Fig. 4

Hypothetical relationships between germline PRS, risk factor, mutational signature, and diagnosis of cancer. a Exposure is associated with the outcome due to collider bias. Exposure (A) will be associated with outcome (Y) within levels of their common effect (L) even if there is no causal effect of exposure (A) on the outcome (Y). b Cancer PRS is associated with mutational signature due to collider bias. Cancer diagnosis (D) may or may not have an effect on somatic mutations of certain mutational signature (M). The cancer risk factor (X) is independent of cancer PRS (G) in the general population and is also associated with mutational signatures (M). Conditioning on diagnosis (D, i.e., studying cancer cases only) would induce collider bias on the relationship between cancer PRS (G) and mutational signature (M). If the cancer risk factor (X) is positively associated with both cancer diagnosis (D) and mutational signature (M), then an inverse association between cancer PRS (G) and mutational signature (M) is likely to be observed. c Three possible relationships between cancer or non-cancer PRS, mutational signature, and cancer diagnosis assuming no reverse causation. (i) Indirect effect: PRS (G) has an indirect effect on tumor development and diagnosis (D) through inducing somatic mutations of certain mutational signature (M); (ii) non-carcinogenic effect: PRS (G) has an effect on inducing somatic mutations of certain mutational signature (M) but neither PRS (G) nor somatic mutations (M) has an effect on tumor development and diagnosis (D); (iii) direct (and indirect) effect: PRS (G) has a direct effect on tumor development and diagnosis (D) that is not through the effect of somatic mutations (M) and may or may not have an indirect effect through somatic mutations (M). In this case, conditioning on diagnosis (D, i.e., studying cancer cases only) would induce collider bias on the relationship between PRS (G) and mutational signature (M)