Friday, September 12, 2014

Combinations in the Alternative DSM-5 Model for Personality Disorders

Facets organized within Trait Domains:
DSM 5 Personality Disorder Map 
An alternative model for diagnosing personality disorders (PDs) appeared first in the DSM -5 section III, as an option to standard model, whose combinatorial death I described in the previous post. Here is the combinatorics of the alternative model.  The catastrophe tames in the right direction but the model still gives an absurdly large number of combinations that can lead to a PD diagnosis. 

The new model is based on five domains: negative affectivity, detachment, antagonism, disinhibition, and psychoticism. Twenty-five lower-order facets, or constellations of trait behaviors constitute the broader domains. Seven distinct diagnoses are defined by the same method as before, but with different numbers and types of listed traits.  


Combinations in the Alternative Model

One of the diagnoses, PD - trait specified, is a grab bag for all people who do not fit into one of the six primary diagnoses. Considering just the six gives a sum of 1100 PD phenotypes, ignoring specifiers that would only increase this number.  See the previous post for abbreviations. The diagnostic criteria add up to the following combinations:

  • AsPD: At least 2 out of 4 AND at least 6 out of 7 others = 11*8 = 88
  • Avoidant: At least 2 out of 4 AND at least 3 out of 4 others = 11*5 = 55
  • BPD:  At least 2 out of 4 AND and at least 4 out of 7, one of which must be among 3 possibilities = 11*60 = 660
  • NPD: At least 2 out of 4 AND 2 out of 2 = 11*1= 11
  • Ob-COPD: at least 2 out of 4 AND at least 2 out of 3 = 11*4 = 44
  • Schizotypal: at least 2 out of 4 AND at least 4 out of 6 = 11*22 = 242

If a person met the criteria for all six of these diseases, they could do so in 88*55*660*11*44*242 = 3.7*10^(11), or about four hundred billion ways. Adding up all possible ways to get a diagnosis of at least one of these disorders (which is entirely consistent with these these rules -- at least X out of Y, in this case at least one out of six) gives about 10^(12), or one trillion combinations of symptoms qualifying for a PD diagnosis.


Combinatorial Death

The alternative model is a great success compared to the standard approach! It brings down the number of possible combinations by about nine orders of magnitude. Still, one trillion combinations of supposedly clinically significant observable traits, for about one billion people who could encounter a psychiatrist in their life time, is overkill. Indeed one trillion is larger than the number of people who will live on earth for the next 3000 years. Using such a system with built in-runaway to define six diagnoses is absurd.

A reasonable conclusion is that the symptom list and criteria under which they line up together to signify disease is inadequate. The common notion that to delineate disease better, one should have more criteria rather than less is false. In fact the opposite is true, to avoid combinatorial catastrophe. 


Looking Forward

It's a long term project to examine on-going literature in the field and present a take on developing better diagnostic criteria and data structures for personality disorders -- to identify the appropriate axes that can parse human experience and the relationships to self and others more sharply. Perhaps a tree-like data structure is needed: just as genera branch into species -- specific traits could branch into others, implying a hierarchical structure. This could firmly tame combinatorial explosion. That's all speculative -- I look forward to seeing how this goes.

Some claim that a categorical model is ill-suited for personality disorders and Psychiatry should move to a continuous spectrum picture.  This is, however, not what I am saying. Instead, my point is that if one is to use a categorical model it must be more categorical than it is at present. The explosion of combinations arises from issues emanating from e.g. choices like 4 out of 7 AND 2 out of 4...  If a model instead stipulated for some disorder 5 out of 5 AND 0 out of 6, that would only leave one combination. 


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