SimRMDEFF {phase1RMD}

Simulation for an Adaptive, Multi-Stage Phase I Dose-Finding Design

Description

A function to implement simulation for an adaptive, multi-stage phase 1 dose-finding design incorporating a continuous efficacy outcome and toxicity data from multiple treatment cycles, proposed by Du et al(2017)

Usage

SimRMDEFF(numTrials = 100, trialSize = 36, doses = 1:6, cycles = 1:6,  
          eff.structure = c(0.1, 0.2, 0.3, 0.4, 0.7, 0.9), 
          eff.sd = 0.2, tox.target = 0.28, p1 = 0.2, p2 = 0.2, 
          ps1 = 0.2, StrDose = 1, chSize = 3, 
          tox.matrix = NULL, 
          proxy.thrd = 0.1, thrd1 = 0.28, thrd2 = 0.28, 
          wm = matrix(c(0, 0.5, 0.75, 1  , 1.5, 
                        0, 0.5, 0.75, 1 , 1.5, 
                        0, 0  , 0   , 0.5, 1  ), 
                        byrow = T, ncol = 5), 
          toxmax = 2.5, toxtype = NULL, intercept.alpha = NULL, 
          coef.beta = NULL, cycle.gamma = NULL, 
          param.ctrl = list())

Arguments

numTrials

An integer specifying the number of simulations.

trialSize

The maximum sample size for trial simulation. Default is 36. Must be the multiple of cohort size, represented by chSize.

doses

A vector of doses that users are going to explore. Default is 1:6, where dose 1 through dose 6 are being tested.

cycles

A vector of cycles that the treatment plans to go through. Default is 1:6, where patients will experience up to 6 cycles of the treatment.

eff.structure

A vector of the mean values of efficacy outcome for each dose level explored. Default is c(0.1, 0.2, 0.3, 0.4, 0.7, 0.9), corresponding to dose 1 through dose 6, where the efficacy increases with dose.

eff.sd

The standard deviation for generating the efficacy outcome for each patient. Default is 0.2, which already gives large skewness/variation.

tox.target

The target toxicity at cycle 1 of the treatment. Default is 0.28.

p1

The probability cutoff for cycle 1 toxicity. Default is 0.2. See Details below.

p2

The probability cutoff for later cycles toxicity beyond cycle 1. Default is 0.2. See Details below.

ps1

The probability cutoff for defining allowable (safe) doses in stage 1. Default is 0.2. See Details below.

StrDose

A number to specify the starting dose. Default is 1.

chSize

The cohort size of patients recruited. Default is 3.

tox.matrix

Optional. A four-dimension array specifying the probabilities of the occurrences of certain grades for certain types of toxicities, at each dose level and cycle under consideration. Dimension 1 refers to doses; dimension 2 corresponds to cycles of the treatment; dimension 3 regards the types of toxicities while dimenion 4 relates to grades. If null, which is default choice, the arguments toxtype, intercept.alpha, coef.beta, cycle.gamma must be provided to simulate this array.

proxy.thrd

A distance parameter to define efficacious doses. Any dose whose predicted efficacy is within proxy.thrd away from the largest one among the safe doses will be declared an efficacious dose.

thrd1

An upper bound of toxicity for cycle 1 of the treatment. Default is 0.28. See Details below.

thrd2

An upper bound of toxicity for late cycles of the treatment, beyond cycle 1. Default is 0.28. See Details below.

wm

Clinical weight matrix, where toxicity types define the rows while the toxicity grades define the columns. Usually solicited from physicians.

toxmax

The normalization constant used in computing nTTP score. For details, see Ezzalfani et al(2013).

toxtype

Only specified when tox.matrix is null. This argument, a character vector, specifies toxicity types considered in the trial.

intercept.alpha

Only specified when tox.matrix is null. A four element numeric vector specifying the intercepts for the cumulative probabilities of the occurrences of grades 0-4 of toxicities in proportional odds model. See Details below.

coef.beta

Only specified when tox.matrix is null. A n numeric vector specifying the slope for dose in proportional odds model for n types of toxicities. See Details below.

cycle.gamma

Only specified when tox.matrix is null. A scalar controlling the cycle effect in simulation in proportional odds model. See Details below.

param.ctrl

A list specifying the prior distribution for the parameters. p1_beta_intercept, the prior mean of intercept of toxicity model assuming a normal prior; p2_beta_intercept, the precision (inverse of variance) of intercept of toxicity model assuming a normal prior; p1_beta_cycle, the prior mean of cycle effect of toxicity model assuming a normal prior; p2_beta_cycle, the precision (inverse of variance) of cycle effect of toxicity model assuming a normal prior; p1_beta_dose, the prior minimum of dose effect of toxicity model assuming a uniform prior; p2_beta_dose, the prior maximum of dose effect of toxicity model assuming a uniform prior; p1_alpha, the prior mean vector of the parameters from efficacy model assuming a multivariate normal prior; p2_alpha, the prior precision matrix (inverse of covariance matrix) of the parameters from efficacy model assuming a multivariate normal prior; p1_gamma0, the prior mean of association parameter \gamma (See Du et al(2017)) of two submodels of the joint model assuming a normal prior; p2_gamma0, the prior precision (inverse of variance) of association parameter \gamma of two submodels of the joint model assuming a normal prior. Default is non-informative priors.

Details

p1,p2,thrd1 and thrd2 are used to define allowable (safe) doses through the two probability conditions:

P(tox1 < thrd1) > p1

P(tox2 < thrd2) > p2

, where tox1 and tox2 denote the toxicity at cycle 1 of the treament and later cycles, respectively. In stage 1, ps1 acts as p1 and p2.

The user can explore different dose-efficacy patterns using the argument eff.structure. For example, eff.structure = c(0.5, 0.5, 0.5, 0.5, 0.5, 0.5) corresponds to a flat relationship where the efficacy does not change with dose.

When tox.matrix is null, the probability matrices of the occurrences of certain grades for certain types of toxicities, at each dose level and cycle will be simulated from a proportional odds model that takes toxtype, intercept.alpha, coef.beta and cycle.gamma as the inputs. The model is as follows:

logit(c_j) = \alpha_j + \beta * dose + \gamma * cycle, j=0,1,2,3

where given a dose and cycle, c_j is the cumulative probabilities of occurrences of toxicities grades up to j; \alpha_0, \alpha_1, \alpha_2, \alpha_3 are the intercepts, making up intercept.alpha; coef.beta stores \beta for different types of toxicities while cycle.gamma acts as \gamma, controlling the cycle effect. The probability for the occurrence of a certain grade of a certain toxicity type at a given dose and cycle is obtained from taking the corresponding differences between cumulative probabilities.

Value

A list with the following components:

op.table

A table reporting the operating characteristics of the trial simulation.

sc

The assumed true mean longitudinal toxicity and efficacy structure for each dose level under investigation, along with the probability of DLT event, for cycle 1 of the treatment.

Examples

#######Dose 5 target toxicity dose, flat cycle effect#####################

###############a flat dose-efficacy pattern###############################

# simul <- SimRMDEFF(toxtype = c("H", "L", "M"), 
                   # intercept.alpha = c(1.9, 2.3, 2.6, 3.1), 
                   # coef.beta = c(-0.3, -0.2, -0.25), 
                   # cycle.gamma = 0, tox.target = 0.23, 
                   # thrd1 = 0.23, thrd2 = 0.23,
                   # eff.structure = rep(0.5, 6),
                   # p1 = 0.1, p2 = 0.1, ps1 = 0.1, 
                   # numTrials = 1)