Table 1.
Details on the distribution of covariates and the effects each covariate had on the outcome and exposure in Scenarios 1‐6
| Covariates, X | Distribution of covariatesa | Effect of covariates | Confounders | Effect of confounders | |
|---|---|---|---|---|---|
| on outcome, β | on exposure, α | ||||
| S1 | (X 1,X 2) | X 1,X 2∼N(0,1) | (−1,1) | (X 2) | (ln(2)) |
| S2 | (X 1,X 2,X 3,X 4) | X 1,X 2,X 3,X 4∼N(0,1) | (−1,1,−1,−1) | (X 2,X 3,X 4) | (ln(2),ln(2),ln(2)) |
| S3 | (X 1,X 2,X 3,X 4) | X 1∼N(0,1) | (−1,1,−1−1) | (X 2,X 3,X 4) | (ln(2),ln(2),ln(2)) |
| (X 2,X 3,X 4)∼MVN(μ,Σ) | |||||
| S4 | (X 1,X 2,X 3,X 4) | X 1∼N(0,1) | (−1,1,−1,−1) | (X 2,X 3,X 4) | (ln(2),−ln(2),ln(2)) |
| (X 2,X 3,X 4)∼MVN(μ,Σ) | |||||
| S5 | (X 1,X 2,X 3,X 4) | X 1∼N(0,1) | (−1,1,−1.−1) | (X 2,X 3,X 4) | (ln(1.65),ln(1.65),ln(1.65)) |
| (X 2,X 3,X 4)∼MVN(μ,Σ) | |||||
| S6 | (X 1,X 2,X 3,X 4) | X 1∼N(0,1) | (−1,1,−1,−1) | (X 2,X 3,X 4) | (ln(1.25),ln(1.25),ln(1.25)) |
| (X 2,X 3,X 4)∼MVN(μ,Σ) |
a
μ=(0,0,0) and Σ has variances equal to 1 with correlation 0.5. Scenarios 7‐8 used baseline data from Scenario 6.