CCT was significantly associated with glaucoma incidence in a simulated longitudinal population-based study when adjusted for measured IOP, but not crudely. Additionally, CCT was crudely associated with glaucoma incidence in a simulated study in which the participants were selected on measured IOP. These findings indicate the presence of collider bias, and this collider bias might explain the observed “independent” harmful association of a thin cornea in population-based studies and randomized controlled glaucoma trials.
In LALES, the observed adjusted OR for CCT was 1.30 per 40 µm decrease in CCT (see the
Table). This value aligns well with the results of the simulations (see
Fig. 3, right panel). The crude OR for CCT was not significant in LALES, which also agrees with our simulations (see
Fig. 3, left panel). In OHTS, the observed crude and adjusted OR were 1.88 and 1.71 per 40 µm decrease in CCT, respectively (see the
Table). These values are in the range of the simulations as well (see
Fig. 4, middle and right panels), although somewhat at the upper edge. Hence, the simulations of both LALES and OHTS do not only qualitatively but also quantitatively agree with the original observations, which further supports our hypothesis that collider bias may spuriously induce an association between CCT and glaucoma in two scenarios: adjusting for or selecting on measured IOP. Following parsimony, it is plausible that the observed significant CCT-glaucoma associations in LALES and OHTS were solely due to this collider bias. “Mutatis mutandis” the same may be the case in EMGT. The fact that the crude associations in both LALES and EMGT were not significant further weakens the concept of a biological association between CCT and glaucoma. It is not possible to exclude the possibility of small biological effects though.
Another important approach to assessing causality of associations is Mendelian randomization. If an exposure is causally associated with an outcome, then we would expect genetic factors robustly associated with the exposure to also associate with the outcome in turn. Given the random allocation of genotype at conception, this approach is considered analogous to a randomized controlled trial and therefore less susceptible to biases due to confounding and reverse causation. Choquet and colleagues have conducted the largest genomewide association study for CCT to date, identifying nearly 100 significant independent loci.
22 Using this data in a Mendelian randomization experiment, the investigators did not find evidence for a causal relationship between CCT and POAG.
22 This is in agreement with our suggestion that CCT has only been previously associated with POAG due to collider bias, rather than a true biological link.
Simulations are a simplification of reality. Especially in the simulation of OHTS, we ignored the existence of two arms (one treated and one untreated), the different inclusion criteria for both eyes (one eye had to have an IOP between 24 and 32 mm Hg and the other eye between 21 and 32 mm Hg), and the fact that the IOP distribution in the general population is reasonably normally distributed, but not toward the higher pressures, which were the ones that were included in the OHTS simulations. With these limitations, we used as realistic as possible estimates of all involved variables. With these estimates, the incidences of glaucoma in the simulations and the original studies agreed seemingly well (LALES = 4-year incidence simulated 96 of 3681 versus observed 87 of 3772; and OHTS = 5-year incidence simulated 8.6% versus observed 4.4% in the medication group and 9.5% in the observation group). As expected, due to selection based on high measured IOP, the CCT of the participants in the OHTS simulations (mean 599 µm and SD 35 µm; see the Results section) was greater than the CCT of the underlying general population (mean 540 µm and SD 40 µm; see the Methods section). In the original OHTS cohort,
23 mean (SD) CCT was 573 (39) µm – also clearly greater than that of the general population from which the OHTS participants were recruited, but the difference appears less pronounced than in the simulations. This could be related to the simplifications we made in the simulations (listed above). Both LALES and OHTS adjusted for several possible confounders, including age, in their IOPm-adjusted analysis. In our simulations, we adjusted only for IOPm, to present the effect of collider bias as clearly as possible. Age is formally not a confounding factor in the simulations; age is admittedly strongly associated with the outcome (incident glaucoma) but – in the simulated data – uncorrelated with the predictor of interest, CCT. To explore the effect of also considering age in the analyses, we added age to our IOPm-adjusted models. The results as presented in the right panel of
Figure 3 were very similar, whereas the point estimates in the right panel of
Figure 4 slightly increased. This slight increase might be due to an increase in precision of the model fit, related to the strong association between age and glaucoma risk (i.e. adjusting for age reduces noise for examining other associations).
Our findings question whether CCT is biologically associated with glaucoma and suggest that current evidence may be explained by collider bias. However, a lack of a biological relationship does not suggest that CCT is not important clinically. In fact, our simulations show that CCT is a powerful way of helping uncover variation in true IOP given measured IOP. So, whereas we would not wish to use CCT alone as a factor to identify people at high risk of glaucoma in the general population, using CCT in combination with measured IOP may be superior to using measured IOP alone. Additionally, in a setting where patients are selected for higher IOP (i.e. in a typical glaucoma clinic), then CCT will also be a helpful clinical parameter, by helping to stratify patients and identify patients whose true IOP may not be raised but just have high measured IOP due to a thicker CCT.
Researchers interested in examining causal relationships need to be aware of collider bias to avoid subsequent spurious interpretation of biased results. Here, we provide some practical steps to avoid such pitfalls. First, it is good practice to identify relevant covariables for the relationship of interest, and determine whether they will be potential confounders or troublesome colliders. A common pitfall is to assume that all covariables associated with the main exposure or outcome are confounding factors which should be adjusted for in multivariable models. However, only by considering the directions of the causal effects rather than simply any associations can researchers reliably differentiate between confounding factors and colliders. As such, drawing a directed acyclic graph at the outset of a study can help identify confounding factors (which should be adjusted for) and colliders (which should not be adjusted for or selected on when examining the causal nature of a relationship). It is also important to decide whether the study cohort is already selected on the basis of a collider. As illustrated in the OHTS example and our simulations, simply selecting on a collider (measured IOP >24 mm Hg in our example) can induce an artifactual crude association between CCT and glaucoma. It is not just adjusting for a collider that induces bias. In this situation, given there is no easy remedy if all study participants are already selected on the collider, it is important to be aware that any significant association may not be causal and state this clearly in the discussion to avoid misinterpretation by others. If the study population is not selected on a collider, but a collider covariable exists in the analytical dataset, researchers must be careful in the construction of multivariable models and the subsequent interpretation of results. A general recommendation is that crude associations are presented in addition to multivariable models. If an association only becomes apparent after adjusting for covariables, then it must be considered whether one or more of the adjusting covariables are colliders and that the observed association is spurious and not causal. It should be noted that collider bias is apparent whether considering variables as continuous traits or as categorized variables (e.g. dichotomized or tertiles). We additionally analyzed our simulations considering CCT as a tertile variable rather than a continuous trait, and the same collider bias was demonstrated (data not shown). Last, it should be stressed that there are situations in which it is appropriate to include collider variables in multivariable models. If the aim of the study is not to examine the biological causality of a relationship, but simply to build the most predictive model of an outcome, then including colliders may be appropriate. For example, in the OHTS scenario, even though CCT is likely not biologically related to glaucoma risk, in a population selected on measured IOP it is significantly predictive of glaucoma (due to the collider bias we have described). Therefore, CCT should be included in glaucoma prediction models as long as they are applied to a similarly selected population (i.e. patients with ocular hypertension), and that causal inferences are not made.