From TCHUR@doh.health.nsw.gov.au Tue Dec 28 23:47:45 1999 Received: from mxu1.u.washington.edu (mxu1.u.washington.edu [140.142.32.8]) by lists.u.washington.edu (8.9.3+UW99.09/8.9.3+UW99.09) with ESMTP id XAA35764 for ; Tue, 28 Dec 1999 23:47:44 -0800 Received: from burnia.dmz.health.nsw.gov.au (burnia.dmz.health.nsw.gov.au [203.5.110.252]) by mxu1.u.washington.edu (8.9.3+UW99.09/8.9.3+UW99.09) with SMTP id XAA28163 for ; Tue, 28 Dec 1999 23:47:42 -0800 Received: by burnia.dmz.health.nsw.gov.au; (5.65v4.0/1.3/10May95) id AA12036; Wed, 29 Dec 1999 18:47:36 +1100 Received: from doh_email (doh-email.ccf.health.nsw.gov.au [203.5.108.57]) by health.nsw.gov.au (PMDF V5.2-29 #30386) with SMTP id <01JK31DXS4ZG000LWJ@health.nsw.gov.au> for waphgis@u.washington.edu; Wed, 29 Dec 1999 18:47:30 AUSTRALIA/NSW Received: from DOH_HUB-Message_Server by doh_email with Novell_GroupWise; Wed, 29 Dec 1999 18:47:30 +1100 Date: Wed, 29 Dec 1999 18:47:22 +1100 From: Tim CHURCHES Subject: Re: small area CIs with hospitalization data To: Steven.Macdonald@DOH.WA.GOV, waphgis@u.washington.edu Message-Id: Mime-Version: 1.0 X-Mailer: Novell GroupWise 5.5.2 Content-Type: text/plain; charset=US-ASCII Content-Disposition: inline Content-Transfer-Encoding: quoted-printable Steve, A few suggestions, but no packaged solutions :-( You could fit a log-linear model to the count and population data (using a = Poisson link functions) and then apply a scaling factor to adjust for the = extra-Poisson variation. You could fit a mixed effects model in which the random effects accounts = for the extra variation you are observing. This is similar equivalent to = performing an empirical Bayesian adjustment - there is a moderate literature on = empirical Bayesian models (and my favourite, constrained empirical = Bayesian models). You could fit a fully Bayesian model using BUGS or WinBUGS. No easy answers, I'm afraid. Tim Churches >>> "Macdonald, Steven" 12/24/99 06:21am >>> Colleagues - Here is a query for the statistically-minded. =20 If you are a data analyst looking at the magnitude of a problem ("public health burden") from a particular condition using hospitalization data for = a small area, you calculate hospitalization rates with hospital discharge events in the numerator, and census-based population estimates in the denominator. A preferred method is to calculate confidence intervals = around the rate for the small area, and compare it to a standard, such as a = target from Healthy People 2000, or the rate for a whole state. =20 If the events were statistically unique, as they are with death data, = you'd use the Poisson distribution as the basis for the calculation of the CI. However, in this dataset individuals can be hospitalized multiple times, = and it is at least theoretically possible for there to be more events in the numerator than there are persons in the denominator. Here we have "extra-Poisson" variation. This means that the variance estimates from Poisson are too small and the resultant CIs too narrow.=20 It is not appropriate for the solution to involve "un-duplication" of the dataset, since the purpose of the analysis is to estimate the public = health burden, and each hospitalization is an adverse event which we would like = to prevent if possible.=20 An alternate method for calculation of the CI might be to use the negative binomial distribution. However, I cannot find any description of exactly how to do this anywhere in any text which I own (I do have quite a few). And, it would seem that in order to apply that distribution, you would = need to know both the number of events and the ratio of events to persons (or perhaps even the frequency distribution of repeat hospitalizations); if = the latter is unknown, it may not be possible to use this distribution. =20 Further, it would be useful to know at what point this moves from being merely an interesting academic problem to one with real consequences: is = it possible to establish a threshold, perhaps based on the combination of the number of events and the ratio of events to persons, beyond which standard distributions (Poisson/binomial/normal) are adequate approximations? =20 In the absence of a method for calculation of negative-binomial CIs, I = have recommended that data analysts adjust their alpha levels when they suspect extra-Poisson variation: use Poisson 99% CIs instead of Poisson 95% CIs, = for example. =20 However, I'd prefer a better solution. --Steve Steven C Macdonald PhD, MPH Office of Epidemiology Washington State Department of Health phone 360-236-4253 fax 360-236-4245 email NICE webpage **This message may be confidential. If you received it by mistake, please notify the sender and destroy the message. All non-confidential messages = to and from the Department of Health may be disclosed to the public.** [Note: DOH has switched to a new email software program. You'll notice that my "signature" above shows a new email address; the old one will continue to work for some time, I'm told....] .