Statistical Methods in Medical Research 4ed

esponses on an individual to a suitable scalar quantity, which can then be
analysed simply, is the key idea behind the important approach to the analysis
of longitudinal data that is outlined in the next subsection.
Summary measures
12.6 Longitudinal data 435
Perhaps the principal difficulty in analysing longitudinal data is coping with the
dependency that is likely to exist between responses on the same individual.
However, there is no more difficulty in assuming that responses from different
individuals are independent than in other areas of data analysis (this assumes, for
simplicity, that the individuals in the analysis are not embedded in a larger
design, such as a complex survey (see §19.2) or a cluster-randomized trial (see
§18.9), which may itself induce dependence). Consequently, if the responses on
individual i, y i, together with other information, such as the times of the
responses, ti, say, are used to compute a suitable scalar (i.e. a single value), si,
say, then the si are independent and can be analysed using straightforward
statistical methods. The value of this approach, which can be called the summary
measures method, rests on the ability of the analyst to be able to specify a suitable
function of the observations that can capture an important feature of the
response of each individual. For this reason the method is sometimes referred
to as response feature analysis (Crowder & Hand, 1990). The method has a long
history, an early use being by Wishart (1938). More recent discussions can be
found in Healy (1981), Yates (1982) and Matthews et al. (1990).
If, for example, the response of interest is the overall level of a blood
chemistry measurement, then the simple average of the responses on an individual
may be adequate. If the effect of some treatment on this quantity is being
assessed then it may be sensible to omit the first few determinations from the
average, so as to allow the treatment time to have its effect. A rate of change
might best be summarized by defining si to be the regression slope of y i on ti.
Summaries based on the time-scale may be particularly important from a clinical
point of view: the time that a quantity, such as a drug concentration, is above a
therapeutic level or the time to a maximum response may be suitable summaries.
It may be that more than one feature of the data is of interest and it would then
be legitimate to define and analyse a summary for each such feature. Simple
bivariate analyses of summaries are also possible, although they seem to be little
used in practice. Judgement should be exercised in the number of summaries that
are to be analysed; summaries should correspond to distinct features of the
response and in practice there are unlikely to be more than two or three of these.
The choice of summary measure should be guided by what is clinically or
biologically reasonable and germane to the purpose of the study. Indeed, it is
preferable to define the summary before the data are collected, as this may help
to focus attention on the purpose of the investigation and the most appropriate