Fig 1.
DAG of Mendelian randomization method.
Abbreviation: DAG, directed acyclic graph.
Fig 2.
DAG demonstrating the issue of collider bias in studies with participants selected according to disease status.
In this situation, collider bias can induce an association (dashed line) between any factors (A, C, and U) that affect disease incidence (or other study selection criteria). When 1 or more of these factors are also associated with disease progression (C, U), a path is opened up from A to disease progression through the induced association. If A is a genetic risk factor, it can appear that there is an association between genetic risk factor A and disease progression only because of the induced association with C or U. If C is measured and can be adjusted for, then the induced association is blocked, but unmeasured U cannot be adjusted for in the analysis. Only when the genetic risk factor for progression is not also a risk factor for incidence (i.e., B) will it not be affected by selection bias. The arrows in Figure 2 show causal paths between variables—e.g., that variable A causes disease incidence. A collider is a variable which has 2 paths entering it, e.g., disease incidence. A path is blocked by a collider—i.e., the path from A to disease progression is blocked by disease incidence. If a collider is conditioned on, then that path is unblocked—i.e., if disease incidence is conditioned upon, then the path from A to disease progression becomes unblocked (i.e., collider bias may occur). Abbreviation: DAG, directed acyclic graph.
Fig 3.
DAG to demonstrate how the introduction of collider bias through the selection of cases (grey paths) can impact an MR analysis between an exposure and disease progression as an outcome.
Associations are induced because SNP causes disease (via exposure), and thus conditioning on disease induces an association between all variables causing disease. In a model not adjusting for exposure (e.g., relating SNP to progression), there is an association between SNP and the confounders, which biases the SNP-progression association. Abbreviations: DAG, direct acyclic graph; MR, Mendelian randomization.
Table 1.
Estimated effects of the risk factor for incidence only (A) and the risk factor for incidence and progression (C) from Fig 2 under different degrees of unmeasured confounding of incidence and progression.