Date: Wed, 2 Jun 2004 09:36:16 -0700
Reply-To: Dale McLerran <stringplayer_2@YAHOO.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <stringplayer_2@YAHOO.COM>
Subject: Re: The mixed model with spatial correlated data
In-Reply-To: <c3749ef1.0406020221.5339d464@posting.google.com>
Content-Type: text/plain; charset=us-ascii
--- Marine Castaing <castaing@IARC.FR> wrote:
> Hi all of sas group!
>
> It is the first time I write to your group which helps me a lot,
> only
> by reading until now. I have some data of cancer incidences in
> several
> countries of Europe (not the federal one, for sure), 38 exactly. The
> aim is to assess the association between pancreas and kidney cancer
> incidences adjusting for lung cancer incidence (because of the strong
> association there is between pancreas and lung). So I have such data
>
> country1 pancreas incidence kidney inc. lung inc.
> country2 idem idem idem
> country3.....
>
>
> I fitted a mixed model with pancreas incidence as dependant variable
> and kidney and lung incidences as fixed effects. We have not more
> variables in the data set. Then I created a variable 'group' which
> pools nearby countries that might have the same error measurements of
> cancer incidences. I used this variable to take into account the
> spatial correlation we suspect and using SAS I fitted the following
> model:
>
> proc mixed data=globocan3 /*method=ml*/ covtest;
> class group;
> model paf=kif luf /s cl outpred=p;
> repeated/sub=group type=sp(exp)(lat lon) r rcorr;/*lat and lon are
> latitude and longitude and I used those of capitals of the countries
> I
> have so that spatial dependence can be measured by distances between
> countries and in practice distances between capitals (I did not find
> coordinates of centroids of countries on Internet)*/
> run;
When you artificially create groups in this manner, then you have
a problem where adjacent countries fall into different groups.
Let's say that you had a group which was eastern European countries
including of Poland, Czech Republic, Slovakia, Hungary, ... and
another group of western European countries including Germany,
Austria, and others. Now, Germany is adjacent to both Poland and
the Czech Republic while Austria is adjacent to the Czech Republic
and Hungary and also very close to Slovakia. But your model would
imply that there should be no spatial correlation between Germany
and Poland or between Austria and Hungary or between any of those
other countries which are close to each other.
I would be highly critical of such a model. Rather, if you believe
that there are spatial covariances at play, then you should not
arbitrarily fix the covariance between some adjacent countries to
zero. It is not well documented that the MIXED procedure can fit
a model which allows the entire error vector to be treated as the
realization of the errors of a single subject. That is, it is
possible to fit your spatial covariance structure without arbitrarily
separating countries into groups. In order to indicate a single
subject, you must specify SUBJECT=INTERCEPT on your REPEATED
statement. Thus, a spatial covariance structure for all of Europe
would be achieved by specifying:
proc mixed data=globocan3 /*method=ml*/ covtest;
model paf=kif luf /s cl outpred=p;
repeated/sub=intercept type=sp(exp)(lat lon) r rcorr;
run;
Now, there might be cultural/economic/technological differences
between countries in your different groups which affect pancreas,
kidney, and lung incidence rates. Your group variable might
be useful as a fixed effect in accounting for an overall increase
in the pancreas cancer incidence rate without a corresponding
increase in the kidney and lung cancer incidence rates in different
regions of Europe. Thus, you might want to fit the model
proc mixed data=globocan3 /*method=ml*/ covtest;
class group;
model paf=kif luf group /s cl outpred=p;
repeated/sub=intercept type=sp(exp)(lat lon) r rcorr;
run;
>
> Right now, I have 2 questions about it:
> - Can I fit such a model given that these data are not individual
> data
> but data of countries?
Yes, that is permissable.
> - Can we decide to choose the ML method rather than the REML one if
> the AIC criteria is better?
No, you cannot compare the AIC from ML with the AIC from REML. I
would advise just staying with the REML estimates.
> Thank you for your help!
>
> Marine
=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------
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