The distribution of bad outcomes in the model was: 1,446 for aripiprazole (RL = 9.76%), 2,387 for ziprasidone (RL = 24.80%), 5,352 for risperidone (RL = 32.63%), 5,798 for olanzapine (RL = 35.03%), 6,120 for sertraline (RL = 46.72%), 10,343 for trazodone (RL = 269.57%), 13,345 for amitriptyline (RL = 387.50%), and 15,036 for lithium (RL = 1,062.86%). The regression equation is: serious outcomes = –5,677.7 + 3,015.7 × ln (RL).
Some doctors may argue that such a data set is too small to make a meaningful model. However, the number of possible ways of ranking the drugs by bad outcomes is 8! = 40,320, so the probability of guessing the right sequence is P = .000024801. To appreciate how small this probability is, imagine trying to find a person of interest in half a football stadium on Superbowl Sunday.
The RL composite index correctly predicted the ranking order of serious outcomes for the 8 medications and may be useful for finding such outcomes in any drug class. For example, with angiotensin-converting enzyme inhibitors (n = 11) the number of possible combinations is 11! = 39,916,800. The probability of guessing the right sequence is like finding a person of interest in Poland. The model predicts the following decreasing sequence: 1) captopril, 2) fosinopril, 3) quinapril, 4) benazepril, 5) enalapril, 6) lisinopril, 7) moexipril, 8) perindopril, 9) cilazapril, 10) ramipril, 11) trandolapril. The predicted number of bad outcomes is highest for captopril, and lowest for trandolapril. The usefulness of the machine learning algorithm becomes immediately apparent.
Data can inform prescribing
Analytics can expose a critical flaw in the academic psychiatry paradigm for prescribing medications. For example, some doctors may regard lithium as the “gold standard” for treating certain mood disorders, but there is evidence that olanzapine is “significantly more effective than lithium in preventing recurrence of manic and mixed episodes.”4 Olanzapine is also 30 times safer than lithium based on its RL index, and had 9,238 fewer bad outcomes based on the 15-year data from U.S. poison control centers.2 A patient who intends to attempt suicide would easily be able to find the lethal dose of lithium from a “suicide” web site, and would quickly be able to figure out that the monthly amount of lithium his or her psychiatrist prescribed, would exceed the lethal dose.
When academia and reality collide, the use of analytics will have the final word by preventing suicide in the short term and reducing the number of bad outcomes in the long term. The irony of data science is that mathematical models can find optimal solutions to complex problems in a fraction of a second, but it may take years for a paradigm shift.