SimPRMD {phase1PRMD}

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

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 \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.

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, \ldots, zd} from multivariate Gaussian distribution

z ~ MVN(\mu, V)

, where \mu and V are specified by eff.structure and eff.Sigma, respectively. Define \phi be the density of N(0, \sigma^2) with CDF \Phi, and \sigma^2 is set by eff.sd_trans. Then the efficacy response is calculated by taking the CDF of z:

x={x1, \ldots, xd} = \Phi(z) = { \Phi(z1), \ldots, \Phi(zd)}

is the generated efficacy response. Notice here the variance parameter \sigma^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, \ldots, zd} from multivariate Gaussian distribution

z ~ MVN(\mu, V)

, where \mu and V are specified by eff.structure and eff.Sigma, respectively. Define \phi be the density of N(0, \sigma^2) with CDF \Phi, where \sigma^2 is set by eff.sd_trans. Then the efficacy measure is generated by taking the CDF of z:

x={x1, \ldots, xd} = \Phi(z) = { \Phi(z1), \ldots, \Phi(zd)}

. Notice here the variance parameter \sigma^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)