DoseFinding (version 0.6-3)

gFitDRModel: Generalized fitting of dose-response models to raw dose-response estimates

Description

The function fits a dose-response model to raw dose-response estimates (obtained for example from an ANOVA type model), by optimizing the generalized least squares objective function: $$(f(dose,\theta)-drEst)'vCov^{-1}(f(dose,\theta)-drEst)$$ where drEst are the response estimates at the dose-levels dose and vCov the associated covariance matrix. This approach is rather general: drEst and vCov can be the output from another model fitting procedure like generalized linear models, survival models or even mixed models. The underlying optimizer is similar to the bndnls option in the fitDRModel function: First a grid-search optimization is used for the non-linear parameters of the dose-response model, then the nlminb optimizer starts from the best value found on the grid. gFitDRModel will always return an estimate (the best of the two optimizations, usually the estimate from nlminb unless it failed). Inference capabilities (confidence intervals, etc) for gFitDRModel fits, will be added in later releases of the DoseFinding package.

Usage

gFitDRModel(dose, drEst, vCov, model = NULL, intercept = TRUE,
              bnds = NULL, start = NULL, gridSize = list(dim1 = 30,
              dim2 = 144), nlminbcontrol = list(), off = NULL,
              scal = NULL)

Arguments

dose

Numeric specifying the dose variable.

drEst

Numeric specifying the response estimate corresponding to the doses in dose

vCov

Covariance matrix associated with the dose-response estimate specified via drEst

model

Dose-response model to fit, possible models are "linlog", "linear", "quadratic", "emax", "exponential", "sigEmax", "betaMod" and "logistic", see DR-Models.

intercept

Whether or not to include an intercept in the model. Models without intercept are of interest for example for fitting placebo-corrected estimates (note that the linear in log and the logistic model cannot be fitted without intercept)

bnds

Bounds for the nonlinear parameters, need to be finite. Per default the bounds are determined with getBnds function is used (max(dose) as input parameter).

start

Optional starting values for the nonlinear parameters of the dose-response model. If equal to NULL a grid search is first performed to find a suitable starting value

gridSize

List with two components (dim1, dim2) giving the size of the grid used for "bndnls" optimization for 1-dim and 2-dim case (in 2-dim case the smallest generalized lattice point set larger than or equal to the number given is used)

nlminbcontrol

List of parameters to be used in the calls to the nlminb function. See the control argument of nlminb for details

off

Fixed offset parameter needed when the linear in log model is used. See also documentation of the linear in log model: "linlog". A reasonable default is to use (maximum dose)*0.1 for off

scal

Fixed scale parameter needed when the beta model is used. See also documentation of the beta model: betaMod A reasonable default is to use (maximum dose)*1.2 for scal.

Value

• An object of class gDRMod. A list with entries
• coef
  A vector containing the coefficients of the fitted model.
• gRSS2
  The residual sum of squares of the fitted model under the generalized least squares criterion
• data
  The dose response data set to which the model has been fitted
• Additionally the object contains a variety of additional information as attributes.

See Also

fitDRModel, linear, linlog, sigEmax, emax, quadratic, logistic, betaMod, exponential, coef.gDRMod, predict.gDRMod, vcov.gDRMod,plot.gDRMod

Examples

## apply to normal data (fitDRModel leads to the same results)
  data(biom)
  ## produce first stage fit (using dose as factor)
  anMod <- lm(resp~factor(dose)-1, data=biom)
  drFit <- coef(anMod)
  vCov <- vcov(anMod)
  dose <- sort(unique(biom$dose))
  ## now fit an emax model to these estimates
  gfit <- gFitDRModel(dose, drFit, vCov, model = "emax",
                      bnds = c(0.01, 2))
  ## a lot of things can be done with gDRMod objects
  print(gfit)
  summary(gfit)
  coef(gfit)
  ## see ?vcov.gDRMod for the caveats of the asymptotic
  ## inference statements
  vcov(gfit)
  predict(gfit, se.fit = TRUE)
  plot(gfit, CI=TRUE, plotData = "meansCI")

  ## example for binary data (migraine)
  data(migraine)
  PFrate <- migraine$painfree/migraine$ntrt
  doseVec <- migraine$dose
  doseVecFac <- as.factor(migraine$dose)
  ## fit logistic regression with dose as factor
  logfit <- glm(PFrate~doseVecFac-1, family = binomial,
                weights = migraine$ntrt)
  drEst <- coef(logfit)
  vCov <- vcov(logfit)
  ## now fit an Emax model (on logit scale)
  gfit2 <- gFitDRModel(doseVec, drEst, vCov, model = "emax", bnds = c(0,300))
  ## model fit on logit scale
  plot(gfit2)

  ## now fit placebo adjusted data
  data(biom)
  ## produce first stage fit (using dose as factor)
  anMod <- lm(resp~factor(dose), data=biom)
  ## estimates (contrasts to placebo)
  drFitC <- coef(anMod)[-1]
  vCovC <- vcov(anMod)[-1,-1]
  dose <- sort(unique(biom$dose))[-1]
  ## now fit an emax model to these estimates
  gfit3 <- gFitDRModel(dose, drFitC, vCovC, model = "emax",
                      bnds = c(0.01, 2), intercept = FALSE)
  plot(gfit3, plotData = "meansCI")