clinDR (version 2.4.1)

SeEmax: Asymptotic SE for dose response estimates from a 3- or 4- parameter Emax model

Description

Compute the asymptotic SE for dose response estimates based on the asymptotic variance-covariance matrix from the fit of a 3- or 4-parameter Emax model

Usage

SeEmax(fit, doselev, modType, dref=0, nbase=0, x=NULL, 
				binary=FALSE, clev=0.9)

Value

Returns a list:

doselev

Doses to evaluate

dref

Differences in response between doselev and dref are computed.

fitpred

Estimated dose response at doselev

sepred

SE for estimated dose responses

fitdif

Estimated response at doselev minus estimated response at placebo

sedif

SE for fitdif estimated differences

fitref

Estimated dose response at the reference dose.

seref

SE for the estimated dose response at the reference dose

covref

The covariance between each estimated response and the estimated response at the reference dose. These covariances can be used to compute asymptotic variances of differences after back-transformation (e.g., for logistic regression with binary data).

Arguments

fit

Output of nls fit to a 3- or 4-parameter Emax model. The order of the parameters in the fit must be (log(ed50),emax,e0) or (log(ed50),lambda,emax,e0). Alternatively, fit can be a list with the first element the coefficient vector, and the second element the variance-covariance matrix. List input can be used with multiple protocols and baseline covariates (see details).

doselev

SEs are evaluated at vector of doses

modType

modType=3,4 for a 3 or 4 parameter model.

dref

A reference dose (0 by default) for contrasts, but other values can be specified. If specified, a single reference value must be given.

nbase

The number of baseline predictors included in the model.

x

The model is evaluated at baseline covariate values, x. If x is a matrix, then each row is a vector of baseline predictors, and the results are for the dose response averaged over all of the predictors in x.

binary

Emax model on logistic scale, then backtransformed.

clev

Confidence level for intervals.

Author

Neal Thomas

Details

The Emax models supported by SeEmax should now be fit using fitEmax and predict.fitEmax. SeEmax remains available primarily for backward compatibility.

SeEmax can be used with models that allow different placebo response for multiple protocols by selecting the intercept for a specific protocol. Coeficients for baseline covariates can also be included following the intercept. The variance-covariance matrix from the full model must be subsetted to match the included coeficients (i.e., the rows and columns corresponding to the omitted intercepts must be removed). List input must be used for the more general models.

References

Bates, D. M. and Watts, D. G. (1988) Nonlinear Regression Analysis and Its Applications, Wiley

See Also

fitEmax

Examples

if (FALSE) {

## this example changes the random number seed
doselev<-c(0,5,25,50,100,250)
n<-c(78,81,81,81,77,80)
dose<-rep(doselev,n)

### population parameters for simulation
e0<-2.465375 
ed50<-67.481113 
led50<-log(ed50)
lambda=1.8

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

sdy<-7.967897
pop<-c(led50=led50,lambda=lambda,emax=emax,e0=e0)    
meanresp<-emaxfun(dose,pop)  
y<-rnorm(sum(n),meanresp,sdy)
nls.fit<-nls(y ~ e0 + (emax * dose^lambda)/(dose^lambda + exp(led50*lambda)), 
                         start = pop, control = nls.control(
                         maxiter = 100),trace=TRUE,na.action=na.omit)


SeEmax(nls.fit,doselev=c(60,120),modType=4)
SeEmax(list(coef(nls.fit),vcov(nls.fit)),c(60,120),modType=4)
}
# \dontshow{

## this example changes the random number seed
doselev<-c(0,5,25,50,100,250)
n<-c(78,81,81,81,77,80)
dose<-rep(doselev,n)

### population parameters for simulation
e0<-2.465375 
ed50<-67.481113 
led50<-log(ed50)

dtarget<-100
diftarget<-9.032497
lambda=1.8
emax<-solveEmax(diftarget,dtarget,log(ed50),lambda,e0)

sdy<-7.967897
pop<-c(led50=led50,lambda=lambda,emax=emax,e0=e0)    
meanresp<-emaxfun(dose,pop)  
y<-rnorm(sum(n),meanresp,sdy)
nls.fit<-nls(y ~ e0 + (emax * dose^lambda)/(dose^lambda + exp(led50*lambda)), 
                         start = pop, control = nls.control(
                         maxiter = 100),trace=TRUE,na.action=na.omit)


SeEmax(nls.fit,doselev=c(60,120),modType=4)
# }