Accounting for Time Limits In Study

[Pavel314]

I seem to recall from a stat class (long ago and far away) that there is a
way to account for events which may happen after a study is completed; any
clues will be appreciated. Here's the problem:

Patients come to an urgent care center for treatment of various complaints.
After being patched up or given a pill, many of them receive a referral to
the hospital which operates the urgent care center for further care or
diagnosis. They could be referred to many specialties; cardiology,
radiology, podiatry, etc. The object of the study is to determine what
percentage of referred patients actually show up at the hospital within 60
days of the referral from the urgent care center. A first pass at the raw
data from this study and similar studies done in the past indicates that 60
days is a generous margin to assume cause-and-effect between the referral
and the hospital visit, although further analysis may change the window.

The problem is that we have data from when the clinic opened in December
through May for both the clinic and the hospital. But for a patient who gets
a referral in May, the 60-day window extends somewhere into July, for which
we have no data. We could just consider referrals made through March,
leaving the downstream window complete through May, but I hate to ignore all
of those April and May referrals, most of which probably showed up in April
or May.

I considered Cox Proportional Hazards and the unadjusted Kaplan-Meiers,
neither of which I've used in this century or in any real life applications,
but neither seems to fit. The Poisson regression looks promising; I'll see
how that works out tomorrow.

Any ideas on the best way to proceed?

Thanks,

Paul