Clustering and a dissimilarity measure for methadone dosage time series

Abstract

In this work we analyse data for 314 participants of a methadone study over 180 days. Dosages in milligram were converted for better interpretability to seven categories in which six categories have an ordinal scale for representing dosages and one category for missing dosages. We develop a dissimilarity measure and cluster the time series using “partitioning around medoids” (PAM). The dissimilarity measure is based on assessing the interpretative dissimilarity between categories. It quantifies the structure of the categories which is partly categorical, partly ordinal and also involves quantitative information. The principle behind the measure can be used for other applications as well, in which there is more information about the meaning of categories than just that they are “ordinal” or “categorical”.