Disease progress models linear

The linear disease progress model (Equation 20.2) assumes a constant rate of change of a biomarker or clinical outcome that reflects the disease status (S) at any time, t, from the initial observation of the patient — for example, at the time of entry into a clinical trial. The rate of change can be defined in terms of a baseline disease status (Sq) and a slope (a), which reflects the change from baseline status with time ... 

Finally a disease progress model can reflect more complex drug action. Phenomena such as a drug concentration-effect delay tolerance and rebound to both placebo and active treatments can be made using a linear offset model. These effects can be accounted for by including the appropriate terms. For instance a delay in onset can be accounted for by the addition of an effect compartment and tolerance and rebound... 

As with the offset model for the linear disease progress model, the effect of drug would be expected to disappear on cessation of therapy in this offset model. Again, a delay to the onset of drug effect can be incorporated with the use of an effect compartment component. 

The terminology presented here is consistent with terminology described and used previously (13, 14). In order to demonstrate the different types of drug action, example plots were generated using a simple linear disease progression model. 

The linear model assumes a constant rate of change of the disease status over time. The linear model can be dehned in terms of a baseline disease status ( o) and a slope parameter (a) and t is time after the initial observation of the disease. The equation for the linear model is given below and a NONMEM control stream implementing the linear disease progression model is provided in Table 21.2. 

EXAMPLE EOR THE SIMPLE LINEAR DISEASE PROGRESSION MODEL... 

As with the linear model of disease progress, the consequences of therapeutic intervention on the asymptotic model of disease progress can be described by including terms to account for the expected action of a drug. Drugs may exert an immediate and transient symptomatic effect, they may act to alter the progress of the disease, such as shortening the time to recovery, or they may do both. 

Structural Models of Disease Progression 21.3.2.1 Linear Models of Disease Progression... 

TABLE 21.2 Example NONMEM Code 1 Linear Model of Disease Progression with No Drug Effect... 

An example fragment of a NONMEM control stream for a linear model of disease progression with a symptomatic drug effect is provided in Table 21.3, and an example is included in the appendix. 

In some cases, therefore, the linear model can be a reasonable approximation for disease progression when the disease is observed over a relatively short period of time or if the number of individuals experiencing complete recovery is limited. For example, the trajectory of the United Parkinson s Disease Rating Score (UPDRS— a measure of Parkinson s disease) has been described using Gompertz functions (20), which exhibit an asymptotic increase to a maximum score. However, over... 

With a linear model, there are two basic drug effect patterns possible. Symptomatic drug action will improve patient status but has no impact on the rate of progress, or the drug can alter the rate of progress of the disease, resulting in a protective or disease modifying action. 

With the exponential asymptotic model, the effect of drug can be described as symptomatic or as disease modifying or as a combination of both. In the case of the symptomatic benefit, as was seen with the linear model for progression, the drug effect, E(t), is added directly to the function for disease status. 

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