Package 'phase1PRMD'

Efficacy response generation parameters

Description

A list of 4 records the parameters for efficacy measure generation. This serves as an example of the parameter settings for efficacy measure generation in function SimPRMD. Check eff_summary or SimPRMD to see the examples of using dataset eff in generating efficacy measure.

Usage

eff

Format

An object of class list of length 4.

Value

Dose_Cycle_Meff	Dose-cycle mean efficacy matrix. An array of 4 dimension providing the mean of the multivariate Gaussian distribution in efficacy data generation. The dimension of the Dose-cycle mean efficacy matrix is 5 5 6 6 which represents dose efficacy pattern, cycle efficacy pattern, dose and cycle. Patterns are ordered in a way that the first is increasing, the second is flat, the third is platform, the fourth is decreasing, and the fifth is quadratic efficacy across dose levels and cycles.
Sigma	A 6 by 6 matrix, the covariance matrix of the multivariate Guassian distribution in efficacy data generation.
sd_trans	A positive number controls the skewness of the distribution of the efficacy response
eff.M	An array recording the corresponding mean of the generated efficacy data with parameters specified by eff$Dose_Cycle_Meff, eff$Sigma, and eff$sd_trans

---

Suggest the input eff.structure of function SimPRMD with selected eff.sd_tran

Description

Suggest the input eff.structure of function SimPRMD with selected eff.sd_tran for given efficacy mean matrix and efficacy standard deviation

Usage

eff_suggest(eff.M, eff.sd, eff.sd_trans, n.sim = 30000)

Arguments

eff.M	The efficacy mean matrix whose (i,j)th element save the target mean of the efficacy data
eff.sd	The target standard deviation matrix for all dose and cycles. Notice that the generated efficacy may have different standard deviation matrix due to the correlations across cycles
eff.sd_trans	The eff.sd_trans for test. Notice variance of the generated efficacy data will be effected by eff.sd_trans.
n.sim	The number of simulations for the numerical calculation in the function. The default is 30,000

Value

eff.suggest

The matrix suggested for the input eff.structure of function SimPRMD

Examples

# Provide an target efficacy mean matrix for all dose and cycles
eff.M <- matrix(rep(3:8/10, 6), nrow = 6, ncol = 6)

# Give a target standard deviation matrix for all dose and cycles
# Notice that the generated efficacy may have difference standard deviation
# matrix due to the correlations across cycles
eff.sd <- matrix(0.2, nrow = 6, ncol = 6)

# Select a eff.sd_trans for testing. The efficacy variance are mainly
# controlled by the eff.sd_trans
eff.sd_trans <- 1.5  # or other positive value
eff.structure <- eff_suggest(eff.M = eff.M, eff.sd = eff.sd,
                             eff.sd_trans = eff.sd_trans)

# check whether the suggested eff.M and the selected sd_trans
# generate the desirable scenario
eff.Sigma <- diag(6)
diag(eff.Sigma[-1,]) = 0.5
diag(eff.Sigma[, -1]) = 0.5
eff.check <- eff_summary(eff.structure = eff.structure,
                         eff.Sigma = eff.Sigma,
                         eff.sd_trans = eff.sd_trans,
                         plot.flag = FALSE)
eff.check$eff.M
eff.check$eff.cor.ls

---

Compute the summary statistics of efficacy measure with specified parameters.

Description

Numerically compute the Mean, mariginal standard deviance and mariginal correlation matrix of efficacy measure generated with specified parameters. The function provides plots of marginal density of generated efficacy and correlation matrix for each dose. Check details to see the efficacy data generation procedures.

Usage

eff_summary(
  eff.structure,
  eff.Sigma,
  eff.sd_trans,
  n.sim = 3e+05,
  seed = 123,
  plot.flag = F,
  plot.title = T
)

Arguments

eff.structure	A matrix providing the mean of the multivariate Gaussian distribution in efficacy data generation. Specifically, the $(i, j)$th element represents the mean value of $i$th dose and $j$th cycle of the Gaussian distribution for efficacy data generation.
eff.Sigma	The covariance matrix of the multivariate Guassian distribution in efficacy data generation.
eff.sd_trans	A positive number controling the skewness of the distribution of the efficacy response.
n.sim	Number of simulations for calculation summary statistics. Default is 300,000
seed	The seed of R's random number generator. Default is 123
plot.flag	Whether output the marginal density, and correlation matrix or not. Default is FALSE.
plot.title	Whether display the title of the plot or not. Default is TRUE

Details

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.

Value

eff.M	A matrix recording the efficacy mean whose $(i, j)$th element represents the efficacy mean of $i$th dose level and $j$th cycle
eff.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

Examples

data("eff")       # load eff.RData from package phase1PRMD. Details see "?eff"
eff.structure = eff$Dose_Cycle_Meff["plat", "dec", , ]
eff.Sigma = eff$Sigma
eff.sd_trans = eff$sd_trans

# res <- eff_summary(eff.structure, eff.Sigma, eff.sd_trans, n.sim = 300000,
#                    seed = 123)
# res
# set a special cases and check the density and correlation plots
# eff_summary(eff.structure = matrix(eff.structure[cbind(c(1:6), c(1:6))],
#                                   nrow = 1, ncol = 6),
#             eff.Sigma, eff.sd_trans, n.sim = 300000, seed = 123,
#             plot.flag = TRUE, plot.title = FALSE)

---

Generate the mean nTTP score and the probability of observing DLT for all doses and cycles

Description

nTTP_summary generates the mean nTTP score and the probability of observing DLT for all doses and cycles

Usage

nTTP_summary(Tox.prob.M, nTTP.all, wm)

Arguments

Tox.prob.M	Toxicity probability matrix with 4 dimension: dose, cycle, type, grade. Tox.prob.M can be the output of the build-in matrix of function GenToxProb in package phase1RMD. See more details about how to generate toxicity probability matrices in the help document of GenToxProb.
nTTP.all	The output of nTTP.array
wm	(numerical matrix) Toxicity weighted matrix, with row be the type of the toxicity and column be the toxicity grade

Value

mnTTP.M	matrix of mean nTTP for all doses and cycles
pDLT.M	matrix of probability of observing DLT for all doses and cycles

Examples

data("prob")

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

nTTP.all <- nTTP.array(wm, toxmax)

tox.matrix <- prob["MTD4", "flat", , , , ]

nTTP_summary(tox.matrix, nTTP.all, wm)

---

Generate the nTTP dictionary

Description

nTTP.array generates the nTTP dictionary for all combination of toxicity type and grade with a given toxicity weighted matrix. Used in function nTTP_summary for checking the toxicity scenario.

Usage

nTTP.array(wm, toxmax)

Arguments

wm	(numeric matrix, m by n) Toxicity weighted matrix, with row be the type of the toxicity and column be the toxicity grade
toxmax	(scalar) Normalized constant for nTTP

Value

An m dimensional array with dimension $(n, n, \ldots, n)$. The $(d1, d2 ,\ldots,dm), {di, i = 1\ldots, m} \in (1, \ldots, n)$th element is the nTTP when the grade of $i$th type of toxicity has $di$th toxicity grade.

Examples

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

nTTP.array(wm, toxmax)

---

A list of patient information

Description

The data "patlist_sim" is a trial generated by "SimPRMD". The model utilized for generating trial is a 3-stage model with individualized dose modification. The MTD = 4 and the MED = 1 since the dose-efficacy pattern when generating the trial was set to be flat. The dose-toxicity trend and efficacy-cycle trend are flat. There are in total 12 cohorts with 3 patients in each cohort. This also serves as an example of the input data of function RunPRMD.

Usage

patlist_sim

Format

An object of class list of length 6.

Value

PatID	denotes the patient ID where the elements are specified by cohort and subject number. For example, "cohort2subject3" denotes the third subject in the second cohort
dose	records the dose assigned for each patient on different cycles
cycle	shows the treatment cycle
nTTP	records th corresponding nTTP score.
dlt	indicates whether a DLT event is observed or not?
efficacy	provides the continuous efficacy for each cycle. The range of efficacy measure is (0, 1).

---

Display patient records

Description

Display patient records in a human-readable table. Each cell contains 3 values including observed nTTP, DLT, and dose assignment. The higher the dose, the warmer the cell background color is. The black color of the records indicates DLT equals 1.

Usage

patlist.display(patlist, n.dose, n.cycle)

Arguments

patlist	A list of the patient treatment records, which must contains the following variables: PatID denotes the patient ID where the elements are specified by cohort and subject number. For example, "cohort2subject3" denotes the third subject in the second cohort dose records the dose level assigned for each patient through the whole treatment cycle shows the treatment cycle information of each record nTTP records the corresponding nTTP score. dlt indicates whether a DLT event is observed or not?
n.dose	The number of dose in the study
n.cycle	The number of cycle in the study

---

Plot nTTP and efficacy boxplots of a RunPRMD object

Description

Plot nTTP boxplots of a RunPRMD object. Plot efficacy boxplots when implementing RunPRMD with option effcy.flag == TRUE.

Usage

## S3 method for class 'RunPRMD'
plot(x, ..., select_cycle = x$cycles)

Arguments

x	RunPRMD object to summarise
...	other arguments ignored (for compatibility with generic)
select_cycle	A vector indication the cycle in the boxplot. Default is cycle of x.

Examples

## Check ?RunPRMD for example

---

Plots of a SimPRMD object

Description

Plot the predictive probability of nTTP < target toxicity for all cycles and doses , the mean nTTP vs cycle1 and cycle > 2 for all doses of a SimPRMD object. Plot median treatment duration boxplot along with the DLT drop off rate when implementing SimPRMD with option DLT.drop.flag = TRUE.

Usage

## S3 method for class 'SimPRMD'
plot(x, ..., title.add = TRUE)

Arguments

x	SimPRMD object to summarise
...	other arguments ignored (for compatibility with generic)
title.add	controls whether there is a title on plots or not.

Examples

## Check ?SimPRMD for example

---

Displays a useful description of a summary.RunPRMD object

Description

Displays a useful description of a summary.RunPRMD object. Call by link{summary.RunPRMD}. Check link{summary.RunPRMD} for the details of the print information.

Usage

## S3 method for class 'summary.RunPRMD'
print(x, ...)

Arguments

x	summary.RunPRMD object to summarise
...	other arguments ignored (for compatibility with generic)

---

Displays a useful description of a summary.SimPRMD object

Description

Displays a useful description of a summary.SimPRMD object

Usage

## S3 method for class 'summary.SimPRMD'
print(x, ...)

Arguments

x	summary.SimPRMD object to summarise
...	other arguments ignored (for compatibility with generic)

---

Toxicity probability matrix

Description

A 6 dimension array providing the toxicity probability of different scenarios. The dimension is 4 3 6 6 3 5 which represents scenario, cycle effect, dose level, cycle number, toxicity type, and tox grade. Scenarios are ordered in a way that the first scenario is MTD = dose 2, the second is MTD = dose 3, the third is MTD = dose 4, and the fourth is MTD = dose 5. The three Cycle effect trend are decreasing, flat, and increasing toxicity trend over cycles. There are 6 doses, 6 cycles, 3 toxicity types and 5 toxicity grades.

Usage

prob

Format

An object of class array of dimension 4 x 3 x 6 x 6 x 3 x 5.

---

Implement a Multi-Stage Phase I Dose-Finding Design to recommend dosage selection based on the data collected in the available patient cohorts

Description

A function to implement a Multi-Stage Phase I Dose-Finding Design to recommend dosage selection based on the data collected in the available patient cohorts. 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

RunPRMD(
  seed = 1234,
  patlist,
  patID_act = NULL,
  cycle_act = NULL,
  dose_act = NULL,
  dlt_act = NULL,
  doses = 1:6,
  cycles = 1:6,
  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,
  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
patlist	A list of the patient treatment records, which must contains the following variables: PatID denotes the patient ID where the elements are specified by cohort and subject number. For example, "cohort2subject3" denotes the third subject in the second cohort dose records the dose level assigned for each patient through the whole treatment cycle shows the treatment cycle information of each record nTTP records the corresponding nTTP score. dlt indicates whether a DLT event is observed or not? efficacy provides the continuous efficacy for each cycle. Required when effcy.flag == T. The range of efficacy is (0, 1), use -1 for missing efficacy response. See patlist_sim for an example.
patID_act	A vector recording the patients' ID who need dose recommendation for next cycle. Default is NULL
cycle_act	A vector recording the current cycle of patID_act. Default is NULL
dose_act	A vector recording the current dose level of patID_act. Default is NULL
dlt_act	A vector indicating whether a dlt is observed in current cycle for current patients. Default is NULL
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
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 (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.
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. Will check the convergence of MCMC chains by the potential scale reduction factor (PSRF) when n.chains > 1.
effcy.flag	Whether efficacy data is modeled in the model fitting or not. Default is TRUE.
ICD.flag	Whether we allow individualized dose modification 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 to be less than or equal to the maximum dose tested in first cycle.
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 RunPRMD function implement a Multi-Stage Phase I Dose–Finding Design to recommend dosage selection based on the data collected in the available patient cohorts. The function will automatically identify the model and the stage based on all flags and the records. For the details of argument tox.target, p_tox1, p_tox2, thrd1, thrd2 and ICD_thrd, please check the help document of SimPRMD.

Value

patlist	The input data patlist
doseA	The recommended dose level for cycle 1 for new cohorts
pat_rec	The recommended dose for current patients for next cycle
effcy.flag	The input argument effcy.flag
doses	The input argument doses
cycles	The input argument cycles

Examples

data("patlist_sim")
# check the whole dataset by function patlist.display
patlist.display(patlist_sim, n.dose = 6, n.cycle = 6)

# When we pick the records before 6th cohort enrolled in the study
L <- length(patlist_sim$PatID)
patlist <- lapply(patlist_sim, function(a){a <- a[-(44:L)]})
patlist.display(patlist, n.dose = 6, n.cycle = 6)

#The table shows the current patient in the trial. Now record the active
#patient ID and records as follows

patID_act <- c("cohort1subject1", "cohort1subject2", "cohort1subject3",
               "cohort2subject1", "cohort2subject2", "cohort2subject3",
               "cohort3subject2", "cohort3subject3",
               "cohort4subject1", "cohort4subject2", "cohort4subject3",
               "cohort5subject1", "cohort5subject2", "cohort5subject3")
cycle_act <- c(5, 5, 5, 4, 4, 4, 3, 3, 2, 2, 2, 1, 1 ,1)
dose_act <- c(3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4)
dlt_act <- c(0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)


test <- RunPRMD(patlist = patlist, patID_act = patID_act,
                cycle_act = cycle_act, dose_act = dose_act,
                dlt_act = dlt_act, trialSize = 36, chSize = 3,
                effcy.flag = TRUE, ICD.flag = TRUE, DLT.drop.flag = TRUE,
                IED.flag = TRUE, ICD_thrd = 0.3)

summary(test)
plot(test)
plot(test, select_cycle = 1:2)

---

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 $i$th dose level and $j$th 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)

---

Summary a RunPRMD object

Description

Summary a RunPRMD object. Print the information of recommended dosage selection along with the mean nTTP and the number of DLT for all doses and cycles. Will print the mean efficacy for all doses and cycles when implementing RunPRMD with option effcy.flag = TRUE. The collected data is displayed in a human-readable table whose cell contain 3 values including observed nTTP, DLT, and dose assignment. The higher the dose, the warmer the cell background color is. The black color of the records indicates DLT equals 1.

Usage

## S3 method for class 'RunPRMD'
summary(object, ...)

Arguments

object	RunPRMD object to summarise
...	other arguments ignored (for compatibility with generic)

Value

object	The output of function RunPRMD
mnttp.M	The mean nTTP for all doses and cycles
dlt.count.M	The number of DLT for all doses and cycles
eff.M	The mean efficacy for all doses and cycles. Return NULL when object$effcy.flag == TRUE

Examples

## Check ?RunPRMD for example

---

Summary a SimPRMD object

Description

Summary a SimPRMD object

Usage

## S3 method for class 'SimPRMD'
summary(object, ...)

Arguments

object	SimPRMD object to summarise
...	other arguments ignored (for compatibility with generic)

Value

senerio_sum	Output senerio_sum of function SimPRMD
eff_sum	Output eff_sum of function SimPRMD
n.trial	The number of trials in the simulation
alloc.perc	The dose allocation percentage for cycle1
n.stop	The number of early stop cases
m.n.pat	The average number of patient in each trial
m.dlt.rt	dlt rate
c1_dlt.rt	Cycle 1 dlt rate
cs_dlt.rt	Subsequent cycle (cycle > 1) dlt rate
alloc.perc	Dose allocation of cycle 1
sbsq.alloc	Dose allocation of subsequent cycles (cycle > 1)
rec.prec	The percentage of Recommended doses for cycle 1
effcy.flag	Argument effcy.flag of function SimPRMD
DLT.drop.flag	Argument DLT.drop.flag of function SimPRMD

Examples

## Check ?SimPRMD for example

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