5.8. Concluding Remarks

We conclude this chapter with some comments about missing values in repeated measures. One of the very frequent problems in conducting repeated measures experiments is the failure to follow the subject at all time points. As a result, many repeated measures data sets are not balanced. This further complicates the problem in two ways. First, the standard multivariate methods may no longer be applicable. Second, most computer packages including SAS do not deal with missing values in the multivariate data; for example, SAS ignores all the observations on a particular subject if it finds a missing value for any of the dependent variables in the MODEL statement. This not only reduces the sample size substantially but may also result in a sample that is biased due to this implicit self-selection.

A way to alleviate this problem would be the imputation of missing values before analyzing the data. There are well-respected approaches, based on the EM algorithm, for imputing the missing values in certain cases of missingness patterns and causes (Little and Rubin, 1987, McLachlan and Krishnan, 1997). Unfortunately, the EM algorithms by definition are very problem specific and often require the identification of appropriate sufficient statistics (for conditioning purposes) even to program the estimation procedure. However, it should be remembered that imputing the missing values and their substitution for further analysis may not necessarily be a desirable choice. This type of analysis may cause the variance terms to be underestimated. The SAS MIXED procedure provides some alternative modeling approaches for data sets of this kind. We will discuss these approaches in Chapter 6.