Simulate dose response data and apply 4- or 3- parameter sigmoidal or hyperbolic Bayesian estimation. The prior distribution is input by the user with default values for some parameters based on the empirical distribution estimated from dose response meta-analyses. For binary response data, the Emax model is fit on the logit scale, and then back-transformed
emaxsimB(nsim, genObj, prior, modType = 4,
binary = FALSE, seed=12357,
check = FALSE, nproc=parallel::detectCores(),
negEmax = FALSE, ed50contr = NULL,
lambdacontr = NULL, testMods = NULL,
idmax = length(doselev),
mcmc = mcmc.control(),
customCode=NULL, customParms=NULL,
description = "")A list is returned with class(emaxsim) containing:
User description of simulation
localParm=TRUE when the prior
prior distribution is input using emaxPrior.
Binary response data.
Type of Emax model fit (3 or 4 parameters)
List object with data and function used to generate study data
Matrix with rows containing population parameters for each simulation. Type of parameter depends on constructor function generating study data.
Vector containing the population SD used to generate
continuous data. NULL for binary data.
mcmc input settings
Input prior distribution.
Matrix with posterior median parameter estimates for each simulation:
(led50,lambda,emax,e0,difTarget) or (led50,emax,e0,difTarget). The difTarget are
omitted for the deprecated distribution.
Array with lower posterior (0.025,0.05,0.1) and upper posterior (0.975,0.95,0.9) percentiles of the model parameters. The array ordering is model parameters, simulation, and percentile.
The posterior median of the residual SD for each simulation.
The nsim p-values from the global null test. The p-values are
1-sided computed using MCP-Mod.
The index of the test contrast producing the smallest p-value.
Object of class Mods from R package DoseFinding that defines
the contrasts used in MCP-MOD testing. The functions can be plotted with
DoseFinding loaded.
Goodness of fit test computed by checkMonoEmax.
User input stored for subsequent reference.
Matrix with population means for each dose group
Matrix with rows containing dose group sample means
Matrix with rows containing dose group sample SD
Pooled within-dose group sample variance
Matrix with rows containing dose groups means estimated by the posterior medians of the MCMC generated values.
Matrix with rows containing SE (posterior SD) associated with fitpredv
Matrix with rows containing dose groups mean differences wih placebo estimated by the posterior medians of the differences of the MCMC generated values.
Matrix with rows containing SE (posterior SD) for the differences with placebo
Array with lower posterior (0.025,0.05,0.1) and upper posterior (0.975,0.95,0.9) percentiles of differences between dose group means and placebo. The array ordering is dose group minus placebo, simulation, and percentile.
The proportion of divergent MCMC iterations from each simulated analysis.
Starting random
number seed for each simulated data set set that can be assigned to .Random.seed.
To reproduce the data, the random number generator must also be changed to
RNGkind("L'Ecuyer-CMRG").
Index of default dose group for comparison to placebo (e.g., for plotting Z-statistics).
List with customized output. It will be NULL if customCOde is not specified.
Number of simulation replications
Object containing inputs and function to create simulated
data sets. These objects are created by special constructor
functions; the current choices are FixedMean and RandEmax.
Prior specification through an object of type 'emaxPrior' or 'prior'.
See emaxPrior.control and prior.control for details.
The 'emaxPrior' specifies
the magnitude of the potential effect for a specified dose (typically the highest
anticipated dose and/or the dose in a POC study), while the 'prior' specifies the
theoretical maximum effect (the emax parameter). The 'prior' specification is
deprecated and will be removed.
When modType=3, a hyperbolic Emax model is fit.
When modType=4, a sigmoid Emax model is fit.
When specified, the Emax model is fit on the logit scale, and then the results are back-transformed to proportions.
Seed for random number generator used to create data. A separate
seed can be passed to rstan through the MCMC object.
When TRUE, a single simulated data set is created and the data
and rstan object are returned for convergence checking. The data
are in the form needed for developing customCode. Note that
customCode is not called when check=TRUE.
The number of processors to use in parallel computation of the
simulations, which are divided into equal-sized computational blocks. When nproc=1
a single local processor.
When TRUE, the intended effect is assumed to be negative.
A vector of ED50 values for creating a global null test using the MCP-MOD package DoseFinding based on Emax model-based contrasts. The default is 3 contrasts: the mid-point between pbo and the lowest dose, the mid-point between the 2 highest doses, and the median of the dose levels. When there are <=4 doses including pbo, the median-based contrast is excluded.
Hill parameters matched to the ed50contr. The default value is 1 for each contrast model.
The model object for a MCP-MOD test
created by Mods from package DoseFinding. If
specified, the other contrast inputs are ignored. The Mods
call should
use the unique sorted dose levels. The direction of the trend should be specificed in the call to Mods. The negEmax is stored for use by support functions, but it does not determine the direction of the effect when testMods is specified. The validity of
testMods is not checked.
Index of the default dose group for comparison to placebo. Most analysis functions allow other dose groups to be specified. The default is the index of the highest dose.
MCMC settings created using mcmc.control
An optional user supplied function that computes custom
estimates/decision criteria from each simulated data set and its Bayesian
model fit. The output are stored in a list, customOut, of length
nsim. See the Details section below for a description of the
mandatory inputs to the customCode function.
Optional parameters that can be passed to
customCode.
Optional text describing the simulation setting that is stored with the simulation output.
Neal Thomas
The Bayesian model fits are implemented in rstan using function
fitEmaxB. The function compileStanModels must be
executed once to create compiled STAN
code before emaxsimB can be used.
Continuous data can be simulated from any dose response curve with homogeneous normally distributed residuals.
Binary data are handled similarly. The models are fit on the logit scale and then back-transformed for estimation of dose response. Reduced linear models are selected based on the corresponding likelihood deviance.
MCP-MOD tests are created from contrasts based on the Emax function using
the DoseFinding package. Different
ED50 and lambda (Hill) parameters can be specified to form the contrasts. A contrast
matrix output from the DoseFinding package can be specified instead, allowing for
other contrast choices.
Customized code:
For binary data, the inputs to the function customCode for each simulated data set
will be (parms,pVal,dose,y), where parms is the matrix of parameters
generated from the posterior distribution with columns in the order given in
function emaxfun, pVal is the MCP-MOD p-value, dose and y are
the patient-level simulated data. For continuous data, the inputs
are (parms,residSD,pVal,dose,y), where residSD are the variance
parameters generated from their posterior distribution. The customParms supply other user-inputs
such as a target efficacy level. When it is not null, the customCode
inputs must be (parms,pVal,dose,y,customParms) or (parms,residSD,pVal,dose,y,customParms).
Thomas, N., Sweeney, K., and Somayaji, V. (2014). Meta-analysis of clinical dose response in a large drug development portfolio, Statistics in Biopharmaceutical Research, Vol. 6, No.4, 302-317. <doi:10.1080/19466315.2014.924876>
Thomas, N., and Roy, D. (2016). Analysis of clinical dose-response in small-molecule drug development: 2009-2014. Statistics in Biopharmaceutical Research, Vol. 6, No.4, 302-317 <doi:10.1080/19466315.2016.1256229>
print.emaxsimB,
summary.emaxsimB, plot.emaxsimB,
coef.emaxsimB, sigma.emaxsimB,
emaxfun
if (FALSE) {
### emaxsimB changes the random number seed
nsim<-50
idmax<-5
doselev<-c(0,5,25,50,100)
n<-c(78,81,81,81,77)
Ndose<-length(doselev)
### population parameters for simulation
e0<-2.465375
ed50<-67.481113
dtarget<-100
diftarget<-2.464592
emax<-solveEmax(diftarget,dtarget,log(ed50),1,e0)
sdy<-7.967897
pop<-c(log(ed50),emax,e0)
meanlev<-emaxfun(doselev,pop)
###FixedMean is specialized constructor function for emaxsim
gen<-FixedMean(n,doselev,meanlev,sdy)
prior<-emaxPrior.control(epmu=0,epsca=30,difTargetmu=0,
difTargetsca=30,dTarget=100,p50=50,sigmalow=0.1,
sigmaup=30,parmDF=5)
mcmc<-mcmc.control(chains=1,warmup=500,iter=5000,seed=53453,
propInit=0.15,adapt_delta = 0.95)
### custom code to compute the distribution of the dose yielding
### a target diff with pbo
customCode<-function(parms,residSD,pVal,dose,y,customParms){
target<-customParms
ed50<-exp(parms[,1])
emax<-parms[,2]
td<-ifelse(emax-target>0,ed50*(target/(emax-target)),Inf)
tdest<-median(td)
lb<-quantile(td,0.1)
ub<-quantile(td,0.9)
return(c(td=tdest,lb=lb,ub=ub))
}
D1 <- emaxsimB(nsim,gen, prior, modType=4,seed=12357,mcmc=mcmc,check=FALSE,
customCode=customCode,customParms=1.0)
D1
}
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