Estimating Population Size and the Number of Duplicates on Two Lists
Based only on Birth-dates

Co-Principal Investigators: Eugene Laska, Ph.D., Morris Meisner, Ph.D, Carole Siegel, Ph.D., Joseph Wanderling, MA.

PROJECT GOALS

Methods for statistically estimating the size of a population are required when no simple way exists for full enumeration. The approaches that have received the most attention are capture-recapture methods. For two lists, critical to the classical method is an accurate count of the number of duplicates, the number of individuals appearing on both lists. To obtain the number of duplicates, individuals on the two lists need to be matched, and not uncommonly, identifying information on individuals on one or the other or both lists is either incomplete or in error. We consider a common situation in mental health in which confidentiality constraints limit the information available to the date of birth of each individual on each list. In the previous project period, we developed a method to estimate the number of individuals on both lists. The method was based on the number of individuals on one list whose birth-dates coincide with a birth date of an individual on the other list. This statistic enables calculation of an estimate of the number in common to both lists. We extended the result by introducing another estimate of duplicates, incorporating the sample distribution of birth dates from both lists. These solutions have intrinsic interest and can be used to estimate duplication rates as well as the size of the total population.

Our specific aims are to:

(1) develop a method to estimate the number of individuals who are on both lists. The solution to this estimation problem, which has intrinsic interest in its own right, can be used to
(2) develop a method for estimating the size of the total population.

RESEARCH ACTIVITIES AND RESULTS

Using the sample distributions of observed birth dates and conditioning on the size of each list we were able to write the likelihood of the observations. From this, the maximum likelihood estimates of the size of the population, the probabilities of appearing on each list and the asymptotic variances of these estimators can be obtained numerically.

POLICY IMPLICATIONS

The need for protection of the privacy of individuals may prevent sharing identifying information, yet it is important for the payers and managers of mental health systems to be aware of the number of individuals who use multiple resources, as well as the number in their catchment area who are mentally ill. Without compromising their confidentiality obligations, limited information such as gender, county of residence and date of birth of each individual served by their respective system may be provided enabling the application of the above methods.

PLANS

In New York State, there are a multitude of mental health services providers including two large systems of care who deliver mental health services to veterans. One is the veterans’ administration (VA), and the second is an amalgam of state, county and local mental health agencies under the auspices of the NYSOMH. These agencies provide care to the general population, including many veterans eligible for service from the VA. This information enables an estimate of the number served by both, which in turn permits an estimate of the total population size. We intend to apply the newly developed methods to the NY state data. (See Veterans’ Study: Systems Integration Core).

A packaged program that implements these methods will be made available on this web site.

Publication

Laska EM, Meisner M, Wanderling J., Siegel C. (2003). Estimating duplication rate and population size based only on birth dates. Statistics in Medicine, 22(21).