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Q: Applying Linear Mixed Models to Longitudinal Data ( No Answer,   0 Comments )
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 Subject: Applying Linear Mixed Models to Longitudinal Data Category: Science > Social Sciences Asked by: mbac-ga List Price: \$80.00 Posted: 25 Apr 2006 06:57 PDT Expires: 25 May 2006 06:57 PDT Question ID: 722601
 ```Hi, 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 best. 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 over time? 4. Is there a way to calculate the statistical power of this analysis, post-hoc?``` Clarification of Question by mbac-ga on 25 Apr 2006 07:00 PDT ```Sorry, there's a broken line in the original question. "According to SPSS, the random effect of PaCO2 " Please ignore that line.```