# Simulate Emax Bayesian estimation 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 ```r 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 = "") ``` ## Arguments - `nsim`: Number of simulation replications - `genObj`: 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`: 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. - `modType`: When `modType=3`, a hyperbolic Emax model is fit. When `modType=4`, a sigmoid Emax model is fit. - `binary`: When specified, the Emax model is fit on the logit scale, and then the results are back-transformed to proportions. - `seed`: Seed for random number generator used to create data. A separate seed can be passed to `rstan` through the `MCMC` object. - `check`: 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`. - `nproc`: 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. - `negEmax`: When `TRUE`, the intended effect is assumed to be negative. - `ed50contr`: 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. - `lambdacontr`: Hill parameters matched to the ed50contr. The default value is 1 for each contrast model. - `testMods`: 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. - `idmax`: 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`: MCMC settings created using `mcmc.control` - `customCode`: 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. - `customParms`: Optional parameters that can be passed to `customCode`. - `description`: Optional text describing the simulation setting that is stored with the simulation output. ## Details 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). ## Returns A list is returned with class(emaxsim) containing: - **description**: User description of simulation - **localParm**: `localParm=TRUE` when the prior prior distribution is input using `emaxPrior`. - **binary**: Binary response data. - **modType**: Type of Emax model fit (3 or 4 parameters) - **genObj**: List object with data and function used to generate study data - **pop**: Matrix with rows containing population parameters for each simulation. Type of parameter depends on constructor function generating study data. - **popSD**: Vector containing the population SD used to generate continuous data. `NULL` for binary data. - **mcmc**: mcmc input settings - **prior**: Input prior distribution. - **est**: 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. - **estlb,estub**: 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. - **residSD**: The posterior median of the residual SD for each simulation. - **pVal**: The `nsim` p-values from the global null test. The p-values are 1-sided computed using MCP-Mod. - **selContrast**: The index of the test contrast producing the smallest p-value. - **testMods**: 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. - **gofP**: Goodness of fit test computed by `checkMonoEmax`. - **negEmax**: User input stored for subsequent reference. - **predpop**: Matrix with population means for each dose group - **mv**: Matrix with rows containing dose group sample means - **sdv**: Matrix with rows containing dose group sample SD - **msSat**: Pooled within-dose group sample variance - **fitpredv**: Matrix with rows containing dose groups means estimated by the posterior medians of the MCMC generated values. - **sepredv**: Matrix with rows containing SE (posterior SD) associated with fitpredv - **fitdifv**: Matrix with rows containing dose groups mean differences wih placebo estimated by the posterior medians of the differences of the MCMC generated values. - **sedifv**: Matrix with rows containing SE (posterior SD) for the differences with placebo - **lb,ub**: 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. - **divergence**: The proportion of divergent MCMC iterations from each simulated analysis. - **rseed**: 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")`. - **idmax**: Index of default dose group for comparison to placebo (e.g., for plotting Z-statistics). - **customOut**: List with customized output. It will be `NULL` if `customCOde` is not specified. ## Note The default modType was changed from 3 to 4 for clinDR version >2.0 ## References 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. 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 ## Author(s) Neal Thomas ## See Also `print.emaxsimB`, `summary.emaxsimB`, `plot.emaxsimB`, `coef.emaxsimB`, `sigma.emaxsimB`, `emaxfun` ## Examples ```r ## Not run: ### 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 ## End(Not run) ```

emaxsimB function