Statistical Methods in Medical Research 4ed

depends on the structure in the data, which is often unknown. In effect, each
method imposes implicit assumptions on the type of clustering expected, and if
these assumptions are invalid the results may be meaningless. For this reason we
suggest that cluster analysis should only be used in circumstances where other
multivariate methods are inappropriate, and the results must be interpreted with
a great deal of caution.
Finally, the method of cluster analysis should not be confused with the
problem of determining whether cases of disease occur in clusters in time,
space or families. This problem gives rise to different methods discussed in
§19.13.
Multidimensional scaling
Suppose data are available on a set of individuals and it is possible to derive an
index of similarity, or dissimilarity, between every pair of individuals. This index
would be of the same type as those considered in the discussion of cluster
analysis. Then multidimensional scaling is a method of arranging the individuals
in a space of a few dimensions so that the distances between the points in this
space are nearly the same as the measures of dissimilarity. In particular, if two
dimensions provide an adequate representation, then it is possible to plot the
individuals on a two-dimensional graph, and examination of how the individuals
are arranged on this graph might lead to some useful interpretation. For
example, the individuals might occur in clusters.
The method is, like many multivariate methods, an attempt to reduce dimensionality.
If the dissimilarities are measured using a set of continuous variables,
then the method of principal components has a similar aim.
For more details on this method, see Chatfield and Collins (1980) and Cox
and Cox (2001).
13.5 Concluding remarks
13.5 Concluding remarks 483
All the multivariate methods rely on a large amount of computation and have
only been widely applicable in the last three decades following the development
of computer statistical software. The ease of performing the calculations leads to
a risk that multivariate methods may be applied blindly in circumstances different
from those for which they were designed, and that incorrect conclusions may
be drawn from them.
The majority of data sets are multivariate and therefore multivariate analysis
of some sort is often required. In choosing an approach, it is essential to keep
uppermost in mind the objective of the research and only to use a method of
analysis if it is appropriate for that objective. In many cases, the objective is to
examine the relationship between an outcome variable and a number of possible