Statistical Methods in Medical Research 4ed

444 Further regression models
follow-up. This particular pattern is distinguished from other patterns because
it has recently been studied quite extensively, and will be discussed below.
With missing values in longitudinal data, the analyst is confronted with
the problem of whether or not the values on an individual that are available
can be used in an analysis and, if so, how. A naõÈve approach would simply be to
analyse the data that were available. This could present technical problems for
some methods; for example, repeated measures analysis of variance cannot deal
with unbalanced data in which different individuals are measured different
numbers of times. There are techniques which allow the statistician to impute
values for the missing observations, thereby `completing' the data and allowing
the analysis that was originally intended to be performed. These methods were
widely used in the days before substantial computing power was as readily
available as it is now, because many methods for unbalanced data used to
present formidable computational obstacles. However, this approach is clearly
undesirable if more than a very small proportion of the data is missing. Other
methods, for example, a summary measures analysis using the mean of the
responses on an individual, have no difficulty with unbalanced data. However,
regardless of the ability of any technique to cope with unbalanced data, analyses
which ignore the reasons why values are missing can be seriously misleading. For
example, if the outcome is a blood chemistry measurement that tends to be high
when some chronic condition is particularly active and debilitating, then it may
be on just such occasions that the patient feels too unwell to attend the clinic, so
the missing values are generally the high values. A summary measures mean of
the available values would be biased downwards, as would be the results from
the interindividual stratum in a repeated measures analysis of variance.
It is clear that there are potentially severe difficulties in dealing with missing
values. It is important to know if the fact that an observation is missing is related
to the value that would have been obtained had it not been missing. It is equally
clear that unequivocal statistical evidence is unlikely to be forthcoming on this
issue. Nevertheless, a substantial body of statistical research has recently
emerged on this topic, stemming from the seminal work of Little (1976) and
Rubin (1976), and this will be discussed briefly below. It should also be noted
that, although the problem of missing data can be severe, it does not have to be,
and it is important to keep matters in perspective. If the number of missing
values is small as a proportion of the whole data set, and if the purpose of the
analysis is not focused on extreme aspects of the distribution of the response,
such as determining the top few percentiles, then it is unlikely that naõÈve
approaches will be seriously misleading.
Almost all of the formal methods discussed for this problem stem from the
classification of missing data mechanisms into three groups, described by Little
and Rubin (1987). These are: (i) missing completely at random (MCAR); (ii)
missing at random (MAR); and (iii) processes not in (i) or (ii). The final group