Comparison of intergenerational instrumental variable analyses of body mass index and mortality in UK Biobank

Abstract

Background: An increasing proportion of people have a body mass index (BMI) classified as overweight or obese and published studies disagree whether this will be beneficial or detrimental to health. We applied and evaluated two intergenerational instrumental variable methods to estimate the average causal effect of BMI on mortality in a cohort with many deaths: the parents of UK Biobank participants.

Methods: In Cox regression models, parental BMI was instrumented by offspring BMI using an 'offspring as instrument' (OAI) estimation and by offspring BMI-related genetic variants in a 'proxy-genotype Mendelian randomization' (PGMR) estimation.

Results: Complete-case analyses were performed in parents of 233 361 UK Biobank participants with full phenotypic, genotypic and covariate data. The PGMR method suggested that higher BMI increased mortality with hazard ratios per kg/m2 of 1.02 (95% CI: 1.01, 1.04) for mothers and 1.04 (95% CI: 1.02, 1.05) for fathers. The OAI method gave considerably higher estimates, which varied according to the parent-offspring pairing between 1.08 (95% CI: 1.06, 1.10; mother-son) and 1.23 (95% CI: 1.16, 1.29; father-daughter).

Conclusion: Both methods supported a causal role of higher BMI increasing mortality, although caution is required regarding the immediate causal interpretation of these exact values. Evidence of instrument invalidity from measured covariates was limited for the OAI method and minimal for the PGMR method. The methods are complementary for interrogating the average putative causal effects because the biases are expected to differ between them.

Keywords: Mendelian randomization; UK Biobank; body mass index; instrumental variable; intergenerational; mortality; offspring as instrument; proxy genotype.

Figure 1

Illustration of the probable causal relationships explored in these analyses. The dashed arrow indicates an absent causal relationship. A conventional observational analysis of the effect of parental body mass index (BMI) (BMI_P) on parental mortality (Mort_P) would be confounded by their common environmental causes (E₂). For an unbiased instrumental variables analysis, BMI_P must be a collider on any pathway between the instrument and Mort_P that does not include the causal effect of BMI_P on Mort_P. This means that the instrument must cause BMI_P or they must have a common cause. If BMI_P causes the instrument, estimates will be biased. It is not plausible that the instrument causes BMI_P (dotted line) in either a proxy-genotype Mendelian randomization (PGMR) or an offspring as instrument (OAI) analysis. In a PGMR analysis, the instrument is the offspring’s genotype (G_o). This is not plausibly caused by BMI_P but is associated with it due to their common cause being parental genotype (G_p). Furthermore, G_p is likely to be independent of E₂, making G_o a valid instrument for BMI_P. In an OAI analysis, the instrument is the offspring’s BMI (BMI_o). We must assume that parental BMI does not have a causal effect on offspring BMI but that they are associated due to common genetic (G_P) and environmental (E₁) causes. As discussed above, the common genetic causes are plausibly independent of E₂ but we cannot establish whether E₁ and E₂ are independent; non-independence of E₁ and E₂ would invalidate BMI_O as an instrument

Figure 2

Flowchart of participants included in main analyses. BMI, body mass index

Figure 3

Bias components from measured covariates. Separate analyses were made in the data available for mothers and fathers, and for sons (S) and daughters (D). Bias components are on an arbitrary, relative scale and are comparable between the two instrumental variable (IV) methods for each covariate but not between covariates or sexes. They were therefore scaled for plotting by the absolute magnitude of the larger of each pair for ease of presentation. Plotted bias components are ordered by absolute relative bias [bias in offspring as instrument (OAI)/bias in genetic risk score proxy-genotype Mendelian randomization (GRS-PGMR)]. Error bars are 95% CIs