# Table 1 Variables included in the simulation study, generating models, and notation

Variable description Generating models and notation
Number of simulated data sets N sim
Sample size each data set N obs
Treatment allocated Z i  = 0/1 for standard of care/intervention
Treatment received X i  = 0/1 for standard of care/intervention
Baseline hazard function for time until CVD event $${h}_0\left({t}_c\right)={\gamma}_c{\lambda}_c^{\gamma_c}{t}_c^{\gamma_c-1},\kern0.5em {\lambda}_c=36,\kern0.62em {\gamma}_c=1.2$$
Baseline hazard function for time mortality $${h}_0\left({t}_m\right)={\gamma}_m{\lambda}_m^{\gamma_m},\kern0.5em {\lambda}_m=55,\kern0.5em {\gamma}_c=1.2$$
Individual random effects ε i  ~ N(0, σ 2), σ = 0.7
Intervention effect β = − 0.32
Individual hazard function for time until CVD event $$h\left({t}_{i c}\right) = {h}_0\left({t}_c\right)\ {e}^{\left(\beta {X}_i+{\varepsilon}_i\right)}$$
Individual hazard function for time until mortality $$h\ \left({t}_{i m}\right)={h}_0\left({t}_m\right)\ {e}^{\left({\varepsilon}_i\right)}$$
Probability of a patient refusing intervention if offered and average patient refusal $$\begin{array}{l}{p}_i, p={\varSigma}_i{p}_i/{N}_{obs}\\ {}\end{array}$$
Probability of clinician refusing to offer the intervention to the patient and average clinician refusal $$\begin{array}{l}{q}_i, q={\varSigma}_i{q}_i/{N}_{obs}\\ {}\end{array}$$
Trial follow-up time in years T max = 3
Censoring indicator C i  = I(T ic  ≥ min(T im , T max  ))
Observed outcome Y i  = min(T ic , T im , T max )
Observed trial data {Y i , C i , Z i , X i }