Associations of mortality with own blood pressure usingson’s blood pressure as an instrumental variable

Figures

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  Figure 1. Adjusted hazard ratios (HR) for parental mortality per standard deviation (SD) of own SBP, using son’s SBP as an instrumental variable (IV). SBP was pre-adjusted for regional patterns, secular trends and age at examination and its SD was 10.80 mmHg. Cox proportional hazards models with age as the time axis were adjusted for parental sex and for educational and occupational socioeconomic position. Robust standard errors were clustered by the son’s identity. PM vs F was derived from a Z-test of an additional interaction term between parental sex and son’s SBP. Two-sample IV estimates were made using the ratio method. Mothers and fathers were also modelled separately, without the robust standard errors or the adjustment for parental sex. Plotted data are tabulated in Supplementary Table S8. N = 1,002,031 mothers and 986,075 fathers at risk of mortality.

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  Figure 2. Adjusted hazard ratios (HR) for parental mortality per standard deviation (SD) of own DBP, using son’s DBP as an instrumental variable (IV). DBP was pre-adjusted for regional patterns, secular trends and age at examination and its SD was 9.22 mmHg. Cox proportional hazards models with age as the time axis were adjusted for parental sex and for educational and occupational socioeconomic position. Robust standard errors were clustered by the son’s identity. PM vs F was derived from a Z-test of an additional interaction term between parental sex and son’s DBP. Two-sample IV estimates were made using the ratio method. Mothers and fathers were also modelled separately, without the robust standard errors or the adjustment for parental sex. Plotted data are tabulated in Supplementary Table S9. N = 1,002,031 mothers and 986,075 fathers at risk of mortality.

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  Figure 3. Plots of hazard ratio (HR; relative to the median blood pressure) for parental coronary heart disease (CHD) mortality against a son’s systolic (SBP) or diastolic (DBP) blood pressure. Son’s SBP and DBP were pre-adjusted for regional patterns, secular trends and age at examination. Cox regressions with parental age as the time axis modeled SBP or DBP as cubic splines with 4 knots and were adjusted for the parent’s educational and occupational socioeconomic position. Shaded areas represent 95% confidence intervals. For clarity, plots are truncated at the 1st and 99th percentiles of SBP or DBP.

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  Figure 4. Directed acyclic graph illustrating potential confounders of the effect of blood pressure (BP) on mortality, when a son’s BP is used as an instrument. A conventional estimate of g (the effect of the exposure on the outcome) may be biased due to confounding via pathways such as cd and hi. An IV estimate of the same effect may be biased by confounding via pathway bad, and any such bias is magnified by the reciprocal of the association ef + bac between instrument and exposure. The IV estimate of g is likely to be biased by socio-economic position (SEP; and other environmental or behavioural factors such as smoking behaviour which are associated between generations) but we argue that reverse causation (i.e. confounding by the parent’s health) is unlikely to bias the IV estimate. An unbiased instrumental variables analysis also requires that there be no pathway from instrument to outcome (except via the exposure) and that the association between instrument and exposure is non-null. In the present case, a causal effect of son’s blood pressure on parental BP is implausible; we must further assume that there is no causal effect of parental BP on son’s BP and that the common genetic and…