Our Formula for Calculating an Elevated Likelihood

The question we are trying to answer in each assessment, for each condition is, “How much more likely is the test-taker to have the condition – based on their test results and the published precision rates of those tests - relative to the general adult population in the U.S.?”

It is important to us to share how we arrive at these figures. At MindMetrix, we are not doing any special interpretation of hidden factors, artificial intelligence or novel math designed to obfuscate our approach. Instead, we are simply combining the published accuracy statistics of each test, and using an agreed-upon way of combining multiple test results, statistically, to arrive at a conclusion about how likely it is that a condition is present.

The conventional methods of using sensitivity (probability of a correct positive result) and specificity (probability of a correct negative result) are great tools for understanding the likelihood of having a condition given the results of a specific test. However, they are less useful when combining the results of multiple tests. Taking that into consideration, our approach uses likelihood ratios, which incorporate sensitivity and specificity, but can also account for the results of multiple tests in the most statistically sound way.

We were influenced by Bayes Rule in statistics and this article about diagnostics in ophthalmology, which makes a case for using likelihood ratios in combination with pre-test probability when attempting to determine how one’s test results combine to impact their “post-test” probability of having a given condition.

At a very high level, the formula first looks at the pretest probability for the test-taker (the condition’s prevalence). It then creates a posttest probability based on each positive and negative test result from the test-taker for a given condition. We then compare that posttest probability to the pretest probability in order to display how many times more likely (x elevated) an individual is to have the condition - based on these results.

How the math works

Pretest probability is defined by the prevalence of the condition in the general U.S. adult population.

• We use prevalence data pulled from the DSM-5 for almost all conditions.
• We use sources other than the DSM-5 for approximately 4-5 conditions (e.g., SAMHSA national population survey for substance use disorder).
• For most conditions, the prevalence was reported as the 12-month prevalence estimate or the lifetime prevalence estimate of the condition among adults in the United States. However, there are a handful of cases where the prevalence estimates are reported for a specific subsample drawn from within the larger US adult population. For example, the prevalence among young adult females for Anorexia Nervosa or the prevalence among adults who have experienced a traumatic event within the past month for Adjustment Disorder.

Pretest odds is defined by the odds the test-taker has the target condition, before the rating scales are administered. It is calculated using the pretest probability.

Pretest Odds = (Pretest probability / [1 - pretest probability])

Likelihood ratios are then calculated for each rating scale/test. The formula for Likelihood Ratio (LR) is different for a positive and negative test result.

• The LR for a positive test result is calculated like: Sensitivity/1 - Specificity
• The LR for a negative test result is calculated like: 1 - Sensitivity/Specificity

Posttest Odds Posttest Odds = Pretest Odds x LR1 x LR2 x LR3 ….

Posttest Probability Posttest Probability = Posttest Odds / Posttest Odds + 1

Putting it all together Finally, we compare the tester’s Posttest Probability to the Pretest Probability to get the Elevated Likelihood (x Elevated) for each condition. So, if a test-taker's post-test probability is 10%, and the condition's prevalence (pre-test probability) is 5%, then their likelihood is 2x elevated.