One minor technical question and a more substantial issue regarding mixed-effects models.
More than once in the past year I've come across a statement regarding testing MAR in SPSS, such as
"we tested whether the data were missing at random using SPSS".
I am fairly certain that testing MAR (vs. non-ignorable) is not possible logically or statistically, at least not without external info. What is possible (and relatively straight-forward) is testing MCAR vs. MAR. Please correct me if I have it wrong!
So, can anyone explain what, if any, test SPSS performs (it's not a package I'm familiar with)? Is it a MCAR test?
Now, to the more important issue that I would like to ask about.
It is generally stated that mixed-effects regression is a full-information likelihood method, thus valid under ignorable missingness. In other words, the estimates and standard errors (e.g., as obtained from SAS) are valid even in the case of unbalanced data (i.e., different number of observations per subject) -- provided that's MAR.
But consider this argument. Suppose that we have a study of N=100 subjects, with up to 4 timepoints for each. Suppose that everyone has the first 3 measurements but that the 4th measurement is missing for some subjects. Further suppose that whether Y_4 is missing or not depends on the value of Y_3 (which is always observed -- i.e., MAR for Y_4). Specifically, suppose that the probability of Y_4 missing increases with increasing values of Y_3.
With the mixed model, among the N subjects, some are going to have steeper slopes of Y (increasing) over time and some flatter ones. The former will then have higher probability of Y_4 missing than the latter. Thus, subjects with steeper slopes will be more likely to have fewer datapoints than subjects with flatter slopes. But that means that the former will have somewhat lower "weight" in the estimation of the fixed effect than the latter, and therefore the estimate will be biased (toward the null in this case).
Can you comment on the possible incompatibility of the two lines of thinking?
Thanks in advance,
cd
Constantine Daskalakis, ScD
Assistant Professor,
Biostatistics Section, Division of Clinical Pharmacology,
Thomas Jefferson University,
132 South 10th Street, Philadelphia, PA 19107
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Email: [EMAIL PROTECTED]
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