Compute the baseline parameters needed for sample size calculation for standard win ratio test
base.RdCompute the baseline parameters \(\zeta_0^2\) and \(\boldsymbol\delta_0\)
needed for sample size calculation for standard win ratio test (see WRSS).
The calculation is based
on a Gumbel–Hougaard copula model for survival time \(D^{(a)}\) and nonfatal event
time \(T^{(a)}\) for group \(a\) (1: treatment; 0: control):
$${P}(D^{(a)}>s, T^{(a)}>t) =\exp\left(-\left[\left\{\exp(a\xi_1)\lambda_Ds\right\}^\kappa+
\left\{\exp(a\xi_2)\lambda_Ht\right\}^\kappa\right]^{1/\kappa}\right),$$
where \(\xi_1\) and \(\xi_2\) are the component-wise log-hazard ratios to be used
as effect size in WRSS.
We also assume that patients are recruited uniformly over the period \([0, \tau_b]\)
and followed until time \(\tau\) (\(\tau\geq\tau_b\)), with an exponential
loss-to-follow-up hazard \(\lambda_L\).
Arguments
- lambda_D
Baseline hazard \(\lambda_D\) for death.
- lambda_H
Baseline hazard \(\lambda_H\) for nonfatal event.
- kappa
Gumbel–Hougaard copula correlation parameter \(\kappa\).
- tau_b
Length of the initial (uniform) accrual period \(\tau_b\).
- tau
Total length of follow-up \(\tau\).
- lambda_L
Exponential hazard rate \(\lambda_L\) for random loss to follow-up.
- N
Simulated sample size for monte-carlo integration.
- seed
Seed for monte-carlo simulation.
Value
A list containing real number zeta2 for \(\zeta_0^2\)
and bivariate vector delta for \(\boldsymbol\delta_0\).
References
Mao, L., Kim, K. and Miao, X. (2021). Sample size formula for general win ratio analysis. Biometrics, https://doi.org/10.1111/biom.13501.