generate_data {transmdl}

Generate data for simulation.

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 \Lambda(t) = \rho log(1+t) assumed in simulation

beta_true

parameter \beta

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\left\{-H \{\Lambda(t) \exp ( \beta^T X_{i} ) \}\right\}.

The failure time T_i can be generated by

T_i = \left\{\begin{array}{l l} \exp\{ \frac{U^{-\alpha}-1}{\alpha\rho\exp\{\beta^TX_i \}} \}-1& \alpha > 0, \\ \exp\{ \frac{-log(U)}{\rho\exp\{\beta^TX_i \}} \}-1, & \alpha = 0. \end{array}\right\}

Value

a list containing

X			design matrix
beta_X			X\cdot\beta^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))