PWEALL2-package: Design and Monitoring of Survival Trials Accounting for...

In PWEALL: Design and Monitoring of Survival Trials Accounting for Complex Situations

Design and Monitoring of Survival Trials Accounting for Complex Situations

Description

Calculates various functions needed for design and monitoring survival trials accounting for complex situations such as delayed treatment effect, treatment crossover, non-uniform accrual, and different censoring distributions between groups. The event time distribution is assumed to be piecewise exponential (PWE) distribution and the entry time is assumed to be piecewise uniform distribution. As compared with Version 1.2.1, two more types of hybrid crossover are added. A bug is corrected in the function "pwecx" that calculates the crossover-adjusted survival, distribution, density, hazard and cumulative hazard functions. Also, to generate the crossover-adjusted event time random variable, a more efficient algorithm is used and the output includes crossover indicators.

Details

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There are 5 types of crossover considered in the package: (1) Markov crossover, (2) Semi-Markov crosover, (3) Hybrid crossover-1, (4) Hybrid crossover-2 and (5) Hybrid crossover-3. The first 3 types are described in Luo et al. (2018). The fourth and fifth types are added for Version 1.3.0. The crossover type is determined by the hazard function after crossover \lambda_2^{\bf x}(t\mid u). For Type (1), the Markov crossover,

\lambda_2^{\bf x}(t\mid u)=\lambda_2(t).

For Type (2), the Semi-Markov crossover,

\lambda_2^{\bf x}(t\mid u)=\lambda_2(t-u).

For Type (3), the hybrid crossover-1,

\lambda_2^{\bf x}(t\mid u)=\pi_2\lambda_2(t-u)+(1-\pi_2)\lambda_4(t).

For Type (4), the hazard after crossover is

\lambda_2^{\bf x}(t\mid u)=\frac{\pi_2\lambda_2(t-u)S_2(t-u)+(1-\pi_2)\lambda_4(t)S_4(t)/S_4(u)}{\pi_2 S_2(t-u)+(1-\pi_2)S_4(t)/S_4(u)}.

For Type (5), the hazard after crossover is

\lambda_2^{\bf x}(t\mid u)=\frac{\pi_2\lambda_2(t-u)S_2(t-u)+(1-\pi_2)\lambda_4(t-u)S_4(t-u)}{\pi_2 S_2(t-u)+(1-\pi_2)S_4(t-u)}.

The types (4) and (5) are more closely related to "re-randomization", i.e. when a patient crosses, (s)he will have probability \pi_2 to have hazard \lambda_2 and probability 1-\pi_2 to have hazard \lambda_4. The types (4) and (5) differ in having \lambda_4 as Markov or Semi-markov.

Author(s)

Xiaodong Luo [aut, cre], Xuezhou Mao [ctb], Xun Chen [ctb], Hui Quan [ctb], Sanofi [cph]

Maintainer: Xiaodong Luo <[e-mail]>

References

Luo et al. (2018) Design and monitoring of survival trials in complex scenarios, Statistics in Medicine <doi: https://doi.org/10.1002/sim.7975>.

PWEALL documentation built on Aug. 9, 2023, 9:08 a.m.