The PKPOP model is a variation of the PKLOGIT model which replaced AUCs (\(z_j\)) with AUC of the population (\(z_{k,pop}\)), where \(z_{k,pop}\) is the mean value of the logarithm of AUC at dose k, predicted by the hierarchical model: $$z_{i} \vert \boldsymbol{\beta}, \nu \sim N \left( \beta_0 + \beta_1 \log d_{i}, \nu^{2} \right)$$ where \(\boldsymbol{\beta} = (\beta_0,\beta_1)\) are the regression parameters and \(\nu\) is the standard deviation. and the logistic regression model: $$\mbox{logit}(p_T(z_{k,pop}, \boldsymbol{\beta})) = -\beta_3 + \beta_4 z_{k,pop}$$ with a bivariate Uniform distribution as prior distribution for the parameters \(\boldsymbol{\beta} = (\beta_3, \beta_4)\).
The default choices of the priors are: $$\boldsymbol{\beta} \vert \nu \sim N(m, \nu*beta0),$$ $$\nu \sim Beta(1,1),$$ $$m = (-log(CL_{pop}), 1),$$ where \(Cl_{pop}\) is the population clearance. $$\beta_3 \sim U(0, beta3mean),$$ $$\beta_4 \sim U(0, beta4mean)$$ where default choices are \(Cl_{pop} = 10\), beta0 = 10000, beta3mean = 10 and beta4mean = 5. Therefore, the default choices for model's priors are given by $$betapriors = c(Cl_{pop} = 10, beta0 = 10000, beta3mean = 10, beta4mean = 5)$$
Finally, the PKPOP model has the following stopping rule in toxicity: if $$P(p_T(dose) > theta) > prob$$ then, no dose is suggested and the trial is stopped.
pkpop(y, auc, doses, x, theta, prob = 0.9, options = list(nchains = 4, niter = 4000,
nadapt = 0.8), betapriors = c(10, 10000, 10, 5), thetaL = NULL, p0=NULL,
L=NULL, deltaAUC=NULL, CI = TRUE)A binary vector of patient's toxicity outcomes; TRUE indicates a toxicity, FALSE otherwise.
A vector with the doses panel.
A vector with the dose level assigned to the patients.
The toxicity target.
The threshold of the posterior probability of toxicity for the stopping rule; defaults to 0.9.
A vector with the value for the prior distribution of the regression parameters in the model; defaults to betapriors = c(\(Cl_{pop}\), beta0, beta3mean, beta4mean), where \(Cl_{pop} = 10\), beta0 = 10000, beta3mean = 10 and beta4mean = 5.
A list with the Stan model's options; the number of chains, how many iterations for each chain and the number of warmup iterations; defaults to options = list(nchains = 4, niter = 4000, nadapt = 0.8).
A vector with the computed AUC values of each patient for pktox, pkcrm, pklogit and pkpop; defaults to NULL.
The difference between computed individual AUC and the AUC of the population at the same dose level (defined as an average); argument for pkcov; defaults to NULL.
The skeleton of CRM for pkcrm; defaults to NULL (must be defined only in the PKCRM model).
The AUC threshold to be set before starting the trial for pklogit, pkcrm and pktox; defaults to NULL (must be defined only in the PKCRM model).
A second threshold of AUC; must be defined only in the PKCRM model.
A logical constant indicating the estimated 95% credible interval; defaults to TRUE.
A list is returned, consisting of determination of the next recommended dose and estimations of the model. Objects generated by pkpop contain at least the following components:
The next maximum tolerated dose (MTD); equals to "NA" if the trial has stopped before the end, according to the stopping rules.
The mean values of estimated probabilities of toxicity.
The summary of the estimated probabilities of toxicity if CI = TRUE, otherwise is NULL.
The estimated model's parameters.
Ursino, M., et al, (2017) Dose-finding methods for Phase I clinical trials using pharmacokinetics in small populations, Biometrical Journal, <doi:10.1002/bimj.201600084>.
Toumazi, A., et al, (2018) dfpk: An R-package for Bayesian dose-finding designs using pharmacokinetics (PK) for phase I clinical trials, Computer Methods and Programs in Biomedicine, <doi:10.1016/j.cmpb.2018.01.023>.
Patterson, S., Francis, S., Ireson, M., Webber, D., and Whitehead, J. (1999) A novel bayesian decision procedure for early-phase dose-finding studies. Journal of Biopharmaceutical Statistics, 9 (4), 583-597.
Whitehead, J., Patterson, S., Webber, D., Francis, S., and Zhou, Y. (2001) Easy-to-implement bayesian methods for dose-escalation studies in healthy volunteers. Biostatistics, 2 (1), 47-61.
Whitehead, J., Zhou, Y., Hampson, L., Ledent, E., and Pereira, A. (2007) A bayesian approach for dose-escalation in a phase i clinical trial incorporating pharmacodynamic endpoints. Journal of Biopharmaceutical Statistics, 17 (6), 1117-1129.
# NOT RUN {
# }
# NOT RUN {
doses <- c(12.59972,34.65492,44.69007,60.80685,83.68946,100.37111)
theta <- 0.2 # choice
options <- list(nchains = 2, niter = 4000, nadapt = 0.8)
AUCs <- c(0.43, 1.4, 5.98, 7.98, 11.90, 3.45)
x <- c(1,2,3,4,5,6)
y <- c(FALSE,FALSE,FALSE,FALSE,TRUE,FALSE)
res <- pkpop(y, AUCs, doses, x, theta, options = options)
# }
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