generate_data: Generate data for simulation.

In transmdl: Semiparametric Transformation Models

Description

Generate observed event times, covariates and other data used for simulations in the paper.

Usage

generate_data(n, alpha, rho, beta_true, now_repeat = 1)

Arguments

n	number of subjects
alpha	parameter in transformation function
rho	parameter in baseline cumulative hazard function Λ(t) = ρ log(1+t) assumed in simulation
beta_true	parameter β
now_repeat	number of duplication of simulation

Details

The survival function for t of the ith observation takes the form

S_{i}(t| X_{i}) = \exp≤ft\{-H \{Λ(t) \exp ( β^T X_{i} ) \}\right\}.

The failure time T_i can be generated by

T_i = ≤ft\{\begin{array}{l l} \exp\{ \frac{U^{-α}-1}{αρ\exp\{β^TX_i \}} \}-1& α > 0, \\ \exp\{ \frac{-log(U)}{ρ\exp\{β^TX_i \}} \}-1, & α = 0. \end{array}\right\}

Value

a list containing

X			design matrix
beta_X			X\cdotβ^T
Y			observed event time

References

Abramowitz, M., and Stegun, I.A. (1972). Handbook of Mathematical Functions (9th ed.). Dover Publications, New York. +- Evans, M. and Swartz, T. (2000). Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford University Press.

Liu, Q. and Pierce, D.A. (1994). A note on Gauss-Hermite quadrature. Biometrika 81: 624-629.

Examples

 generate_data(200,0.5,1,c(0.5,-1))

transmdl documentation built on Oct. 14, 2021, 5:07 p.m.