On the mathematical coherence of psychiatric diagnostic categories: A framework for quantifying heterogeneity attributable to polythetic diagnostic criteria
Heterogeneity within psychiatric disorders is both theoretically and practically problematic: for many disorders, it is possible for two individuals to share very few or even no symptoms in common yet share the same diagnosis. Polythetic diagnostic criteria have long been recognized to contribute to this heterogeneity; however, no unified theoretical understanding of the coherence of symptom criteria sets currently exists. Following a theoretical discussion of the concept of validity in psychiatric nosology, a general framework for analyzing the logical and mathematical structure, coherence, and diversity of Diagnostic and Statistical Manual diagnostic categories (DSM-5 and DSM-IV-TR) is proposed, drawing from combinatorial mathematics, set theory, and information theory. Theoretical application of this framework to 18 diagnostic categories indicates that in most categories, two individuals with the same diagnosis may share no symptoms in common, and that any two theoretically possible symptom combinations will share on average less than half their symptoms. Empirical application of this framework to two large datasets indicates that patients who meet symptom criteria for major depressive disorder and posttraumatic stress disorder tend to share approximately three-fifths of symptoms in common. For both disorders in each of the datasets, pairs of individuals were observed in which no common symptoms were shared. Any two individuals with either diagnosis were highly unlikely to exhibit identical symptomatology, and a patient's diagnosis conveyed relatively little information about the particular symptoms they happened to be experiencing. The theoretical and empirical results stemming from this approach have substantive implications for clinical practice, psychiatric epidemiology, and research examining the etiology of psychiatric disorders.
Olbert, Charles Mason, "On the mathematical coherence of psychiatric diagnostic categories: A framework for quantifying heterogeneity attributable to polythetic diagnostic criteria" (2014). ETD Collection for Fordham University. AAI1584352.