# Generate operating characteristics for finding the maximum tolerated dose (MTD) defined by Equivalent Score (ET) using Quasi-CRM design Obtain the operating characteristics of Quasi-CRM design (Yuan et al. 2007) and Robust-Quasi-CRM design (Pan et al. 2014) for finding the maximum tolerated dose (MTD) using Equivalent Score (ET) derived from toxicity grade information ```r get_oc_RQ_CRM(ptox, skeletons, target, score, cohortsize, ncohort, n.earlystop = 100, start.dose = 1, mselection = 1, cutoff.eli = 0.90, ntrial = 10, seed = 100) ``` ## Arguments - `ptox`: true toxicity probability at each dose level - `skeletons`: a matrix to provide multiple skeletons with each row presenting a skeleton. If just one row, the function implements the Quasi-CRM design; if >=2 rows, the function implements the Robust-Quasi-CRM designn - `target`: the target toxicity score - `score`: the vector weight for ordinal toxicity levels - `cohortsize`: the cohort size - `ncohort`: the number of cohort - `n.earlystop`: the early stopping parameter. The default value is n.earlystop = 100 - `start.dose`: the starting dose level. The default value is start.dose = 1 - `mselection`: mselection = 1 (or 0) indicate to use Bayesian model selection (or mode averaging) to make inference across multiple skeletons. The default value is mselection = 1. It only applies to the Robust-Quasi-CRM design - `cutoff.eli`: the cutoff to eliminate an overly toxic dose for safety. The default value is cutoff.eli = 0.90 - `ntrial`: the number of simulated trials. The default value is ntrial = 10 - `seed`: the seed. The default value is seed = 100 ## Returns `get_oc_RQ_CRM()` returns the operating characteristics of (Robust)-Quasi-CRM design as a list object, including: (1) selection percentage at each dose level (2) patients treated at each dose level ## References Yuan, Z., R. Chappell, and H. Bailey. "The continual reassessment method for multiple toxicity grades: a Bayesian quasi-likelihood approach." Biometrics 63, no. 1 (2007): 173-179. Pan, Haitao, Cailin Zhu, Feng Zhang, Ying Yuan, Shemin Zhang, Wenhong Zhang, Chanjuan Li, Ling Wang, and Jielai Xia. "The continual reassessment method for multiple toxicity grades: a Bayesian model selection approach." PloS one 9, no. 5 (2014): e98147. ## Author(s) Chia-Wei Hsu, Haitao Pan, Rongji Mu ## Examples ```r ### Scenario 1 in Yuan et al. (2007) and Pan et al. (2014) target <- 0.47 score <- c(0, 0.5, 1, 1.5) cohortsize <- 3 ncohort <- 10 ntrial <- 10 ptox <- matrix(nrow = 4, ncol = 6) ptox[1,] <- c(0.83, 0.75, 0.62, 0.51, 0.34, 0.19) ptox[2,] <- c(0.12, 0.15, 0.18, 0.19, 0.16, 0.11) ptox[3,] <- c(0.04, 0.07, 0.11, 0.14, 0.15, 0.11) ptox[4,] <- c(0.01, 0.03, 0.09, 0.16, 0.35, 0.59) ### specify one skeleton (Quasi-CRM design) p1 <- c(0.11, 0.25, 0.40, 0.55, 0.75, 0.85) get_oc_RQ_CRM(ptox = ptox, skeletons = p1, target = target, score = score, cohortsize = cohortsize, ncohort = ncohort, ntrial = ntrial) ########################################### ### specify three skeletons (Quasi-CRM design) p1 <- c(0.11, 0.25, 0.40, 0.55, 0.75, 0.85) p2 <- c(0.05, 0.10, 0.15, 0.25, 0.40, 0.65) p3 <- c(0.20, 0.40, 0.60, 0.75, 0.85, 0.95) skeletons <- rbind(p1, p2, p3) get_oc_RQ_CRM(ptox = ptox, skeletons = skeletons, target = target, score = score, cohortsize = cohortsize, ncohort = ncohort, ntrial = ntrial) ```

get_oc_RQ_CRM function