Model inverse Bateman

Inverse Bateman The inverse Bateman function describes transient recovery from a baseline disease severity score, followed by reoccurrence of the disease, and is also useful for describing diseases that exhibit cyclical episodes. The function can also be implemented to describe a transient placebo response when warranted. For example, Holford et al. (25) used the inverse Bateman function to describe the time course of depression in placebo-treated patients. This model was selected for this work in part because of the transient response seen in placebo-treated patients and in part because of the cyclical nature of the disease where patients would be expected to improve and worsen over the course of treatment. Therefore, the first exponential process describes the recovery phase and the second exponential process is used to account for onset of disease in the next episode. 

FIGURE 21.10 Example profile of inverse bateman disease progression model with symptomatic drug action. 

Cyclical Modification of Inverse Bateman Function A cosine function can be used to describe patterns similar to the exponential and inverse Bateman models and can therefore be used as the function for disease progress. However, this same cosine function can also be used to impose a cyclical modulation on another function. 

Code 6 Inverse Bateman Model of Disease Effect... 

In this equation, the disease progression model is evaluated at any time t and the cosine function is added to the overall disease progression model to determine the status. Here, SADamp and Phase define the amplitude of the underlying cyclical change in disease severity score and the time to the maximum worsening of that score. A plot of an inverse Bateman function with a cyclical component is provided in Figure 21.11. 

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