mcpmod_simulation {MCPModBC}

Simulation to obtain operating characteristics for MCP-Mod design

Description

It simulates dose-finding trials using MCP-Mod design with Maximum Likelihood Estimator and Fisher Information (MLE), Maximum Likelihood Estimator and second-order Fisher Information (MLE2), Cox and Snell's Bias-Corrected Estimator and Fisher Information (BCE), Cox and Snell's Bias-Corrected Estimator and second-order Fisher Information (BCE2), and Firth Bias-Corrected estimators (Firth) as discussed in Diniz, Magalhães and Gallardo.

Usage

mcpmod_simulation(doses, parm, sample.size, model.true,
  models.candidate, selModel = "AIC",significance.level = 0.025,
  Delta, distr = "weibull", censoring.rate = NULL,
  sigma.estimator = NULL, n.cores, seed,n.sim)

Arguments

doses

a numeric vector indicating the doses that will be considered in the clinical trial.

parm

a named list of true values for the simulation. See more details in data_generator.

sample.size

a numeric vector indicating the sample sizes per dose in the clinical trial to be evaluated in the simulation study.

model.true

a character value indicating the true functional form of dose-response curve. See more details in model_response.

models.candidate

an object of class 'Mods'. See more details in Mods.

selModel

a character value indicating the model selection criterion for dose estimation. See more details in MCPMod.

significance.level

a numeric value indicating the significance level when evaluating proof-of-concept based on an one-sided Wald test.

Delta

a numerical value indicating the target effect size used for the target dose. See TD.

distr

a character value indicating the distribution of the response variable. Currently, the only option available is 'weibull'.

censoring.rate

a numeric value between 0 and 1 indicating the censoring rate when generated data. It is required when distr = "weibull".

sigma.estimator

a character value indicating whether the estimator for sigma should be a maximum likelihood or jackknife estimator. It is required when distr = "weibull". Options are "mle" and "jackknife".

n.cores

a numeric value indicating the number of cores to be used in the 'simulation performed in parallel. Use parallel::detectCores() to check the number of cores available.

seed

an integer value, containing the random number generator (RNG) state for random number generation.

n.sim

a numerical value indicating the number of simulated trials.

Value

An object of class mcpmod_simulation with the following components:

mle: a matrix of dimension n.sim \times 4 with results when using the MCP-Mod approach with MLE;

mle2: a matrix of dimension n.sim \times 4 with results when using the MCP-Mod approach with MLE2;

bce: a matrix of dimension n.sim \times 4 with results when using the MCP-Mod approach with BCE;

bce2: a matrix of dimension n.sim \times 4 with results when using the MCP-Mod approach with BCE2;

firth: a matrix of dimension n.sim \times 4 with results when using the MCP-Mod approach with Firth's estimator;

All matrices contain the following columns: (1) the first column indicates whether proof-of-concept (1 = "yes", 0 = "no"), in other words, the p-value of Wald test was statistically significant; (2) the second column indicates whether the true model was selected to estimate the dose-response curve (1 = "yes", 0 = "no") when proof-of-concept is demonstrated; (3) the third column contains the estimated target dose; (4) the fourth column contains the sample size considered in the trial.

conditions: a list containing the conditions of the simulation.

Author(s)

Diniz, M.A., Gallardo D.I., Magalhaes, T.M.

References

Bretz F, Pinheiro JC, Branson M. Combining multiple comparisons and modeling techniques in dose‐response studies. Biometrics. 2005 Sep;61(3):738-48.

Bornkamp B, Pinheiro J, Bretz F. MCPMod: An R package for the design and analysis of dose-finding studies. Journal of Statistical Software. 2009 Feb 20;29:1-23.

Diniz, Márcio A. and Gallardo, Diego I. and Magalhães, Tiago M. (2023). Improved inference for MCP-Mod approach for time-to-event endpoints with small sample sizes. arXiv <doi.org/10.48550/arXiv.2301.00325>

Pinheiro J, Bornkamp B, Glimm E, Bretz F. Model‐based dose finding under model uncertainty using general parametric models. Statistics in medicine. 2014 May 10;33(10):1646-61.

Examples

library(DoseFinding)
library(MCPModBC)

## doses scenarios 
doses <- c(0, 5, 25, 50, 100)
nd <- length(doses)
sample.size <- 25

# shape parameter
sigma.true <- 0.5

# median survival time for placebo dose
mst.control <- 4 

# maximum hazard ratio between active dose and placebo dose 
hr.ratio <- 4  
# minimum hazard ratio between active dose and placebo dose
hr.Delta <- 2 

# hazard rate for placebo dose
placEff <- log(mst.control/(log(2)^sigma.true)) 

# maximum hazard rate for active dose
maxEff <- log((mst.control*(hr.ratio^sigma.true))/(log(2)^sigma.true))

# minimum hazard rate for active dose
minEff.Delta <- log((mst.control*(hr.Delta^sigma.true))/(log(2)^sigma.true))
Delta <- (minEff.Delta - placEff)
	
## MCP Parameters 
significance.level <- 0.05
selModel <- "AIC"

emax <- guesst(d = doses[4], p = 0.5, model="emax")
exp <- guesst(d = doses[4], p = 0.1, model="exponential", Maxd = doses[nd])
logit <- guesst(d = c(doses[3], doses[4]), p = c(0.1,0.8), "logistic",  
	Maxd= doses[nd])
betam <- guesst(d = doses[2], p = 0.3, "betaMod", scal=120, dMax=50, 
	Maxd= doses[nd])

models.candidate <- Mods(emax = emax, linear = NULL,
                         exponential = exp, logistic = logit,
                         betaMod = betam, doses = doses,
                         placEff = placEff, maxEff = (maxEff- placEff))
plot(models.candidate)

## Simulation Parameters
n.sim <- 10
seed <- 1234 
n.cores <- 1

## True Model
model.true <- "emax"
response <- model_response(doses = doses,
                           distr = "weibull", 
                           model.true = model.true, 
                           models.candidate = models.candidate) 
lambda.true <- response$lambda
parm <- list(lambda = lambda.true, sigma = sigma.true)

## Scenario: Censoring 10%
censoring.rate <- 0.1

test <- mcpmod_simulation(doses = doses,
           parm = parm, sample.size = sample.size,
           model.true = model.true,
           models.candidate = models.candidate,
           selModel = selModel,
           significance.level = significance.level,
           Delta = Delta, distr = "weibull",
           censoring.rate = censoring.rate,
           sigma.estimator = "jackknife",
           n.cores = n.cores, seed = seed, n.sim = n.sim)

test
summary(test)