**Date:** Wed, 5 May 2010 17:33:45 -0400
**Reply-To:** Sigurd Hermansen <HERMANS1@WESTAT.COM>
**Sender:** "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
**From:** Sigurd Hermansen <HERMANS1@WESTAT.COM>
**Subject:** Re: Analyzing trend in Surveillance Data
**In-Reply-To:** <201005051304.o45AkruH027126@malibu.cc.uga.edu>
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I won't try to speak for the original poster of the questions, but will agree with you and Steve: the observations for one year would be unlikely to be independent of observations for prior years. What this means for tests of differences in means and homogeneity of variances seems difficult to assess.

A strong trend would show up clearly in five annual observations in a sample of this size. The problem with serial dependence of annual observations has to do more with the idea that shocks (dramatic events) in one year do not become realized immediately in observations in that time interval but carry over to subsequent intervals of time. By the time an observer recognizes an increasing trend in an outcome measure, the event that caused the increase may have occurred one or more time intervals earlier.

Heterogeneity in variances could lead to underestimates of estimation errors. The numbers of observations in this case should make confidence intervals narrow enough on one end. Underestimates of confidence intervals would likely be the result of the asymmetric distribution of a relatively rare event. Very small rates of errors in observations of one outcome value will in binary outcomes spill over into the other outcome value. Also, a very small rate of missing outcome values may leave missing values outnumbering the rare outcome value.

I don't see a major downside to pooling these annual observations into, say, an estimate of five-year incidence. The chisq test result seems irrelevant. One might also find a chisq of 1.84 for differences in annual numbers of samples of Hawaiian beach water containing ice as detected in 500K samples per year.
S

-----Original Message-----
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of SUBSCRIBE SAS-L JingJu11 S
Sent: Wednesday, May 05, 2010 9:04 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: Re: Analyzing trend in Surveillance Data

I thought this was a huge data set. The validity for ChiSq test may be
damaged by the fact that the observations among years are not independent
(are they?).