Interpretation of interaction with time in random effects model

Rich Ulrich

2014-08-11 02:23:22 UTC

Post by r***@gmail.com
. list if id<5
+----------------------------------------------+
| id time exposure outcome outcome_bl |
|----------------------------------------------|
1. | 1 1 2 34.14907 33.98133 |
2. | 1 2 2 36.89132 33.98133 |
3. | 1 3 2 37.09322 33.98133 |
4. | 2 1 2 24.22013 21.2088 |
5. | 2 2 2 25.23487 21.2088 |
|----------------------------------------------|
6. | 3 1 1 31.93662 32.69796 |
7. | 3 2 1 37.16611 32.69796 |
8. | 3 3 1 33.71714 32.69796 |
9. | 4 1 2 25.69123 25.6259 |
10. | 4 2 2 25.60167 25.6259 |
|----------------------------------------------|
11. | 4 3 2 22.32802 25.6259 |
+----------------------------------------------+
I am using a random effects repeated measures analysis, with the outcome at baseline as a covariate, together with exposure, time and the interaction of time and exposure.

- I think you mean to say, "of exposure group 4".
Note, however, that this is a contrast (apparently) of group
four versus group one. Check what STATA tells you about
the construction of the contrasts that it reports.

Post by r***@gmail.com
. gen diff=outcome-outcome_bl
. table exposure time, c(mean diff)
-------------------------------------------
| time
exposure | 1 2 3
----------+--------------------------------
1 | -.0730373 .1984727 .0705481
2 | -.4656163 .1813771 .1950545
3 | -.5124291 -1.245556 .6545261
4 | -1.534946 -.0874589 .847056
-------------------------------------------
Would it be fair when writing up the results below to say that the only significant effect was exposure group 4 at time 1? Or am I misunderstanding the interpretation of the main effect in the presence of interactions?

Okay, you do not have a confirmed interaction. However, it
is probably wise to be wary when there is some sense that
there might be one. The interaction in the table (below) reports
Group4-contrast by Time3-contrast; Group 4 has a large and
negative coefficient; the oddest store in your extra table of
means seems to be Group4 by Time3 cell

Here is another problem. In a conservative style of testing,
you also fail to confirmed strong evidence of a main effect. You
have one d.f. in a contrast that tests at less than 0.05; you do
not have an overall test on the three d.f. which make up the
4-group factor. If you convert that largest z to a chi-squared,
it is not large enough to make the 3 d.f. test significant.

If Group1 is a control group that is intentionally being
contrasted, then you *do* have p= 0.015 which would beat
the limit for a Bonferroni correction for 3 tests at 5%.

The problem that I have with looking at the means that you do
look at is (1) they are mean differences from baseline, and not
the regressed-change differences that the procedure was,
in fact, testing; that can matter (even) when the data are complete,
but the potential for a problem is compounded by the Missing:

(2) You have said nothing about those one-third of the data points
which are Missing. Do they reflect anything about the scores
otherwise collected on the subjects? Do they have no logical
connection to the level of scoring? Does Missing increase with time?

You hope that the Baselines were collected before groups were
assigned, and that the groups are (therefore) equivalent at Base;
and that dropouts are not associated with higher or lower scores
at Base or at the other points that were collected. Those assumptions
should be checked.

The safest, lazy way to report the testing is that nothing is
significant by strict standards. I might want to report the
exploratory trends if they are not an artifact of Missing.

Post by r***@gmail.com
Thank you
Rena
Iteration 0: log likelihood = -3527.7256
Iteration 1: log likelihood = -3527.7182
Iteration 2: log likelihood = -3527.7182
Mixed-effects ML regression Number of obs = 1405
Group variable: id Number of groups = 688
Obs per group: min = 1
avg = 2.0
max = 3
Wald chi2(12) = 2885.85

- Most of that chi2 owes to the covariate, squaring 53.43.

Post by r***@gmail.com
Log likelihood = -3527.7182 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
outcome | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
exposure |
2 | -.3427129 .3312138 -1.03 0.301 -.99188 .3064542
3 | -.2236166 1.019724 -0.22 0.826 -2.222239 1.775006
4 | -1.291953 .5311281 -2.43 0.015 -2.332945 -.2509614
|
time |
2 | .3840982 .3167607 1.21 0.225 -.2367413 1.004938
3 | .1534453 .3200552 0.48 0.632 -.4738513 .7807419

I always wonder whether time-trends should be considered for
the( linear trend + other), instead of by period. The absence of
linear trend suggests to me (as a refutable presumption) that
period probably does not matter.

Post by r***@gmail.com
|
exposure#time |
2 2 | .2322221 .3692434 0.63 0.529 -.4914817 .9559259
2 3 | .3565169 .3904371 0.91 0.361 -.4087257 1.12176
3 2 | -1.295537 1.049529 -1.23 0.217 -3.352576 .7615025
3 3 | .2487972 1.249102 0.20 0.842 -2.199398 2.696992
4 2 | .5126085 .6681532 0.77 0.443 -.7969478 1.822165
4 3 | 1.400178 .741296 1.89 0.059 -.0527351 2.853092
|
outcome_bl | .972069 .0181939 53.43 0.000 .9364095 1.007728
_cons | .5444925 .5156786 1.06 0.291 -.466219 1.555204
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity |
sd(_cons) | 2.194716 .1090333 1.99109 2.419168
-----------------------------+------------------------------------------------
sd(Residual) | 2.335483 .0639805 2.21339 2.46431
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 162.80 Prob >= chibar2 = 0.0000

- I don't know what this last is testing.

--
Rich Ulrich