Mendelian randomisation with coarsened exposures

Abstract

A key assumption in Mendelian randomisation is that the relationship between the genetic instruments and the outcome is fully mediated by the exposure, known as the exclusion restriction assumption. However, in epidemiological studies, the exposure is often a coarsened approximation to some latent continuous trait. For example, latent liability to schizophrenia can be thought of as underlying the binary diagnosis measure. Genetically driven variation in the outcome can exist within categories of the exposure measurement, thus violating this assumption. We propose a framework to clarify this violation, deriving a simple expression for the resulting bias and showing that it may inflate or deflate effect estimates but will not reverse their sign. We then characterise a set of assumptions and a straightforward method for estimating the effect of SD increases in the latent exposure. Our method relies on a sensitivity parameter which can be interpreted as the genetic variance of the latent exposure. We show that this method can be applied in both the onesample and two-sample settings. We conclude by demonstrating our method in an applied example and reanalysing two papers which are likely to suffer from this type of bias, allowing meaningful interpretation of their effect sizes.

Is genetic liability to ADHD and ASD causally linked to educational attainment?

“…ADHD, ASD) are often approximated by continuous latent liabilities, assuming that they are normally distributed in the population. 27 , 28 Under liability-threshold models of inheritance, an individual’s liability will be phenotypically expressed after the threshold has been exceeded, depending on the synergy of genetic variation, environmental factors and chance. 29–32 This seems to be supported for ADHD and ASD, as high polygenic risk to the conditions has been associated with sub-threshold phenotypic expressions (traits) in the general population.…”

Estimation of causal effects of a time-varying exposure at multiple time points through Multivariable Mendelian randomization

“…The observed effect in the MR estimates of childhood body size on smoking are due to a combination of the effect of SNPs associated with childhood body size also having an effect on adult body size and an indirect effect of childhood body size on smoking behaviour through its effect on adult body size. Steiger filtering [41] between adult body size and the outcome removed very few ( 5) SNPs for any of the smoking behaviours and did not change the results obtained, results given in Supplementary Table 2.…”

“…[2][3][4] As genetic variants which do not change during an individual's lifetime are used as instruments the estimated effects are interpreted as the lifetime effect of the genetically predicted exposure, or genetic liability for an exposure if that exposure is binary. [5] Many exposures, such as BMI, may have varying effects on any particular outcome over the course of an individual's lifetime. Higher BMI in childhood is observationally associated with many health outcomes later in life.…”

“…[2–4] As genetic variants which do not change during an individual’s lifetime are used as instruments the estimated effects are interpreted as the lifetime effect of the genetically predicted exposure, or genetic liability for an exposure if that exposure is binary. [5]…”

Examining risk factors for weight change during midlife: A Mendelian randomization study

“…MR has been successfully applied to estimate the genetically predicted effect of biological, behavioural and socioeconomic exposures on disease risk (22)(23)(24)(25). MR investigations have also been extended to evaluate the genetically predicted effects of disease liability on outcomes (26), which includes diseases that typically have a late-onset in the lifecourse, such as dementia. Whilst latent liability to dementia can be thought of as probabilistically underlying the binary diagnosis measure, results are therefore interpreted on the liability scale (27,28).…”