# pkpop: Dose finding method PKPOP. In dfpk: Bayesian Dose-Finding Designs using Pharmacokinetics (PK) for Phase I Clinical Trials

## Description

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{β}, ν \sim N ≤ft( β_0 + β_1 \log d_{i}, ν^{2} \right)

where \boldsymbol{β} = (β_0,β_1) are the regression parameters and ν is the standard deviation. and the logistic regression model:

\mbox{logit}(p_T(z_{k,pop}, \boldsymbol{β})) = -β_3 + β_4 z_{k,pop}

with a bivariate Uniform distribution as prior distribution for the parameters \boldsymbol{β} = (β_3, β_4).

The default choices of the priors are:

\boldsymbol{β} \vert ν \sim N(m, ν*beta0),

ν \sim Beta(1,1),

m = (-log(CL_{pop}), 1),

where Cl_{pop} is the population clearance.

β_3 \sim U(0, beta3mean),

β_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.

## Usage

 1 2 3 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) 

## Arguments

 y A binary vector of patient's toxicity outcomes; TRUE indicates a toxicity, FALSE otherwise. doses A vector with the doses panel. x A vector with the dose level assigned to the patients. theta The toxicity target. prob The threshold of the posterior probability of toxicity for the stopping rule; defaults to 0.9. betapriors 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. options 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). auc A vector with the computed AUC values of each patient for pktox, pkcrm, pklogit and pkpop; defaults to NULL. deltaAUC 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. p0 The skeleton of CRM for pkcrm; defaults to NULL (must be defined only in the PKCRM model). L 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). thetaL A second threshold of AUC; must be defined only in the PKCRM model. CI A logical constant indicating the estimated 95% credible interval; defaults to TRUE.

## Value

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:

 newDose The next maximum tolerated dose (MTD); equals to "NA" if the trial has stopped before the end, according to the stopping rules. pstim The mean values of estimated probabilities of toxicity. p_sum The summary of the estimated probabilities of toxicity if CI = TRUE, otherwise is NULL. parameters The estimated model's parameters.

## Author(s)

Artemis Toumazi [email protected], Moreno Ursino [email protected], Sarah Zohar [email protected]

## References

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.

pklogit, sim.data, nsim, nextDose

## Examples

  1 2 3 4 5 6 7 8 9 10 11  ## 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) ## End(Not run) 

dfpk documentation built on Nov. 9, 2018, 5:05 p.m.