I'm working on a validation study. We are evaluating the accuracy of a
transcutaneous CO2 sensor (TcPCO2) in estimating arterial carbon
dioxide tension (PaCO2). PaCO2 samples are the "gold standard." We
have studied n=13 subjects in whom we sampled TcPCO2 and PaCO2 at
regularly-spaced time intervals. Not all subjects completed all 5
measurements. A Bland-Altman analysis was performed reporting
unsatisfactory limits of agreement.
A secondary hypothesis was to test for between-subject variations in
the relationship between PaCO2 and TcPCO2. To do this, and in order to
account for repeated measurements and missing values, I'm trying to
use linear mixed models in SPSS 13.0.
The first step was to check for significant fixed effects of factors
and covariates such as time, mean arterial pressure and PaCO2, of
course. As expected, only PaCO2 seems to correlate significantly.
I then proceeded to check for the covariance structure of the model.
Using likelihood ratio tests, I've found that a first-order
auto-regressive [AR(1)] variance/covariance matrix describes the model
Finally, I wanted to check for significant between-subject variations
in the TcPCO2/PaCO2 regression coefficient. According to SPSS 14.0
Advanced Statistical Procedures Companion, you would this by adding a
random effect of PaCO2 to the model, always grouping by subject - in
what I believe is called a random-coefficient model.
According to SPSS, the random effect of PaCO2
I hope the intro is clear enough, so on to the questions:
1. The Companion states that the rho in a AR(1) matrix can be seen as
an intraclass correlation coefficient. But what is the "class" in
"intraclass," here? Is it the fraction of within-subject variance
explained by the passing of time, or the fraction of between-subject
variability explained by different time trends?
2. SPSS performs a Wald test on both the diagonal and the rho of the
auto-regressive covariance structure. What do a "significant" rho and
a "non-significant" diagonal mean?
3. The random effect of PaCO2 (random between-subject variations in
the TcPCO2/PaCO2 regression coefficient) is only significant when *not*
accounting for repeated measurements. When using the AR(1) matrix, it
loses statistical significance. Is it safe to say that the apparent
random effect of PaCO2 can actually be explained by different trends
4. Is there a way to calculate the statistical power of this analysis, post-hoc?