R: Bayesian fit of hyperbolic or sigmoidal Emax models to...

fitEmaxB {clinDR}

R Documentation

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

Description

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.

Usage

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

Arguments

`y`	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`	Dose for each patient.
`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`	modType=3 (default) for the 3-parameter hyperbolic Emax model. modType=4 for the 4-parameter sigmoidal Emax model.
`prot`	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.
`count`	Counts for the number of patients when the `Y` are dose continuous group means or binary 0/1 values. Default is 1 (ungrouped data).
`xbase`	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.
`binary`	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.
`msSat`	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.
`vcest`	The input, `Y`, can be estimates of dose group responses from a first-stage model. The `vcest` is the variance-covariance matrix of the model-based estimates. The most common usage is when a saturated model is fit using maximum likelihood estimation to longitudinal data to produce dose group estimates that are valid under the MAR assumption for missing values. Other applications are possible, see the Pinheiro, et al reference. The `count` and `msSat` are ignored when `vcest` is specified. Covariates `xbase` cannot be specified with `vcest`, but covariates can be included in the first stage modeling.
`pboAdj`	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.
`mcmc`	Inputs controlling `rstan` execution. See `mcmc.control` for details.
`estan`	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.
`diagnostics`	Printed output from rstan. See `Details` for more information.
`nproc`	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.

Details

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), Thomas and Roy (2016), and Wu, et al (2017).

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 with the 4-parameter model 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.

Value

A list assigned class "fitEmaxB" with:

`estanfit`	The `rstan` object with the model fit.
`y`, `dose`, `prot`, `count`, `nbase[rows of xbase]`, `xbase`, `dimFit[rows of vcest]`, `vcest`, `modType`, `binary`, `pboAdj`, `msSat`, `prior`, `mcmc`, `localParm[TRUE when emaxPrior specified]`	Input values.

Note

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

Author(s)

Neal Thomas

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. <doi:10.1080/19466315.2014.924876>

Pinheiro, J., Bornkamp, B., Glimm, E., and Bretz, F. (2014). Model-based dose finding under model uncertainty using general parametric models, Vol. 33, No. 10, 1646-1661 <doi:/10.1002/sim.6052>

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>

Wu, J., Banerjee, A., Jin, B. Menon, M. S., Martin, S. and Heatherington, A. (2017). Clinical dose response for a broad set of biological products: A model-based meta-analysis. Statistical Methods in Medical Research. <doi:10.1177/0962280216684528>

Examples

## Not run: 

data("metaData")
exdat<-metaData[metaData$taid==1,]

prior<-emaxPrior.control(epmu=0,epsca=4,difTargetmu=0,difTargetsca=4,dTarget=20,
				p50=(2+5)/2,
				sigmalow=0.01,sigmaup=3)
										
mcmc<-mcmc.control(chains=3)

msSat<-sum((exdat$sampsize-1)*(exdat$sd)^2)/(sum(exdat$sampsize)-length(exdat$sampsize))
fitout<-fitEmaxB(exdat$rslt,exdat$dose,prior,modType=4,prot=exdat$protid,
				count=exdat$sampsize,msSat=msSat,mcmc=mcmc)
plot(fitout)

## End(Not run)

[Package clinDR version 2.4.1 Index]