stoch_pred: A stochastic prediction results
In lilywang1988/GSMC: Group Sequential Design for Maxcombo tests

Description Usage Arguments Value Author(s) References

A stochastic-process way of prediction of the expected event ratio (D), mean difference (μ), and the information(variance) using stoch_pred or the covariance using stoch_pred.cov.

stoch_pred(eps, p, b, tau, omega, lambda, theta, rho, gamma, R)

stoch_pred.cov(
  eps,
  p,
  b,
  tau,
  omega,
  lambda,
  theta,
  rho1,
  gamma1,
  rho2,
  gamma2,
  R
)

`eps`	delayed treatment effect time.
`p`	probability of treatment assignment.
`b`	the number of sub-intervals at each time point, the larger the finer splitting for more accurate computation. Usually b = 30 is sufficient.
`omega`	the minimum follow-up time for all the patients. Note that Hasegawa(2014) assumes that the accrual is uniform between time 0 and R, and there does not exist any censoring except for the administrative censoring at the ending time τ. Thus this value omega is equivalent to `tau-R`.
`lambda`	the hazard for the control group.
`theta`	the hazard ratio after the delayed time `eps` for the treatment arm.
`rho, rho1, rho2`	the first parameter for Fleming Harrington weighted log-rank test:W(t)=S^ρ(t^-)(1-S(t^-))^γ.
`gamma, gamma1, gamma2`	the second parameter for Fleming Harrington weighted log-rank test:W(t)=S^ρ(t^-)(1-S(t^-))^γ.
`R`	the accrual period.

`sum_D`	the mean expected event ratio. Once being multiplied by `n`, it will become the stochastically predicted event size.
`inf or covariance`	the information/variance or covariance (averaged for each subject), should be multiplied by `n`, which gives the stochastically predicted information.
`E.star`	the unit mean, corresponding to E^* in Hasegawa(2014), or the \tilde{μ} of formula (8) in Wang et al(2021).
`trt_vs_ctrl_N`	the ratio of the samples sizes between the two arms, treatment vs control, corresponding to the time vector `t_vec`.
`t_vec`	the time sequence corresponding to `trt_vs_ctrl_N`.

Lili Wang

Hasegawa, T. (2014). Sample size determination for the weighted log‐rank test with the Fleming–Harrington class of weights in cancer vaccine studies. Pharmaceutical statistics, 13(2), 128-135. Wang, L., Luo, X., & Zheng, C. (2021). A Simulation-free Group Sequential Design with Max-combo Tests in the Presence of Non-proportional Hazards. Journal of Pharmaceutical Statistics.

lilywang1988/GSMC documentation built on March 9, 2021, 5:25 p.m.