Re: A few questions on applied linear mixed models

Hi and thanks for your reply.

Let me clarify things. The main outcome in this study (which I did not
design but am analyzing) is the accuracy in estimating PaCO2 using
TcPCO2. Therefore the Bland-Altman analysis should provide enough
information to address the main outcome.

I'd like to add a rough analysis of the performance across subjects as
a sidenote (and as "pilot" for a future study). I started my model with
a few fixed factors which I believed might influence the TcPCO2
reading: PaCO2, of course, then time and mean arterial pressure (MAP).
Only the first was a significant covariate.

In order to improve the fit of the model (and account for repeated
measurements), I then added a covariance structure. The AR matrix was
the best-fitting, and did improve the model according to a likelihood
ratio test. It also fits the data plots quite nicely - the scatter of
TcPCO2 measurement seems to disperse over time. However, I'm still
wondering what a "statistically significant" rho means... From what I
gather, rho in this case is equal to the intraclass correlation
coefficient. But what does an ICC mean when it comes from the
covariance structure? Is it about variance over time or between
subjects? In other words, what class is it "intraclass" for?

Finally, I checked for a random effect of PaCO2, as well. I did this
because I wanted to check for significant variations of the slope of
the PaCO2/TcPCO2 relationship across subjects. My question was: are
there any random variations of the slope between different subjects?
Or, in other words, is TcPCO2 equally related to PaCO2 in all subjects,
or does it work "differently" in some?

To my understanding, you would do this by checking for a random effect
of PaCO2 when "clustering" the data by subject (subject grouping in
SPSS terms.) I have retained the AR covariance structure in this model,
as well, in order to account for possible covariances over time. If I'm
getting it right, this should be a random-slope model with a covariance
structure for repeated measurements. Apparently, only a small and
non-significant fraction of the variance (and error) in the regression
are caused by differences in the slope of this relationship. However,
when removing the AR covariance structure, the random effect of PaCO2
becomes significant.

I'm not sure what to make of this last result. Interestingly, in the
model with the AR structure and an insignificant PaCO2 random effect,
the variance of the model is roughly equivalent to the width of the
limits of agreement in the Bland-Altman analysis.

Finally, in order to design a study which specifically addresses this
point, I'm looking for ways to calculate the statistical power of this
analysis

.