"Mixed model ANOVA with random effect"--is this the correct analysis? Question about an analysis that was done for a study I'm reviewing:
The study compared two methods of taking patient core temperature around surgery at a single center; Apx. N=200, temp was taken for all patients at 4 timepoints (pre, intraop, post1, post2) simultaneously with both systems.
The write-up says they used a "Mixed model ANOVA with patient included as a random effect."
I'm not a statistician but this doesn't sound right? Why would you use patient as a random effect? Also, from the looks of their table [mean(sd) at each time point for both systems, then the mean(sd) of the difference, then a p-value], it looks like they really just used multiple Wilcoxon or t-tests).
i.e. what would be a correct test in this case? and should it involve random effects? Thank you.
 A: You would use patient as a random effect because there are repeated measures within each patient. This means that observations within one patient may be more similar to each other than observations between patients. In other words there will be correlation within each cluster (patient). In order to handle this non-independence of observations, it is common to include the clustering variable (patient in this case) as a random effect. 
Including patient as a random effect is a perfectly reasonable thing to do here, and if it was not done, that would likely be a mistake unless another method to control for clustering was used (such as generalised estimating equations, which is obviously not the case here).
A: When the same patient provides repeated response measurements over time (e.g., core temperature), the use of a random patient effect is a natural way to capture the within-patient correlation (or similarity) of those measurements over time. 
Mixed Model Anova is an analysis which can be applied to analyze repeated measures data for a set of subjects. It's not clear what fixed effects were investigated in this analysis from the description you provide - the fixed effects of Method and Time and their interaction? You can ask clarifications about that.  Also, it seems the analysis in question assumed that the correlation between core temperatures for the same patient on the same treatment did not depend on how close/far in time those measurements were.  I have a feeling there may be correlation between measurements coming from the same patient at the same time point - not clear whether the analysis used could adequately deal with this, so perhaps that could be listed as a limitation.
Since the difference in mean values of core temperature between Methods was tested at each of the four time points, you should also ask for clarification on whether the reported p-values for these tests were adjusted for testing multiplicity.
