pktox: Dose finding method PKTOX.

Description

The PKTOX model is essentially the PKLOGIT model with a probit regression model replacing the logistic regression, that is given by: $p_{T} (z, β) = Φ (- β_{2} + β_{3} z)$ with a bivariate Uniform distribution as prior distribution for the parameters $β = (β_{2}, β_{3})$ and the hierarchical model of PK-toxicity for $z_{i}$ given as: $z_{i} | β, ν \sim N (β_{0} + β_{1} \log d_{i}, ν^{2})$ where $β = (β_{0}, β_{1})$ are the regression parameters and $ν$ is the standard deviation.

The default choices of the priors are: $β | ν \sim N (m, ν * b e t a 0)$ $ν \sim B e t a (1, 1)$ $m = (- l o g (C L_{p o p}), 1)$ where $C l_{p o p}$ is the population clearance. $β_{2} \sim U (0, b e t a 2 m e a n)$ $β_{3} \sim U (0, b e t a 3 m e a n)$ where default choices are $C l_{p o p} = 10$ , beta0 = 10000, beta2mean = 20 and beta3mean = 10.

Finally, the PKTOX model has the following stopping rule in toxicity: if $P (p_{T} (d o s e) > t h e t a) > p r o b$ then, no dose are suggested and the trial is stopped.

Usage

pktox(y, auc, doses, x, theta, prob = 0.9, options = list(nchains = 4, niter = 4000, 
      nadapt = 0.8), betapriors = c(10, 10000, 20, 10), thetaL = NULL, 
      p0=NULL, L=NULL, deltaAUC=NULL)

Arguments

A binary vector of patient's toxicity outcomes; TRUE indicates a toxicity, FALSE otherwise.

doses

A vector with the doses panel.

A vector with the dose level assigned to the patients.

theta

The toxicity target.

prob

The probability for the stopping rule.

betapriors

A vector with the value for the prior distribution of the regression parameters in the model; defaults to $C l_{p o p} = 10$ , beta0 = 10000, beta2mean = 20 and beta3mean = 10.

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.

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).

thetaL

A second threshold of AUC; must be defined only in the PKCRM model.

Value

A list is returned, consisting of determination of the next recommended dose and estimations of the model. Objects generated by pktox 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.

parameters

The estimated model's parameters.

References

Ursino, M., et al, (2017) Dose-finding methods for Phase I clinical trials using pharmacokinetics in small populations, Biometrical Journal.

Whitehead, J., Zhou, Y., Hampson, L., Ledent, E., and Pereira, A. (2007) A bayesian approach for dose-escalation in a phase i clincial trial incorporating pharmacodynamic endpoints. Journal of Biopharmaceutical Statistics, 17 (6), 1117-1129.

Examples

Run this code


    doses <- c(12.59972,34.65492,44.69007,60.80685,83.68946,100.37111)
    theta <- 0.2
    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 <- pktox(y, AUCs, doses, x, theta, options = options)

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