and specialist records), the estimator underestimates the hidden population. When negatively dependent, it overestimates. Using three or more sources with log-linear models allows modeling dependencies.

4. Homogeneous Capture Probabilities

Within each source, all individuals should have the same probability of being captured. If some individuals are more likely to appear in a registry (e.g., severe cases, urban residents), the estimator will be biased. Models Mh and Mth account for individual heterogeneity.

Practical Recommendations

  • Use at least 3 sources when possible — this allows fitting models that relax the independence assumption
  • Compare multiple models (M₀, Mt, Mh, Mth, Mb, Mbh) and prefer the one with lowest BIC
  • If model selection yields very different N̂ values, conduct sensitivity analysis
  • Report confidence intervals to communicate uncertainty
  • If possible, validate estimates against an independent data source or expert judgment

Interpretation: Incidence or Prevalence?

Whether the estimated N̂ represents incidence or prevalence depends on the study design, not on the estimator itself. If the data sources capture newly diagnosed cases over a defined period (e.g., one year of new diagnoses), the estimate reflects incidence. If the data sources capture existing cases at a given point or period, the estimate reflects prevalence. The researcher is responsible for interpreting the results according to their study design and case definitions.