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Date:         Wed, 25 Mar 2009 11:45:24 -0400
Reply-To:     Kevin Viel <citam.sasl@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kevin Viel <citam.sasl@GMAIL.COM>
Subject:      Re: How can I detect any real deviation from a uniform monthly
              distribution?

On Tue, 24 Mar 2009 08:04:12 -0700, Irin later <irinfigvam@YAHOO.COM> wrote:

>I have a file of unique patients who had diagnosis "Depression" during the calendar year. >For each of the patients I have Month of Birth value (1-12). > >I expect seasonal variations in the diagnosis of depression (depending on what was >the month of the birth value). >How can I validate or disprove this hypothesis? How can I detect any real deviation >from a uniform monthly distribution? >? >How to implement it in SAS code? > >Could you, please, give me a hand?

Both Mary and Peter have suggested that you might need controls, as a way to estimate the number of births in a given month among your *study* population. This is the minimum, as numerous and important confounders likely exists. However, if you are willing to (tenuously) assume that births are constant across months, perhaps a stronger argument in a large population, then you might expect an equal distribution of months. I have simulated this below and show one way to test it.

Note that the seasons below are very artificial.

proc plan seed = 1 ; factors P = 144000 ordered M = 1 of 12 / NoPrint ; output out = depmon ; run ;

/* proc freq data = depmon ; tables M ; run ; */

data depmonseason ; set depmon ; select ( M ) ; when ( 1 , 2 , 3 ) Season = "Winter" ; when ( 4 , 5 , 6 ) Season = "Spring" ; when ( 7 , 8 , 9 ) Season = "Summer" ; when ( 10 , 11 , 12 ) Season = "Fall" ; otherwise put M= ; end ; run ;

proc freq data = depmonseason ; tables M Season / chisq ; run ;

Importantly, the following shows that the proportions are compared to each other per say, and not to that expected from N / 12, where N = the sample size. This is unlikely to occur as you might expect at least one birth in each month.

proc freq data = depmonseason ( where = ( M ~ in ( 1 , 2 ))) ; tables M / chisq ; run ;

The next step would be a multiple regression, the type of which would depend on your hypothesis (more births in the winter versus other months, which could be logisitic). You could then control for some covariates of interest. Again, you might be assuming that birth occur equally in each month.

HTH,

Kevin


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