Combinatorial Optimization of Clustering Decisions: An Approach to Refine Psychiatric Diagnoses

Abstract

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the “diagnosis” group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the “diagnosis” to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.

Keywords:

• Optimization
• alcohol use disorder
• diagnosis
• cluster analysis

Notes

1 The summary of the problem statement was greatly influenced by a reviewer of this manuscript and we would like to recognize them for their input.

2 This procedure is computationally intensive and impractical with more than 30 items on a standard desktop computer.

3 See similar arguments as applied to K-means clustering in Steinley and Brusco (2011).

4 Depending on the objective function, this could also be a minimum. Furthermore, this process for determining the optimal decision rule, indicates that optimal is defined as the “best” possible value of the objective function as applied to any decision rule.

5 For more information on symptoms and diagnostic standards according to the DSM-IV and the DSM-5, please refer to the following link: https://pubs.niaaa.nih.gov/publications/dsmfactsheet/dsmfact.pdf.

6 The response options for the questions “During the last 12 months, what was the LARGEST number of drinks that you drank in a single day?” and “Counting all types of alcohol combined, how many drinks did you USUALLY have on days when you drank during the last 12 months?” were open ended with a maximum accepted value of 98.

The response options for the questions “During the last 12 months, about how often did you drink ANY alcoholic beverage?” and “About how often during the last 12 months did you drink [LARGEST number of drinks] in a single day?” were

1 = Every day;

2 = Nearly every day;

3 = 3 to 4 times a week;

4 = 2 times a week;

5 = Once a week;

6 = 2 to 3 times a month;

7 = Once a month;

8 = 7 to 11 times in the last year;

9 = 3 to 6 times in the last year;

10 = 1 or 2 times in the last year.

The response options for the questions

“During the last 12 months, about how often did you drink FIVE OR MORE drinks in a period of TWO HOURS OR LESS? [MALES ONLY],” “During the last 12 months, about how often did you drink FOUR OR MORE drinks in a period of TWO HOURS OR LESS? [FEMALES ONLY],” and “During the last 12 months, about how often did you drink enough to feel intoxicated or drunk, that is, when your speech was slurred, you felt unsteady on your feet, or you had blurred vision?” were

1 = Every day;

2 = Nearly every day;

3 = 3 to 4 times a week;

4 = 2 times a week;

5 = Once a week;

6 = 2 to 3 times a month;

7 = Once a month;

8 = 7 to 11 times in the last year;

9 = 3 to 6 times in the last year;

10 = 1 or 2 times in the last year;

11 = Never in the last year.

7 The upper and lower bounds on of the derivation for the nondiagnostic and diagnostic groups, respectively, are controlled by the prevalence rate and the overlap of clusters. Therefore, it is possible for these bounds to be above 1 or below 0 (e.g., rule diagnoses 50% of sample and overlap is set to 80%). For this reason, the bounds are fixed at 0 or 1 in these cases).