fitEmaxB {clinDR}R Documentation

Bayesian fit of hyperbolic or sigmoidal Emax models to continuous/binary dose response data.


Uses Rpackage rstan to fit a Bayesian hyperbolic or sigmoidal Emax model. Different intercepts for multiple protocol-data are supported. For binary data, the Emax model is on the logit scale.


fitEmaxB(y, dose, prior, modType = 4, prot = rep(1, length(y)), 
	count = rep(1, length(y)), xbase=NULL,
	binary = FALSE, msSat = NULL,
	pboAdj = FALSE, mcmc = mcmc.control(), estan = NULL, 
	diagnostics = FALSE, nproc = getOption("mc.cores", 1L))



Outcome for each patient. Missing Y values are are not permitted. Dose/protocol group means for grouped continuous data. For binary data, y must be 0/1 and counts must be supplied for each 0/1 value.


Dose for each patient.


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=3 (default) for the 3-parameter hyperbolic Emax model. modType=4 for the 4-parameter sigmoidal Emax model.


Protocol (group) membership used to create multiple intercepts. The default is a single protocol. The prior disribution for the placebo response is re-used independently for each intercept.


Counts for the number of patients when the Y are dose continuous group means or binary 0/1 values. Default is 1 (ungrouped data).


A matrix of baseline covariates with rows corresponding to y that enter as linear additive predictors. The baseline covariates must be centered about their (protocol-specific) means. xbase does not include an intercept or protocol indicators. Covariates cannnot be specified with PBO adjusted or aggregated input.


When TRUE, the y are assumed to be coded 0/1, and the means reported are proportions. The Emax model is specified on the logit scale, and proportions are estimated from the model by back-transformation.


If continuous Y are dose/protocol group means rather than individual measurements, the within group variance, msSat, should be supplied. This variance is the mean square from the model saturated in dose and protocol. It is used to improve the residual variance estimate for the Emax model. If it is not supplied, the residual SD (and associated SE) will have low degrees of freedom.


For published data with only pbo-adjusted dose group means and SEs, the model is fit without an intercept(s). If initial parameters are supplied, the intercept (E0) should be assigned 0. A zero for the placebo mean should not be included in Y. This option is not available for binary data. Potential correlation between between placebo-adjusted means is ignored.


Inputs controlling rstan execution. See mcmc.control for details.


The compiled rstan Emax model is usually loaded automatically. It can be load to an object using the function selEstan and passed to fitEmaxB for repeated executions to improve efficiency and stability.


Printed output from rstan. See Details for more information.


The number of processor requested for STAN MCMC computations. Defaults to the value set by the rstan installation. When set explicitly, nproc is usually 1 or the number of MCMC chains. If greater than the number of chains, it is set to the number of chains.


The function compileStanModels must be executed once to create compiled STAN code before fitEmaxB can be used.

MCMC fit of a Bayesian hyperbolic or sigmoidal Emax model. The prior distributions available are based on the publication Thomas, Sweeney, and Somayaji (2014) and Thomas and Roy (2016).

The posterior distributions are complex because the distributions of the Emax and ED50 parameters change substantially as a function of the lambda, often creating 'funnel' type conditions. Small numbers of divergences are common and do not appear easily avoided. Extensive simulation using evaluations with emaxsimB support the utility of the resulting approximate posterior distributions. The number of divergences can be viewed using diagnostics=TRUE. The usual convergence diagnostics should always be checked.


A list assigned class "fitEmaxB" with:


The rstan object with the model fit.

y, dose, prot, count, modType, binary, pboAdj, nbase, msSat, prior, mcmc

Input values.


The default modType was changed from 3 to 4 for clinDR version >2.0


Neal Thomas


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>

See Also

fitEmax, predict.fitEmaxB, plot.fitEmaxB, coef.fitEmaxB


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[Package clinDR version 2.3.5 Index]