PLACE: 1104 Gilman

SPEAKER: Professor Karen Kafadar
                    Department of Mathematics, University of Colorado - Denver

TITLE: Measuring the Effect of Length Biased Sampling
              When the Variable Being Sampled is Unobserved
 

ABSTRACT:

Length biased sampling arises when items are sampled in proportion to their
values on a random variable of interest.  For example, older units may be
more likely to be sampled simply because they have been in service for a
longer period of time.  The effect of this sampling bias on the estimate of
the true population mean is well known when this random variable, say X, is
observable.

A more difficult situation arises when X is not observed, but the outcome
of another random variable, say Y, is observed and is known to be
correlated with X.  This context may arise in an inspection program,
wherein units with longer degradation phases are more likely to surface
during a periodic routine inspection than units with shorter degradation
phases.  The mean lifetime of all units is then a function of the mean of
the length-biased sampled units and the correlation between X and Y.

The importance of this problem arises in evaluating such an inspection
program. The specific context which motivated this research is the
evaluation of a cancer screening program:  the preclinical phase (during
which disease can be screen-detected) corresponds to the degradation phase,
and the point of clinical detection corresponds to the time at which the
need for repair is discovered.  If length biased sampling is ignored, the
estimate of the true population mean is greatly inflated.  We discuss
theoretical as well as practical aspects of estimation of the true
population mean in such situations.

(This work was performed in collaboration with Philip C. Prorok at
the National Cancer Institute.)

COFFEE:  3:45 p.m., 104 Snedecor Hall