fitEmax {clinDR}

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

Description

Calls Newton-Raphson optimizers, nls and nlm, for a 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

fitEmax(y,dose,iparm,xparm,modType=4,
	prot=rep(1,length(y)),count=rep(1,length(y)),xbase=NULL,
	binary=FALSE,diagnostics=TRUE,msSat=NULL,
	pboAdj=rep(FALSE,max(prot)),optObj=TRUE)

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.

iparm

Optional starting values for the Newton-Raphson algorithm. The order of the variables is (log(ED50),Emax,E0) or (log(ED50),lambda,Emax,E0). Note the transformation of ED50. If there is more than one protocol, the E0 is automatically duplicated.

xparm

Optional starting values for the baseline covariate slopes (if any). xparm must be specified when iparm and xbase are specified. startEmax is used to obtain starting values if no starting values are specified.

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.

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.

diagnostics

Print trace information per iteration and any error messages from the optimizing methods. Printing can be suppressed for use in simulation studies.

binary

When TRUE, the y are assumed to be coded 0/1, and the 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 for goodness-of-fit (GOF) testing, and to improve the residual variance estimate for the Emax model. If it is not supplied, statistics needed for GOF will not be available, and the residual SD (and associated SE) will have low degrees of freedom.

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.

optObj

Include the output object from the R optimization code in the fitEmax output.

Details

Fits the 3- or 4- Emax model using nls. A newton-raphson algorithm is tried first followed by a partial linear optimatization if needed. Binary data are fit using nlm.

Value

A list assigned class "fitEmax" with:

fit

The parameter estimates and their variance-covariance matrix.

y, dose, modType, prot, count, binary, pboAdj

Input values.

gofTest

Goodness of fit p-value based on likelihood ratio comparison of the model to a saturated fit.

nll

-2*loglikelihood for the Emax model and the saturated model. Residual sums of squares are returned for continuous data models. These statistics can be used to construct other tests using multiple calls to fitEmax (e.g., 3 vs 4 parameter Emax models, or a common intercept model across protocols).

df

Residual degrees of freedom for the Emax model and the saturated model.

optobj

When requested, the fit object returned by the R optimation functions.

Author(s)

Neal Thomas

See Also

nls, nlm, nllogis, predict.fitEmax, plot.fitEmax, coef.fitEmax

Examples

## the example changes the random number seed

doselev<-c(0,5,25,50,100,350)
n<-c(78,81,81,81,77,80)

### population parameters for simulation
e0<-2.465375 
ed50<-67.481113 

dtarget<-100
diftarget<-9.032497
emax<-solveEmax(diftarget,dtarget,log(ed50),1,e0)


sdy<-8.0
pop<-c(log(ed50),emax,e0)    
dose<-rep(doselev,n)
meanlev<-emaxfun(dose,pop)  

y<-rnorm(sum(n),meanlev,sdy)

testout<-fitEmax(y,dose,modType=4)