Suppose that we have a dataset where individuals are measured in the same condition over three different time points (1,2,3). There are several missing values in each time point over different individuals. This is a usual repeated measures design where we want to compare differences between time points at the global level and with pairwise comparisons (1-2,1-3,2-3).

Repeated measures ANOVA uses listwise deletion (only uses complete cases). Nevertheless, the function pairwise.t.test() (stats package) using paired=TRUE is able to handle the NAs using a pairwise deletion (if we compare timepoint 1 with timepoint 2, only individuals with some NAs in those timepoints will be excluded, therefore one individual with only NAs in timepoint 3 will be used for the previous comparison).

In this way, for each comparison using the pairwise paired t-test, we are using a different subset of individuals. My questions are: ¿Is this type of approach correct? ¿Should we use listwise deletion also in the pairwise comparison? ¿Is it meaningful to compare p-values when we use a different subset of data in each case, even though the missing mechanism would be MCAR?

From my point of view, it will be better instead to use the pairwise paired t-test comparisons, use a mixed model which will handle better the missing values, but it will be great to know what are (if there is some) the problems of the pairwise paired t-test with pairwise deletion.

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    $\begingroup$ My feeling is that this question is not concrete enough for a straight answer. But first impression was: maybe you are looking for a partially-overlapping paired t-test, that can make use of paired and non-paired data at the same time? See R package Patiallyoverlapping and references therein. $\endgroup$ Nov 24 at 11:56
  • $\begingroup$ Are multiple imputation approaches out of the question? $\endgroup$
    – Roland
    Nov 24 at 12:09
  • $\begingroup$ @KarolisKoncevičius The question is more related to understanding what problems of methodology can occur when using a pairwise paired t-test with different subsets (i.e. pairwise deletion). Since I`m pretty sure that the mixed model can handle this type of design with missing data. $\endgroup$
    – rubeenmp
    Nov 24 at 14:14
  • $\begingroup$ @Roland, yes, I will like to know, why for repeated measures ANOVA we only use complete cases (i.e. listwise deletion) and the post hoc comparison can be done using some excluded individuals for the global analysis? From a methodological point of view, the post hoc should be done with the dataset used for the global analysis, but since the pairwise paired t-test can include more individuals why not go directly to post hoc. In my opinion, going to the pairwise paired t-test with different subsets shouldn´t be done since one group is using different individuals depending on the comparison. $\endgroup$
    – rubeenmp
    Nov 24 at 14:26

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