Equivalence Testing

Subsequently, we further test our hypothesis by comparing the frequencies of the variants with the highest \(\mathbb{P}(j=4)\) against the frequencies of schizophrenia and bipolar disorder across Canada.  We manually extract demographic distributions for each of the top 10% of variants for SCZ and BPD with the highest probability of being placed in \(j\) = 4 from the Genome Aggregation Database (gnomAD) browser v2.1.1 and v3.1.2 \citep{r2014}. Any variant that was not recorded in either version of gnomAD was excluded from the study, resulting in a variant population size of n = 66 and n = 37 for SCZ and BPD, respectively.  Additionally, the age and sex frequency distributions of SCZ and BPD crude prevalence in Canada from the 2019–2020 fiscal year were recorded from the Canadian Chronic Disease Surveillance System (CCDSS; \citealp{canada2019}).  Any individual outside of >30, 50–55, or <80 age brackets in addition to any individual who could not be classified as male or female at birth were excluded from analysis.
A two one–sided test (TOST) was used to find a possible correlation between the predicted frequency sets (based on AKAP11 variants) and observed frequency sets (based on CCDSS).  Lower and upper equivalence bounds are \(\mathrm{\pm}\)1.1 for SCZ and\(\mathrm{\pm}\)2.3 for BPD, and a failure to show that each data set violates these bounds using t tests is sufficient evidence for equivalence \citep{Lakens2017}.  Similarly, we perform the Shapiro–Wilk and F–Test to test for equal variance and normal distribution, ensuring appropriate use of the t test.