Main panel
The main panel is again split up into three vertical subpanels, labeled as Candidate Model 1, Candidate Model 2 and Candidate Model 3. Thus it allows to simultaneously compare three different dose-response models. So far the linear model, the emax model and the sigmoidal emax model are implemented. Let \(d\) denote the dose within the specified dose range. Then the models are defined as follows
\[ \mathrm{response}_{lin}= E_0+Slope \cdot d,\] \[ \mathrm{response}_{emax}=E_0 + \frac{E_{max} d }{ED_{50} + d},\] \[ \mathrm{response}_{sig}=E_0 + \frac{E_{max} d^h }{ED_{50}^h + d^h},\] Here, \(d\) denotes the dose, \(E_0\) is the placebo response, \(E_{max}\)is the maximal treatment effect, \(ED_{50}\) is the half effect dose, i.e. the dose at which half of the maximal effect is reached, and \(h\) is the Hill parameter which determines the steepness of the response increase/decrease.
Each of the three vertical candidate panels consists of three parts: a top part to choose the model parameters and plot the corresponding dose-response curve, a middle part to visualize the optimal design and a bottom part in which a user-defined design can be compared with the optimal design.
In the top part, the values of the respective model parameters can be entered in the Parameters tab. The Plot tab next to the Parameters tab visualizes the dose-response curve based on the chosen model and the corresponding model parameters.
In the middle part, the optimal design based on the chosen dose-response model and corresponding parameter values is visualized by black vertical lines, taking into account the number of patients, the dose restrictions and the optimality criterion selected in the left sidebar panel. Additionally, the optimal design is tabulated underneath the plots.
In the bottom part, a user defined design can be entered by specifying dose levels in the Dose levels input box and the corresponding number of patients in the Patients input box (separated by semicolon, respectively). The user defined design is additionally visualized in the optimal design plot by green dots. The user defined design is not bound by the dose restrictions selected in the left sidebar panel and dose levels apart from these could be specified. Underneath the input boxes for the user defined design the properties of the design in tabular form are shown. In the first line, the total number of patients entered is shown. In the second line the efficiency of the user defined design compared to the optimal design (under the chosen dose restrictions) is shown in percentage. In the last line this efficiency is converted to the number of patients which would additionally be needed to achieve the same precision in the parameter estimation (O’Quigley et al., 2017).
By choosing the Simulation tab next to the Parameters and Plot tab in the top part of the panel, another plot appears. Here it is possible to visualize simulated realizations of dose-response measurements and the corresponding effect on the estimation of the dose-response curve. The underlying design, i.e. the dose levels and the number of patients per dose level, can be selected to be any of the three optimal designs or any of the three user defined designs specified in the three candidate model panels. Response realizations are randomly drawn from a normal distribution with mean equal to the value of the true curve and variance based on the population standard deviation specified in the left sidebar panel. The true and the estimated curve together with the corresponding confidence interval are shown. True curve here refers to the specified candidate model in the corresponding panel.