Table 1 Simulation Variables: Φ(·) is the cumulative distribution functions for the standard normal distribution and F1 is the cumulative distribution function for the time-to-event that has log-hazard of β1,β2,β3 in periods 1,2 and 3 respectively
| Variable | Symbol | Generation |
|---|---|---|
| Correlated Uniform Marginals | (Y0,Y1) | ∼ copula(ρ) |
| Omitted Covariate | U | Φ−1(Y0) |
| Instrumental Variable | W | ∼ N(0,1) |
| Potential Outcome if not Exposed | T0 | −log(Y0) |
| Potential Outcome if Exposed | T1 | \(F_{1}^{-1}(Y_{1})\) |
| Exposure | X | Pr [X=1]= logistic (αUXU+αWXW) |