[R] Advice on analyzing a mixed effects survival model?

From: Kevin Crowston <crowston_at_syr.edu>
Date: Thu, 14 Feb 2008 10:05:54 -1000


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:

lm.t<-lme(fixed = log(time) ~ treat + task + found,

                   data = data2,
                   random = ~ 1 | subj)

l.t <-lmer(log(time) ~ treat + (1|subj) + (1|task))

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

*PS: The attachment named "PGP.sig" of type "application/pgp- signature" is an electronic signature that may be used to verify that this email came from me if you have PGP or GPG. Otherwise, you may safely ignore the attachment.



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