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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

From: Time dependent hazard ratio estimation using instrumental variables without conditioning on an omitted covariate

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)