Use of an Entropy Measure to Dichotomize a Variable

Numerous cut-off points have been identified in the literature for the 6-item Kessler Psychological Distress Scale (K6) used in Canadian population-based surveys. The rationale for selecting a cut-off point is often absent or poorly documented. The purpose of this paper is to present a new approach to identifying the rationale for the selection using only the distribution of K6 scores. An entropy measure was computed initially from the distribution of observed scores in the 25 K6 categories and subsequently for all possible cut-off points (two categories). This exercise was done using Quebec data from four cycles (2005, 2007-2008, 2009-2010 and 2013-2014) of the Canadian Community Health Survey (CCHS). The cut-off point selected is the one that provides a similar amount of information to that found for all 25 categories. The cut-off point selected for the four cycles of the CCHS was 5/6. This method underscores the importance of determining a cut off point empirically rather than adopting one simply because it has been used in previous studies. It also allows for straightforward comparison of results across different surveys and remains flexible enough to be applied to other scales.