Fig 1.
Top: Typical assumptions underlying the causal interpretation of an exposure X or treatment T on an outcome Y following standard regression analysis. Note that we assume NUC implies exchangeability: B = Bottom-left: Assumptions underlying a standard MR analysis using genetic variant G as an IV to estimate the causal effect of X on Y. C = Bottom-right: Assumptions underlying a standard pharmacogenetic analysis.
Fig 2.
Causal diagram explaining the key assumptions leveraged by the methods proposed.
The diagram and notation are consistent with outcome model (2) and the simulation simulation study. Here and throughout the paper, the variable Z represents measured confounders of T and Y and U represents unmeasured confounders.
Table 1.
Columns left to right show: Statistical formulae for GMTE(1), GMTE(0), RGMTE, MR and CAT estimates; Sufficient assumptions each one relies upon to consistently estimate the GMTE (or zero in the case of the GMTE(0) estimate); Estimate-specific confounder test statistics; generic R code to obtain each estimate.
For the GMTE(0) estimate, , for the GMTE(0) estimate T− = 1 − T, T*− = T− G, for the RGMTE estimate T* = TG and
. Note that the GMTE(0) estimate does not directly target the GMTE, but rather zero under the PG assumptions.
Fig 3.
Two statistically uncorrelated estimates are homogenous enough to be meaningfully combined—case (i)—or are too heterogeneous to be combined—case (ii).
Fig 4.
A schematic diagram showing all possible 9 single, two-way or three-way combined estimators of the GMTE that can be calculated using the TWIST framework.
Fig 5.
Distribution of estimates for the CAT, GMTE(1), GMTE(0), RGMTE and MR estimators across six simulation scenarios.
In each case, the true GMTE is fixed at -0.5.
Table 2.
Mean point estimates, standard errors and coverage (of 95% confidence interval) for the CAT, GMTE(1), GMTE(0) RGMTE and MR estimates across six simulation scenarios.
In each case, the true GMTE is fixed at -0.5. Unbiased estimates and associated standard errors/coverages are highlighted in bold.
Table 3.
Mean point estimates, standard errors, coverage (of 95% confidence interval) and heterogeneity test rejection rates for the five combined estimates across six simulation scenarios.
In each case, the true GMTE is fixed at -0.5. Unbiased estimates and associated standard errors/coverage are highlighted in bold.
Fig 6.
Mean standard error of the CAT, GMTE(1), GMTE(0), RGMTE and MR estimates for Scenario 3 as a function of the minor allele frequency of G.
Table 4.
Baseline data on UK Biobank participants in the Clopidogrel analysis set.
*Based on hospital episode statistics data.
Fig 7.
Forest plot of results for the Clopidogrel data.
Blue squares show individual causal estimates as well as combined estimators that pass the heterogeneity test at the 5% level. Black squares show combined estimates that fail the heterogeneity test at the 5% level. Red bar shows the point estimate and confidence interval for the GMTE(0) estimate.
Table 5.
Hazard difference estimates (LoF carriers versus non-carriers) on percentage scale for all single and combined estimates.
Table 6.
Baseline covariates, genetic data and incident CAD cases on statin users and non-users in UK Biobank.
Table 7.
Hazard difference estimates on the % scale for all single and valid combined estimates for the e2e3 and e4e4 genotype groups.
Table 8.
Hazard difference estimates on the % scale for all single and valid combined estimates.
Fig 8.
Hazard difference estimates for the e4e4 versus e3e3 analyses.
Color coding the same as for Fig 7.
Fig 9.
Hazard difference estimates for the e2e3 versus e3e3 analyses.
Color coding the same as for Fig 7.