Abstract
BackgroundPreviously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population.MethodsData collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting.ResultsThe boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap.DiscussionThe results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern.
Highlights
Depression is a major public health concern as one of the leading causes of disease burden worldwide, with an estimated 350 million people of all ages affected around the globe (Moussavi et al, 2007)
In order to explain the aforementioned findings that total depressive symptom scores approximate an exponential pattern in the general population, we proposed a model of ordinal scales for unidimensional latent traits (Tomitaka et al, in press)
To ascertain whether the common mathematical pattern of the boundary curves is specific to the 16 negative affect items following the distribution of the unidimensional latent trait of depressive symptoms, we examined whether the boundary curve of four positive affect items, which do not follow this latent trait distribution, follow the same pattern observed for 16 negative affect items
Summary
Depression is a major public health concern as one of the leading causes of disease burden worldwide, with an estimated 350 million people of all ages affected around the globe (Moussavi et al, 2007). The authors of the present study have observed that the right tail of the distribution of total depressive symptom scores on the Center for Epidemiologic Studies Depression Scale (CES-D) follows an exponential curve, based on data from a national survey of the Japanese population including data from nearly 25,000 respondents (Tomitaka, Kawasaki & Furukawa, 2015a). Discussion: The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern
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