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.
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)A list assigned class "fitEmax" with:
The parameter estimates and their variance-covariance matrix.
Input values.
Goodness of fit p-value based on likelihood ratio comparison of the model to a saturated fit.
-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).
Residual degrees of freedom for the Emax model and the saturated model.
When requested, the fit object returned by the R optimation functions.
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 for each patient.
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.
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=3 (default) for the 3-parameter hyperbolic Emax model. modType=4 for the 4-parameter sigmoidal Emax model.
Protocol (group) membership used to create multiple intercepts. The default is a single protocol.
Counts for the number of patients when the Y are dose
continuous group means or binary 0/1 values.
Default is 1 (ungrouped data).
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.
Print trace information per iteration and any error messages from the optimizing methods. Printing can be suppressed for use in simulation studies.
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.
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.
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.
Include the output object from the R optimization code in the fitEmax
output.
Neal Thomas
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.
## 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)
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