Paired t-test following main effect of mixed model with missing data

Question

I am analyzing data for a repeated measures study with missing data. For example here is a 3 X 3 experimental design with three conditions and 3-time measures:

I am using a mixed model for the main effects:

 model1 <- lme(outcomeMeasure ~ condition * time, random = ~1|subject/condition/time, data = exampleData)

anova(model1)
                            numDF denDF  F-value p-value
    (Intercept)                 1    57 892.3397  <.0001
    condition                   2    21   1.6985  0.2066
    time                        2    57   4.5983  0.0363
    condition:time              2    36   0.1513  0.8601

Since time is significant, I would like to follow up with a paired test by averaging across condition to obtain values of each subject's time. As you can see in the example data above, subject 1 is missing an entire condition. When I aggregate the data across time:

timeSubjectMeans <- aggregate(value ~ Subject * time, data = exampleData, FUN = mean)

In order to perform a paired t-test on this data, should I exclude subject 1 because they are missing 1 of the conditions?

Answer 1

With regard to the missing data, the mixed model will give you correct inferences under the more plausible missing at random assumption whereas the t-test only under the more stringent missing completely at random assumption.

Hence, it would be advisable to perform such comparisons via the mixed model, using, e.g., the emmeans package.