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Estimating population size when duplicates are present

E M Laska1, M Meisner, J A Wanderling

  • 1Nathan S. Kline Institute for Psychiatric Research, Statistical Sciences & Epidemiology Division, Orangeburg, New York 10962, USA.

Statistics in Medicine
|August 15, 1996
PubMed
Summary
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This study introduces a method to accurately count unique individuals served by multiple mental health programs. The developed statistical approach corrects for overcounting, providing a precise estimate of unduplicated patient reach.

Area of Science:

  • Health Services Research
  • Biostatistics
  • Public Health

Background:

  • Mental health programs often report patient numbers, leading to overcounting due to individuals accessing multiple services.
  • Accurate estimation of the unduplicated number of individuals served is crucial for effective health care planning and resource allocation.

Purpose of the Study:

  • To develop and validate a statistical method for estimating the unduplicated number of individuals served by a system of K mental health programs.
  • To provide confidence interval estimators for this unduplicated count.

Main Methods:

  • Utilizing a random sample of service recipients to determine the number of programs (Xi) each individual accessed.
  • Applying an intuitive estimator (Y/X) based on the total reported patients (y) and the average number of programs accessed per individual (E(X)).

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Main Results:

  • The proposed estimator Y/X demonstrates desirable statistical properties for estimating the true number of unique individuals (M).
  • Confidence interval estimators were developed to quantify the uncertainty around the estimated unduplicated count.
  • The method was successfully applied to estimate the unduplicated number of individuals served by New York State mental health programs in 1991.

Conclusions:

  • The developed statistical method effectively addresses overcounting in mental health service utilization data.
  • This approach provides a reliable way for health care planners to determine the true reach of mental health systems.
  • Accurate unduplicated counts are essential for informed decision-making in public mental health service delivery.