sas >> Zero Inflated Poisson Models in SAS (repeated measures)

by afdbn » Wed, 18 Feb 2004 17:23:37 GMT

Hi,

I am looking for a reference or a hint as to where I could find more
information regarding ZIP models using SAS. I am interested in using them
in a repeated measures type setting. I found a SAS-L posting
(http://listserv.uga.edu/cgi-bin/wa?A2=ind0205B&L=sas-l&P=R12947) that got
me headed in the right direction but I'm still searching for a way to deal
with repeated measures designs.
Anyone have a suggestion?


David Neal


sas >> Zero Inflated Poisson Models in SAS (repeated measures)

by stringplayer_2 » Thu, 19 Feb 2004 00:56:58 GMT


David,

You need to tell us a little more about your design. Are the
repeats observed at common times across subjects? How many
repeated measures per subject do you have? Correlations induced
by the repeated measures may be handled through appropriate
specification of RANDOM effects. It is that appropriate
specification part which can sometimes be tricky to specify.
That is why more detail is required.

Dale





=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: XXXX@XXXXX.COM
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

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sas >> Zero Inflated Poisson Models in SAS (repeated measures)

by afdbn » Thu, 19 Feb 2004 04:34:57 GMT

Dale,

The design involves three treatment groups that were measured pre, post,
follow-up 1(3month), follow-up 2(6 month), follow-up 3(12 month). There
were literally hundreds of variables collected on each subject for each time
period.(I guess they were going for the shotgun effect) Several of the
variables involve counts that have high frequencies of zeros. We are trying
to narrow the focus a bit before we start any sort of an analysis so I
expect to be dealing with a smaller subset of variables. I'm coming into
the project on the back end so I'm not quite up to speed on all the oddities
of the data but my initial impression is that a ZIP model would be an
appropriate choice.

David

-----Original Message-----
From: SAS(r) Discussion [mailto: XXXX@XXXXX.COM ] On Behalf Of Dale
McLerran
Sent: Wednesday, February 18, 2004 7:57 AM
To: XXXX@XXXXX.COM
Subject: Re: Zero Inflated Poisson Models in SAS (repeated measures)

David,

You need to tell us a little more about your design. Are the
repeats observed at common times across subjects? How many
repeated measures per subject do you have? Correlations induced
by the repeated measures may be handled through appropriate
specification of RANDOM effects. It is that appropriate
specification part which can sometimes be tricky to specify.
That is why more detail is required.

Dale





=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: XXXX@XXXXX.COM
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

__________________________________
Do you Yahoo!?
Yahoo! Mail SpamGuard - Read only the mail you want.
http://antispam.yahoo.com/tools


Zero Inflated Poisson Models in SAS (repeated measures)

by Jay Weedon » Thu, 19 Feb 2004 04:59:17 GMT





It might well be, but if the non-zero observations tend mostly to be
small frequencies (1s & 2s) it might be methodologically simpler to
dichotomize the outcomes as 0 vs >0, and going with a generalized
mixed linear model or a generalized estimating equations model. Do you
have a lot of missing data?

How you're going to deal with hundreds of outcomes is a different
problem!

JW


Zero Inflated Poisson Models in SAS (repeated measures)

by stringplayer_2 » Thu, 19 Feb 2004 06:24:01 GMT

avid,

I am glad to see that repeated measures were obtained at fixed
time points. Since the observations are not equally spaced and
include observations in different phases of the experimental
design (pre-treatment, post-treatment, and follow-up measures),
I would think that either of two different models would be
appropriate:

1) Each participant has a subject-specific stochastic element
affecting the probability of having a zero value as well as a
stochastic element affecting the expectation of the Poisson
component. That is, the subject-specific responses are time
invariant. The subject-specific effects on the zero-inflation
probability model may or may not be correlated with the subject-
specific effect that operates on the Poisson expectation.

2) There are different subject-specific effects for each of the
five measurement periods, but there is some positive covariance
structure to the five subject-specific effects. Again, one
might want to consider a model in which the zero-inflation
random effects are independent of the expectation random effects
as well as a model in which the zero-inflation random effects
are correlated with the random effects operating on the
Poisson expectation.


Before going into the code for modeling the random effects which
would be appropriate for this repeated measures design, let me
first point you to a more complete discussion of ZIP models than
the posting which you found in the archives. The more complete
posting is also in the archives at

http://listserv.uga.edu/cgi-bin/wa?A2=ind0208A&L=sas-l&P=R16978&D=0

Now, when you look at that posting, you see that we have two
eta's, one which models the zero-inflation probability and one
which models the Poisson expectation. You probably should add
random effects to each of these linear terms. Time invariant
random effects would be modeled as

proc nlmixed data=mydata;
eta_prob = b0_prob + b1_prob*x1 + b2_prob*x2;
eta_prob = eta_prob + g0_prob;
p_0 = exp(eta_prob)/(1 + exp(eta_prob));

eta_lambda = b0_lambda + b1_lambda*x1 + b2_lambda*x2;
eta_lambda = eta_lambda + g0_lambda;
lambda = exp(eta_lambda);

/* likelihood structure for ZIP. Note that we cannot generate */
/* the log likelihood for the zero response values directly. We */
/* must generate the likelihood and then take the logarithm due */
/* to the additive nature of the zero likelihood. */
if y=0 then loglike = log(p_0 + (1-p_0)*exp(-lambda));
else loglike = log(1-p_0) + y*log(lambda) -lambda - lgamma(y+1);

model y ~ general(loglike);
random g0_prob g0_lambda ~
normal([0,0],
[exp(2*log_Vprob),
rho*exp(log_Vprob)*exp(log_Vlambda),
exp(2*log_Vlambda)]) subject=subject;

Here I have modeled a nonzero covariance between the zero-
inflation random effect and the Poisson expectation random effect.
If you think that these two terms should be uncorrelated, then
you would just change the random statement to

random g0_prob g0_lambda ~
normal([0,0],
[exp(2*log_Vprob),
0,
exp(2*log_Vlambda)]) subject=subject;


Now, if you believe that the subject-specific stochastic elements
vary over time, then you would need to add time-specific random
effects to the fixed effect portion of your model and model the
covariance structure for 10 random effects as follows:

Zero Inflated Poisson Models in SAS (repeated measures)

by afdbn » Thu, 19 Feb 2004 06:34:20 GMT

hank you Dale, this should get me going in the right direction. I
appreciate your time.

Thanks again

David

-----Original Message-----
From: Dale McLerran [mailto: XXXX@XXXXX.COM ]
Sent: Wednesday, February 18, 2004 1:24 PM
To: David Neal; XXXX@XXXXX.COM
Subject: Re: Zero Inflated Poisson Models in SAS (repeated measures)

David,

I am glad to see that repeated measures were obtained at fixed
time points. Since the observations are not equally spaced and
include observations in different phases of the experimental
design (pre-treatment, post-treatment, and follow-up measures),
I would think that either of two different models would be
appropriate:

1) Each participant has a subject-specific stochastic element
affecting the probability of having a zero value as well as a
stochastic element affecting the expectation of the Poisson
component. That is, the subject-specific responses are time
invariant. The subject-specific effects on the zero-inflation
probability model may or may not be correlated with the subject-
specific effect that operates on the Poisson expectation.

2) There are different subject-specific effects for each of the
five measurement periods, but there is some positive covariance
structure to the five subject-specific effects. Again, one
might want to consider a model in which the zero-inflation
random effects are independent of the expectation random effects
as well as a model in which the zero-inflation random effects
are correlated with the random effects operating on the
Poisson expectation.


Before going into the code for modeling the random effects which
would be appropriate for this repeated measures design, let me
first point you to a more complete discussion of ZIP models than
the posting which you found in the archives. The more complete
posting is also in the archives at

http://listserv.uga.edu/cgi-bin/wa?A2=ind0208A&L=sas-l&P=R16978&D=0

Now, when you look at that posting, you see that we have two
eta's, one which models the zero-inflation probability and one
which models the Poisson expectation. You probably should add
random effects to each of these linear terms. Time invariant
random effects would be modeled as

proc nlmixed data=mydata;
eta_prob = b0_prob + b1_prob*x1 + b2_prob*x2;
eta_prob = eta_prob + g0_prob;
p_0 = exp(eta_prob)/(1 + exp(eta_prob));

eta_lambda = b0_lambda + b1_lambda*x1 + b2_lambda*x2;
eta_lambda = eta_lambda + g0_lambda;
lambda = exp(eta_lambda);

/* likelihood structure for ZIP. Note that we cannot generate */
/* the log likelihood for the zero response values directly. We */
/* must generate the likelihood and then take the logarithm due */
/* to the additive nature of the zero likelihood. */
if y=0 then loglike = log(p_0 + (1-p_0)*exp(-lambda));
else loglike = log(1-p_0) + y*log(lambda) -lambda - lgamma(y+1);

model y ~ general(loglike);
random g0_prob g0_lambda ~
normal([0,0],
[exp(2*log_Vprob),
rho*exp(log_Vprob)*exp(log_Vlambda),
exp(2*log_Vlambda)]) subject=subject;

Here I have modeled a nonzero covariance between the zero-
inflation random effect and the Poisson expectation random effect.
If you think that these two terms should be uncorrelated, then
you would just change the random statement to

random g0_prob g0_lambda ~
normal([0,0],
[exp(2*l

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