[R] Advice on analyzing a mixed effects survival model?
Kevin Crowston
crowston at syr.edu
Thu Feb 14 21:05:54 CET 2008
I have an experiment I'm trying to analyze that's turning out to be
more complicated than I anticipated, so I was hoping for some
suggestions about how to handle it.
The lab experiment is a comparison between two search interfaces.
After a little training, each subject performs 12 information search
tasks, 6 with one interface and 6 with the other, and we measure time
to complete and number of clicks. The overall design is a latin
square: with 12 subjects, the design has each task done before and
after each other one the same number of times, and each is done 6
times with one interface and 6 with the other. Maybe a table will make
it clearer what is happening:
Run Tasks
1 - 12 8 1
11 7 5 4 6
10 3 9 2
2 - 1 12 7
8 4 11 10 5
9 6 2 3
3 - 9 10 2
4 3 7 6 1
5 12 11 8
4 - 3 2 6
9 5 10 11 4
8 7 12 1
5 - 6 3 5
2 11 9 8 10
12 4 1 7
6 - 5 6 11
3 8 2 12 9
1 10 7 4
7 - 7 1 4
12 10 8 9 11
2 5 3 6
8 - 8 11 12
5 1 6 7 3
4 2 10 9
9 - 10 4 9
7 2 1 3 12
6 8 5 11
10 - 11 5 8
6 12 3 1 2
7 9 4 10
11 - 2 9 3
10 6 4 5 7
11 1 8 12
12 - 4 7 10
1 9 12 2 8
3 11 6 5
Run Interface
1 - 0 0 1 1 1
1 0 0 0 1 1 0
2 - 1 0 1 0 1
0 1 0 1 0 1 0
3 - 0 1 0 1 0
1 0 1 0 1 0 1
4 - 1 0 1 0 1
0 1 0 1 0 1 0
5 - 0 1 0 1 0
1 0 1 0 1 0 1
6 - 1 0 1 0 1
0 1 0 1 0 1 0
7 - 0 1 0 1 0
1 0 1 0 1 0 1
8 - 1 0 1 0 1
0 0 1 1 1 0 0
9 - 1 1 1 0 0
0 1 0 1 0 0 1
10 - 0 0 0 1 0 1
0 1 0 1 1 1
11 - 1 1 0 1 1 0
1 0 1 0 0 0
12 - 0 1 0 0 0 1
1 1 0 0 1 1
The resulting data look something like
subject run seq task interface time clicks
1 1 1 12 0 123 18
1 1 2 8 0 197 23
1 1 3 1 1 156 21
....
2 2 1 1 1 87 10
.....
I was planning originally to analyze the data with ANOVA: time (or
probably log(time)) ~ task + subject + interface. Some tasks are
harder than others, some subjects slower, but we control for those to
see the effect of the interface. I did not plan to include an
interaction term: it's not one of our research questions and I don't
think I have enough df anyway. At some point, I would like to test if
there are learning effects by adding the sequence of the task, but
that's for the future.
But as I thought about it, things got complicated: first, the design
is a repeated measures design for subjects at least; second, both task
and subject are best thought of as random factors; and finally,
subjects sometimes do not complete a task, so some of the times and
clicks are right censored. After some reading of the list and of
Pinheiro's Mixed Effects Models, I came up with ways that I think
handle these complications one or two at a time, though I am not
entirely confident that I have it right:
-- one random factor:
lm.t<-lme(fixed = log(time) ~ treat + task + found,
data = data2,
random = ~ 1 | subj)
-- lmer can handle two random factors:
l.t <-lmer(log(time) ~ treat + (1|subj) + (1|task))
-- coxme from the kinship library can handle the censored data with
one random factor:
cm.t<-coxme(Surv(log(time),found=="found") ~ treat + task, random= ~ 1|
subj)
What I haven't found though is a way to analyze the data with censored
data and two random factors. I'm also running into additional
concepts that I don't fully understand though they seem promising,
e.g., frailty models.
So, I am hoping someone on the list can suggest an approach to the
analysis or suggestions of other readings that might help. Thanks!
Kevin Crowston
Syracuse University Phone: +1 (315) 443-1676
School of Information Studies Fax: +1 (866)
265-7407
348 Hinds Hall Web: http://crowston.syr.edu/
Syracuse, NY 13244-4100 USA
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