Estimating
an Annualized Number of Clients
Receiving Service from a One Week Survey Investigators:
Eugene Laska, PhD, Morris Meisner, PhD,, Carole Siegel, PhD
Goals Laska, Meisner and Siegel developed a method (referred to below as EST)
designed to estimate the distinct number of individuals receiving service
from a program in a K week period. EST is based on information collected from
attendees, or a sample of attendees, during a survey week. The data collected
for each client in the survey is the number of weeks since the previous service.
The EST annualization procedure produces a Maximum Likelihood Estimate and
a Confidence Interval for the annualized population size. The procedure is
based on a statistical model with the following two assumptions. The first
is that the probability that a randomly chosen client receives a service in
the survey week is the average of the probabilities of coming in any of the
preceding K-1 weeks. The second is that, for k = 1,2,...,K, the probability
of coming in the survey week after an absence of k previous weeks is the average
of the probabilities of two successive visits that are k weeks apart throughout
the year. Thus the week chosen for the survey should be "typical"
of visit patterns as they occur throughout the K week period. A formal derivation
of the method appears in Laska, Meisner and Siegel, BIOMETRICS,1988,
44:461-472. Also see BIOMETRICS,1989, 45:1347 for corrections to data
in the example.
Computer Programs The above procedure for computing the annualized estimate has been programmed
in SAS and in SPSS. To download these programs, click on the appropriate selection:
In both programs the period of interest is K = 52, so that the number of weeks
since last service can take values from 1 to 52. To download these
programs, click on the appropriate selection:
