SimPRMD: Simulation for a Multi-Stage Phase I Dose-Finding Design

In LuZhangstat/phase1PRMD: Personalized Repeated Measurement Design for Phase I Clinical Trials

Description

A function to implement simulations for a multi-stage phase 1 dose-finding design incorporating a longitudinal continuous efficacy outcome and toxicity data from multiple treatment cycles. The available models include 1-stage model with/without individualized dose modification, 3-stage model with/without individualized dose modification, 3-stage model with individualized dose modification on stage II and 3-stage model with individualized dose modification on stage I and dose modification on stage II.

Usage

SimPRMD(
  seed = 1234,
  numTrials = 100,
  doses = 1:6,
  cycles = 1:6,
  eff.structure = matrix(0, nrow = 6, ncol = 6),
  eff.Sigma = diag(6),
  eff.sd_trans = 1.5,
  tox.target = 0.28,
  p_tox1 = 0.2,
  p_tox2 = 0.2,
  trialSize = 36,
  chSize = 3,
  thrd1 = 0.28,
  thrd2 = 0.28,
  proxy.thrd = 0.1,
  tox.matrix = NULL,
  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(),
  n.iters = 10000,
  burn.in = 5000,
  thin = 2,
  n.chains = 1,
  effcy.flag = T,
  ICD.flag = T,
  DLT.drop.flag = T,
  testedD = T,
  IED.flag = T,
  ICD_thrd = 0.3
)

Arguments

seed	The seed of R's random number generator. Default is 1234
numTrials	An integer specifying the number of simulations
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 matrix provides the mean of the multivariate Gaussian distribution in efficacy data generation. Specifically, the (i, j)th element represents the mean value of ith dose level and jth cycle of the Gaussian distribution for efficacy data generation. Default is a 6 by 6 zero matrix
eff.Sigma	The covariance matrix of the multivariate Guassian distribution in efficacy data generation. See details below.
eff.sd_trans	A positive number controls the skewness of the distribution of the efficacy response. Default is 1.5. See details below.
tox.target	The target toxicity of the treatment. Default is 0.28. See details below.
p_tox1	The probability cutoff for cycle 1 toxicity. Default is 0.2. See details below.
p_tox2	The probability cutoff for later cycles toxicity beyond cycle 1. Default is 0.2. See Details below.
trialSize	The maximum sample size for trial simulation. Default is 36. Must be the multiple of cohort size, represented by chSize
chSize	The cohort size of patients recruited. Default is 3.
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
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.
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 dimension 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.
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 γ (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 γ of two submodels of the joint model assuming a normal prior. Default is non-informative priors.
n.iters	Total number of MCMC simulations. Default is 10,000.
burn.in	Number of burn=ins in the MCMC simulation. Default is 5,000.
thin	Thinning parameter. Default is 2.
n.chains	No. of MCMC chains in Bayesian model fitting. Default is 1
effcy.flag	Whether we include efficacy response in modeling or not?
ICD.flag	Whether we allow dose changing for cycle > 1 in stage 1 model or not? Default is TRUE. See details below
DLT.drop.flag	Whether the patients should suspend the treatment when observing DLT. Default is TRUE
testedD	Default is TRUE. Whether we only allow ICD or IED among cycle 1 tested dose level
IED.flag	Default is TRUE. Whether we allow dose changing for cycle > 1 in stage 2 model or not?
ICD_thrd	The cut-off point of the posterior toxicity probability in defining ICD. Default is 0.3. See details below.

Details

The user can simulation efficacy response with different dose-efficacy and cycle-efficacy pattern using argument eff.structure, eff.Sigma and eff.sd_trans. The sampling process of efficacy response start from generating sample z = {z1, …, zd} from multivariate Gaussian distribution

z ~ MVN(μ, V)

, where μ and V are specified by eff.structure and eff.Sigma, respectively. Define φ be the density of N(0, σ^2) with CDF Φ, and σ^2 is set by eff.sd_trans. Then the efficacy response is calculated by taking the CDF of z:

x={x1, …, xd} = Φ(z) = { Φ(z1), …, Φ(zd)}

is the generated efficacy response. Notice here the variance parameter σ^2_{trans} controls the variance of the generated efficacy.

The user can simulate longitudinal efficacy response with different dose-efficacy and cycle-efficacy pattern using argument eff.structure, eff.Sigma and eff.sd_trans. The sampling process of efficacy response starts from generating z = {z1, …, zd} from multivariate Gaussian distribution

z ~ MVN(μ, V)

, where μ and V are specified by eff.structure and eff.Sigma, respectively. Define φ be the density of N(0, σ^2) with CDF Φ, where σ^2 is set by eff.sd_trans. Then the efficacy measure is generated by taking the CDF of z:

x={x1, …, xd} = Φ(z) = { Φ(z1), …, Φ(zd)}

. Notice here the variance parameter σ^2_{trans} controls the variance of the generated efficacy.

p_tox1, p_tox2, thrd1 and thrd2 are used to define allowable (safe) doses the probability conditions for cycle 1:

P(nTTP1 < thrd1) > p_tox1

and for cycle > 1:

p(nTTP2 < thrd2) > p_tox2

, where nTTP1 and nTTP2 denote the posterior estimate of nTTP for cycle 1 and the average of cycle > 1. When we implement model with individualized dose modification, we only check the condition for cycle 1 for defining allowable (safe) doses.

ICD_thrd are used to find ICD. ICD is defined as the maximum dose which satisfy the condition

P(nTTPi < target.tox) > ICD_thrd

, where nTTPi is the individualized posterior predicted nTTP score. The individualized dose modification for next cycle will not escalate more than 1 dose from the current dose.

Value

senerio_sum	contains mnTTP.M the matrix of mean nTTP for each dose and cycle and pDLT.M matrix of probability of observing DLT for each dose and cycle
eff_sum	When effcy.flag == TRUE, contains eff.M the mean efficacy for each dose and cycle and err.cor.ls A list with a length of dose levels numbers recording the marginal correlation matrix across cycles of efficacy data for each dose level
list_simul	A list of length numTrials. Each element includes patlist which records all the treatment and outcome information; dose_aloca which shows the cycle 1 dose allocation; doseA which saves the recommended dose level for cycle 1 at the end of the phase I simulation, equals "early break" if the trial was stop before finishing the trial; n.cohort indicates the last cohort in the trial; pp.nTTPM gives the posterior probability of nTTP less than target toxicity tox.target for all dose level any cycles and message saves the message of each trial.
chSize	The input argument chSize
sim.time	Time cost in simulation
doses	The input argument doese
cycles	The input argument cycles
effcy.flag	The input argument effcy.flag
proxy.thrd	The input argument proxy.thrd
DLT.drop.flag	The input argument DLT.drop.flag

Examples

data("prob")      # load prob.RData from package phaseI, Details see "?prob"
data("eff")       # load eff.RData from package phaseI. Details see "?eff"

eff.structure = eff$Dose_Cycle_Meff[2, 2, , ]
eff.Sigma = eff$Sigma
eff.sd_trans = eff$sd_trans

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 = TRUE, ncol
              = 5)                          # weighted matrix for toxicity matrix
                                            # nrow = No.of type; ncol = No. of grade
toxmax <- 2.5
tox.matrix <- prob["MTD4", "flat", , , , ]


#------- a flat dose-toxicity, dose-efficacy, cycle-efficacy pattern------#

simul1 <- SimPRMD(numTrials = 1, tox.matrix = tox.matrix,
                  eff.structure = eff.structure, eff.Sigma = eff.Sigma,
                  eff.sd_trans = eff.sd_trans, wm = wm, toxmax = toxmax,
                  trialSize = 36)

#------- a flat dose-toxicity pattern model ------#

simul2 <- SimPRMD(numTrials = 1, 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, p_tox1 = 0.2, p_tox2 = 0.2,
                  ICD.flag = FALSE, IED.flag = FALSE, effcy.flag = TRUE)

summary(simul2)
plot(simul2)

LuZhangstat/phase1PRMD documentation built on March 14, 2020, 6:54 a.m.