Emax model using Linear Contrast Method Thomas (2006) extended the linear contrast to the sigmoid model and designed a set of linear Emax contrast to describe difference shapes of dose-response curve. model is a flexible Emax Emax model, with varying the model parameters E0, Emax, ED50 or slope or Hill parameters, to approximate many families of dose response models with monotonic response (Thomas 2006), such as the linear, log-linear, or exponential model. The linear contrasts are then generated from the dose response of different curves of possible models, example dose curves Emax Emax are displayed in Figure 3.3. The six dose response profiles in the dose response plots are then described by 6 linear contrasts which are pre-specified in the analysis. A statistical test is constructed on the smallest P-value from a set of contrasts. Bayesian methods are recommended and weighting of the contrasts can be implied by prior distribution (Thomas, 2006). Figure 3.3 Example dose response curves for building linear contrasts. Trend Test in Dose Response Analysis If an assumption is made that an increase in dose will result in an increase in a response variable, possible methodologies in dose response analysis are trend-based or monotonic response analyses. A trend test can be considered as a special case of linear contract method, where the weight is chosen so the trend test is more powerful to detect associations when the assumed trend is true. It is often expected that response increases or decreases monotonically with dose, but not necessarily linear.
Emax model using Linear Contrast Method Thomas (2006) extended the linear contrast to the sigmoid Emax model and designed a set of linear contrast to describe difference shapes of Emax dose-response curve. Emax model is a flexible model, with varying the model parameters E0, Emax, ED50 or slope or Hill parameters, to approximate many families of dose response models with monotonic response (Thomas 2006), such as the linear, log-linear, or exponential model. The linear contrasts are then generated from the dose response of different curves of possible Emax models, example Emax dose curves are displayed in Figure 3.3. The six dose response profiles in the dose response plots are then described by 6 linear contrasts which are pre-specified in the analysis. A statistical test is constructed on the smallest P-value from a set of contrasts. Bayesian methods are recommended and weighting of the contrasts can be implied by prior distribution (Thomas, 2006). Figure 3.3 Example dose response curves for building linear contrasts. Trend Test in Dose Response Analysis If an assumption is made that an increase in dose will result in an increase in a response variable, possible methodologies in dose response analysis are trend-based or monotonic response analyses. A trend test can be considered as a special case of linear contract method, where the weight is chosen so the trend test is more powerful to detect associations when the assumed trend is true. It is often expected that response increases or decreases monotonically with dose, but not necessarily linear.
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