A simulated data set under left truncation and right censoring where censoring can be before left truncation. The left truncation time and the event time are dependent via the two covariates `Z1' and `Z2'. Under the data generating mechanism, the conditional distribution of the censored event time X given covariates follows a Cox proportional hazards model in the full data, and the conditional distribution of the left truncation time given covariates follows a Cox proportional hazards model on the reversed time scale in the full data. The truncation rate is 29.5%; the censoring rate is 16.5%; \(P^*(C<Q) = 0.6057\); and the truth \(P^*(T>3) = 0.623955\).
data(simu_c1)A data frame with 500 rows and 5 variables.
the censored event time X = min(T,C)
the left truncation time
the event indicator
a continous covariate
a binary covariate