# Asymptotic SE for dose response estimates from a 3- or 4- parameter Emax model 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 ```r SeEmax(fit, doselev, modType, dref=0, nbase=0, x=NULL, binary=FALSE, clev=0.9) ``` ## 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. ## Returns 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). ## 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 ## Author(s) Neal Thomas ## See Also `fitEmax` ## Examples ```r ## Not run: ## 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) ## End(Not run) ```

SeEmax function