Interpretation of Mendelian randomization using a single measure of an exposure that varies over time

Abstract

Background: Mendelian randomization (MR) is a powerful tool through which the causal effects of modifiable exposures on outcomes can be estimated from observational data. Most exposures vary throughout the life course, but MR is commonly applied to one measurement of an exposure (e.g. weight measured once between ages 40 and 60 years). It has been argued that MR provides biased causal effect estimates when applied to one measure of an exposure that varies over time.

Methods: We propose an approach that emphasizes the liability that causes the entire exposure trajectory. We demonstrate this approach using simulations and an applied example.

Results: We show that rather than estimating the direct or total causal effect of changing the exposure value at a given time, MR estimates the causal effect of changing the underlying liability for the exposure, scaled to the effect of the liability on the exposure at that time. As such, results from MR conducted at different time points are expected to differ (unless the effect of the liability on exposure is constant over time), as we illustrate by estimating the effect of body mass index measured at different ages on systolic blood pressure.

Conclusion: Univariable MR results should not be interpreted as time-point-specific direct or total causal effects, but as the effect of changing the liability for the exposure. Estimates of how the effects of a genetic variant on an exposure vary over time, together with biological knowledge that provides evidence regarding likely effective exposure periods, are required to interpret time-point-specific causal effects.

Keywords: Mendelian randomization; causal inference; longitudinal; simulation.

Figure 1

Causal diagram showing two exposures and one outcome $G$ , genetic instrument; $L$, liability; $X_0$, exposure measured at time 0; $X_1$, exposure measured at time 1; $Y$, outcome; $U$, confounder. Other sources of variability in the liability, exposures and outcome are not shown in this diagram. There is a problem of under-identification here in that the direct effects of $X_0$ or $X_1$ on $Y$ cannot be estimated with a single liability ($L$).

Figure 2

Directed acyclic graph showing the exposure liability in the context of two exposures and one outcome $G$ , genetic instrument; $L$, liability; $X_0$, exposure measured at time 0; $X_1$, exposure measured at time 1; $Y$, outcome. Note that confounders or other causes of variability in liability, exposures or outcome are not shown.

Figure 3

Simulated parameters $G,\mathrm{ }\mathrm{genotype};\mathrm{ }L$ , liability; $X_0$, exposure measured at time 0; $X_1,\mathrm{ }\mathrm{exposure}\mathrm{ }\mathrm{measured}\mathrm{ }\mathrm{at}\mathrm{ }\mathrm{time}\mathrm{ }1;\mathrm{ }Y,\mathrm{ }\mathrm{outcome};\mathrm{ }U$, confounder.

Figure 4

Linear prediction of mean body mass index at different ages from additive genetic models by FTO rs9939609 genotype FTO, fat mass and obesity-associated gene. AA: two risk variant; AT: one risk variant; TT: zero risk variants.