tools:::Rd_package_description("PWEALL")
tools:::Rd_package_author("PWEALL")
Maintainer: tools:::Rd_package_maintainer("PWEALL")
The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("PWEALL") tools:::Rd_package_indices("PWEALL")
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.
Luo et al. (2018) Design and monitoring of survival trials in complex scenarios, Statistics in Medicine <doi: https://doi.org/10.1002/sim.7975>.