[R] treatment effects with lme (repeated measurements)

Dieter Menne dieter.menne at menne-biomed.de
Fri Dec 3 10:10:46 CET 2010

Steffen Fleischer wrote:
> ..
> We measured the outcome three times repeatedly in the same patient. One
> time before intervention and two times after intervention. I wanted to
> adjust for the correlated data in the repeated measurement and baseline
> differences in the variable in order to get the treatment effect.
> Here the model:
> lme(outcome~treatment*time+baseline; random=~1|id)
> for the data structure:
> id   time  outcome  baseline  treatment
> 1     1         10           5             1
> 1     2         12           5             1
> 2     1............
> .
> .
> alternatively I could use 3 rows per participant, omitting baseline as a
> variable as it would be included in "outcome" and "time" then.
> The model then would be:
> lme(outcome~treatment*time; random=~1|id)

You should be aware that by calling treatments 1 and 2 and not doing an
"as.factor" on it, treat is  considered a continuous variables. With two
variables, the result look similar to what you expect, but you are living on
dangerous ground here. I prefer to always name my variables "Placebo" and
"Antibiotics", forcing them to be factors. But old habit of coding 1/2 die

Time, however, is definitively a continuous variable. When you use the
second version, you effectively fit a linear model through the three data
points, and the interaction term tells you how different the slopes are for
the two treatments. This approach has considerable power when the model
assumption is reasonable, but you must check for this by visual inspection
of the residuals. 

I often use it, but it is always hard work to convince medical researchers
and reviewers to at least consider the idea. The usual reply is "this is not
linear over time"; and my usual answer is: the linear-over-time is the next
step after the "is constant" assumption; which they would immediately accept
without asking that being constant is an assumption. 

In this approach, the slope is an indicator of the trend. The model it is
the more useful, the more points-in-time you have. 

The alternative (essentially your version 1) is to test all values against
baseline (or, better, all differences against zero). This is acceptable for
two (post-treat) points in time; but I remember the many cases where I got
asked: "we have ten points in time, and would like to know after how many
time points the treatment effect is significantly different from zero". Or,
even more fun: we would like to test every time against every other to find
out (what?? That after 3 it's signif, not after 5, again after 7)

I tend to apply a rude Bonferroni correction in that case, which often gets
people down to earth, and we can consider a linear or transformed linear
continuous-in-time model.

Summary: Both approaches are possible. Check your model assumptions. And
don't say "it's not linear" easily. It might be really non-linear. With
large errors we have in medical research, the linear assumption might be
quite good. 


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