  Distance metrics are broadly used in different research areas and
applications, such as bio-informatics, data mining and many other fields.
However, there are some metrics, like pq-gram and Edit Distance used
specifically for data with a hierarchical structure. Other metrics used for
non-hierarchical data are the geometric and Hamming metrics. We have applied
these metrics to The Health Improvement Network (THIN) database which has some
hierarchical data. The THIN data has to be converted into a tree-like structure
for the first group of metrics. For the second group of metrics, the data are
converted into a frequency table or matrix, then for all metrics, all distances
are found and normalised. Based on this particular data set, our research
question: which of these metrics is useful for THIN data? This paper compares
the metrics, particularly the pq-gram metric on finding the similarities of
patients' data. It also investigates the similar patients who have the same
close distances as well as the metrics suitability for clustering the whole
patient population. Our results show that the two groups of metrics perform
differently as they represent different structures of the data. Nevertheless,
all the metrics could represent some similar data of patients as well as
discriminate sufficiently well in clustering the patient population using
$k$-means clustering algorithm.
