Fits dose-response curves for the specified dose-response models, based on the posterior distributions. For the simplified fit, multivariate normal distributions will be approximated and reduced by one-dimensional normal distributions. For the default case, the Nelder-Mead algorithm is used. In detail, for both approaches the mean vector \(\theta^{Y}\) and the covariance \(\Sigma\) of the (mixture) posterior distributions and the corresponding posterior weights \(\tilde{\omega}_{l}\) for \(l \in {1,...,L}\) are used as basis For the full fit a GLS estimator is used to minimize the following expression for the respective dose-response models \(m\) $$ \hat{\theta}_{m}=argmin_{\theta_{m}} \sum_{l=1}^{L} \tilde{\omega}_{l}(\theta_{l_{i}}^{Y}-f(dose_{i},\hat{\theta}_{m}))'\Sigma_{l}^{-1}(\theta_{l_{i}}^{Y}-f(dose_{i},\hat{\theta}_{m}))$$ Therefore the function nloptr of the nloptr package is utilized. In the simplified case \(L=1\), as the dimension of the posterior is reduced to 1 first. The generalized AIC values are calculated via the formula $$gAIC_{m} = \sum_{l=1}^{L} \tilde{\omega}_{l} \sum_{i=0}^{K} \frac{1}{\Sigma_{l_{i,i}}} (\theta_{l_i}^Y - f(dose_{i},\hat{\theta}_{m}))^2 + 2p $$ where \(p\) denotes the number of estimated parameters and \(K\) the number of active dose levels. Here as well for the simplified case the formula reduces to one summand as \(L=1\). Corresponding gAIC based weights for model \(M\) are calculated as outlined in Schorning et al. (2016) $$ \Omega_I (M) = \frac{\exp(-0.5 gAIC_{M})}{\sum_{m=1}^{Q} \exp(-0.5 gAIC_{m})} $$ where \(Q\) denotes the number of models included in the averaging procedure.
Arguments
- models
List of model names for which a fit will be performed.
- dose_levels
A vector containing the different dosage levels.
- posterior
A getPosterior object, containing the (multivariate) posterior distribution per dosage level.
- simple
Boolean variable, defining whether simplified fit will be applied. Default FALSE.
Value
An object of class modelFits. A list containing information about the fitted model coefficients, the prediction per dose group as well as maximum effect and generalized AIC (and corresponding weight) per model.
References
Schorning K, Bornkamp B, Bretz F, Dette H. 2016. Model selection versus model averaging in dose finding studies. Stat Med; 35; 4021-4040.
Examples
posterior_list <- list(Ctrl = RBesT::mixnorm(comp1 = c(w = 1, m = 0, s = 1), sigma = 2),
DG_1 = RBesT::mixnorm(comp1 = c(w = 1, m = 3, s = 1.2), sigma = 2),
DG_2 = RBesT::mixnorm(comp1 = c(w = 1, m = 4, s = 1.5), sigma = 2) ,
DG_3 = RBesT::mixnorm(comp1 = c(w = 1, m = 6, s = 1.2), sigma = 2) ,
DG_4 = RBesT::mixnorm(comp1 = c(w = 1, m = 6.5, s = 1.1), sigma = 2))
models <- c("emax", "exponential", "sigEmax", "linear")
dose_levels <- c(0, 1, 2, 4, 8)
fit <- getModelFits(models = models,
posterior = posterior_list,
dose_levels = dose_levels)
fit_simple <- getModelFits(models = models,
posterior = posterior_list,
dose_levels = dose_levels,
simple = TRUE)