longitudinal with 2 time points
Hi Marc, thanks for your comments. Yes, I am debating between the 2 models as
well.
The first model doesnot have a "time" variable, and there is only 1 level of
nesting: arm within subject. I think the syntax for nesting is (1|subject /
arm) instead of (1|arm/subject).
The 2nd model certainly have a different layout of data with a "time" variable.
It has 2-level nesting: arm within subject within time, so the syntax should
(1|time/subject/arm)?
Now I have a little confusion on how to define the nesting here. Can I define it
as arm within time within subject instead? so the syntax would be
(1|arm/time/subject)? The reason I am thinking of this way is: each subject was
measured at 2 time points (0 & 4), at each time point, measured twice at 2 arms
(left & right).
What is the simplest way to define nesting structure? any principles that we
should follow? Sometimes I feel I can use different nesting structures as they
all sound reasonable to me.
Really wish someone can chime in and share their thoughts.
John
----- Original Message ----
From: Marc Schwartz <marc_schwartz at me.com>
To: array chip <arrayprofile at yahoo.com>
Cc: r-sig-mixed-models at r-project.org
Sent: Tue, August 24, 2010 11:55:36 AM
Subject: Re: [R-sig-ME] longitudinal with 2 time points
Hi John,
Since we have crossed the threshold into mixed models, I am going to provide
some comments, but (notably because I have not used lmer, although I attended
Doug's class a few years ago at useR), will defer to and solicit comments from
the lmer experts on the list.
First, I am not sure, unless we restate the model where Glucose is the response
variable and Time is a covariate, that using Time in the random effects term
make sense. But I could be wrong.
If we stay with and extend the ANCOVA style approach, then I might envision
something like:
lmer(wk4.glucose ~ baseline.glucose + treatment + gender + age +
(1 | arm / subject))
where the random effect term expresses the nesting of arm within subject. I am
also presuming that you are not interested in arm as a main effect. So we are
still concerned with the other main effects as before, but now consider the
variation in the multiple measurements of glucose from each arm within each
subject.
If you restate the model as I noted above, then perhaps:
lmer(glucose ~ time + treatment + gender + age +
(1 | arm / subject / time))
might make sense. From a review of the archives, it would seem that a
multi-level nesting is permitted in lmer formulae random effects terms, so this
would reflect the nesting of arm, within subject, within time. The
interpretation of this model is of course, going to be different than the ANCOVA
based approach above.
Hopefully, this might at least provide a starting point for further discussion
and others with greater expertise will chime in.
Regards,
Marc
P.S. Note that I trimmed some of the thread below, to conserve space...
On Aug 24, 2010, at 3:02 AM, array chip wrote:
Hi Marc, I have to admit that I didn't get a chance to carefully read the article before my previous reply. So I want to wait till now to respond after finally I got a
chance to read the article. Thanks for your excellent explanation below. I agree that the coefficient for treatment is estimating the extent of the difference between treatment and control in the CHANGE of glucose in week 4 from
baseline.
Now my dataset becomes a little bt more complicated: each glucose testing was done twice (blood was draw from left arm and right arm and tested separately. So for each patient, on each time point, there are 2 measurements (from left and right arm separately). So I think I should now include factor "arm" as a random effect: lmer(wk4.glucose ~ baseline.glucose + treatment + gender + age+ (1|subject/time)) What do you think of this model specification? Adiitionally, since I am using mixed model now, if I code a new variable ?time? (either 0 or 4) and new response variable ?y?, how do I specify a mixed model with 2 random effects, one with respect to ?time? variable (2 time points per subject per arm), the other with respect to ?arm? variable (2 arms per subject
per time point)? Thanks a lot! John ----- Original Message ---- From: Marc Schwartz <marc_schwartz at me.com> To: array chip <arrayprofile at yahoo.com> Cc: r-sig-mixed-models at r-project.org Sent: Fri, August 13, 2010 7:24:59 AM Subject: Re: [R-sig-ME] longitudinal with 2 time points John, That you are asking this question indicates that either you have yet to read the article or that you need to re-read it, as you have not comprehended the content. The beta coefficient for treatment IS the difference in mean glucose change between baseline and 4 weeks **attributable to treatment**, after adjusting for any baseline differences in glucose between the two groups. That is also presuming that there is no interaction at baseline. For example, let's say that the beta for treatment is -20. Then, at 4 weeks, given the same baseline glucose level, we would predict that, on average, the treatment group will have a glucose level 20 mg/dl less than the control group. In the absence of an interaction, we would estimate the same average treatment
difference at 4 weeks of 20 mg/dl whether the baseline glucose was 300 mg/dl or 100 mg/dl. However, given regression to the mean, we might reasonably expect the patient with a 300 mg/dl baseline level to have a greater mean reduction at 4 weeks as
compared to the patient with a 100 mg/dl baseline level. We might also expect a patient with a glucose level at the low end of the baseline range (eg. 50 mg/dl) to experience an average increase in glucose level at 4 weeks, presuming that your inclusion/exclusion criteria permitted patients with below normal glucose levels. But the difference will still be, on average, 20 mg/dl between the two treatment groups. So the patient with a 300 mg/dl baseline level might have an average reduction
to 200 mg/dl at 4 weeks on the control treatment, whereas the same patient on the active treatment would have an average reduction to 180 mg/dl (a difference of -20). The patient with a 100 mg/dl baseline level might have an average reduction to
90 mg/dl at 4 weeks on the control treatment, whereas the same patient on the active treatment would have an average reduction to 70 mg/dl (again, a difference of -20). The patient with a 50 mg/dl baseline level might have an average increase to 90 mg/dl at 4 weeks on the control treatment, whereas the same patient on the active treatment would have an average increase to 70 mg/dl (yet again, a difference of -20). So your conclusion would be that on average, between baseline and 4 weeks, glucose levels were reduced by 20 mg/dl more in the active treatment group relative to control. This difference is the vertical separation in the two parallel fitted regression lines as shown in the figure in the paper. So the method is answering exactly the question the investigator is asking. Marc On Aug 13, 2010, at 1:02 AM, array chip wrote:
Marc, Thanks for sharing your insights. Let's take this model as an example: lm(wk4.glucose ~ baseline.glucose + treatment + gender + age) Because the investigator is interested in knowing whether the CHANGE of glucose in week 4 from baseline is different between treatment and control, Is it still legitimate to ask whether and HOW can we test this hypothesis? I think the coefficient of the treatment factor is only testing whether the week 4 glucose
level is different between treatment and control, but not testing whether the CHANGE of week 4 glucose level with respect to baseline is different between treatment and control. Thanks again for your suggestion. Yi