Dear biostars, 

Is there a statistical method to tease whether an elevated polygenic risk score is independent to a monogenic risk? I have a cohort of patient and controls who have undergone whole genome sequencing. I have then done collapsing rare variant testing using SAIGE-GENE and found a gene that is strongly enriched in the disease cohort. I have then applied a validated polygenic risk score (PRS) and again found a statistically significant enrichment in cases over controls both including and excluding those cases that are part of the monogenic hit. 

A subset analysis of the PRS cases and controls with variants that qualified for the monogenic hit show a near doubling of the PRS in cases over controls but the numbers are likely too small to reach statistical significance.

My question is whether there is a method to see if the PRS and monogenic hits are statistically independent from each other. My hypothesis is that those with monogenic risk also have an elevated PRS and it is that which is what pushes them into having the phenotype as the OR of having disease in the presence of the monogenic variants is 2.5 with a penetrance of 0.28.

Many thanks for your time
"Statistical independence" is really a heavy lift; and the only physical way to achieve this would be to have the gene independently **inherited** from all of the other polygenic risk variants; and the only way I can think of for this to happen would for the gene to be on its very own chromosome. Otherwise there will always be mutations in LD with your gene that capture some fraction of the risk. However the **correlation** could be low (if, say, most of the PRS is coming from other loci).

Have you tried simply plotting the burden score (x-axis) and PRS  (y-axis)?