emaxalt {clinDR}

Fit 4- or 3-parameter Emax model substituting simpler curves if convergence not achieved.

Description

ML estimation for 4- and 3-parmeter Emax model. If the 4-parameter model is requested, it is estimated and the 3-parameter model is fit only if the 4-parameter estimation fails. If 3-parameter estimation fails, the linear, log-linear, or exponential model producing the smallest residual SS is substituted. For binary data, the model is fit on the logit scale and then back-transformed.

Usage

emaxalt(y, dose, modType=3,binary=FALSE, 
	iparm=NA,ed50cutoff=2.5*max(doselev), 
	ed50lowcutoff=doselev[2]/1000,switchMod= TRUE,
	truncLambda=6)

Arguments

y

Response vector

dose

Doses corresponding to y

modType

When modType=4, the fitting begins with the 4 parameter model. If estimation fails or modType=3, the 3-parameter estimation is applied. If it fails, a best-fitting model linear in its parameters is selected.

binary

When specified, the Emax model is fit on the logit scale, and then the results are back-transformed to proportions.

iparm

Vector of optional initial values for the Emax fit. Starting values are computed if not specified.

ed50cutoff

Upper allowed limit for ED50 estimates.

ed50lowcutoff

Lower allowed limit for the ED50 estimates.

switchMod

If switchMod is TRUE, the algorithm substitutes a simpler model if (1) convergence is not achieved, (2) the information matrix is not positive definite at the converged values, (3) the ED50 estimates are outside the cutoff bounds. If switchMod is F, only conditions (1) or (2) cause a simpler model to be used.

truncLambda

When modType=4 and the converged estimate of the Hill parameter lambda exceeds truncLambda, the model fit is judged unstable and discarded. Set truncLambda=Inf for no truncation.

Details

The partial linear method is used in nls. If it fails, gauss-newton is attempted. If both methods fail, the next simpler model is attempted. For the 4-parameter model, the next step is the 3-parameter model. For the 3-parameter model, a linear, log-linear log(dose+1.0), and exp(dose/max(dose)) are fit using lm, and the 2-parm fit with the smallest residual SS is selected.

Value

A list assigned class "emaxalt" with the following elements:

dm

Vector containing dose group means

dsd

Vector containing dose group SDs

Sparm

Vector of starting values for 3-parameter Emax fit.

fitType

Character vector with "4", "3", "L", "LL", or "E" for 4-Emax, 3-Emax, linear, log-linear, or exponential when an alternative model is selected.

vc

The variance-covariance matrix of the model parameters stored as a vector. The length is 16, 9, 4 depending on fitType.

fitpred

Dose groups means estimated from the model

residSD

The residual SD based on the selected model.

sepred

SEs for estimates in fitpred

sedif

SEs for model-based estimates of difference with placebo

bigC

bigC= TRUE if the primary fit (from modType) yielded an ED50 >ED50 upper limit.

negC

negC= TRUE if the primary fit (from modType) yielded a ED50 estimate < ED50 lower limit.

est4

4-parmameter Emax fit (ed50,lambda,emax,e0). NA if failed to converge or 3-parameter model requested.

est3

3-parmameter Emax fit (ed50,emax,e0). NA if failed to converge or 4-parameter model successfully fit.

estA

Alternative parameter estimates. NA if Emax model fit successfully

Author(s)

Neal Thomas

See Also

emaxsim, nls

Examples

save.seed<-.Random.seed
set.seed(12357)

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

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

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

sdy<-7.967897
pop<-c(log(ed50),emax,e0)    
meanresp<-emaxfun(dose,pop)  
y<-rnorm(sum(n),meanresp,sdy)

simout<-emaxalt(y,dose)

simout2<-emaxalt(y,dose,modType=4)

.Random.seed<-save.seed