The Inverse Gaussian Model Sample Clauses

The Inverse Gaussian Model. Two hypothetical time paths of depression (one solid and one dashed) showing actual and linear smoothed depression scores. The participant’s depression score under the inverse Gaussian model evolves as Brownian motion with a trend but with random local changes. Reaching the threshold for remission is determined by the patient’s initial severity or baseline position and the rate of recovery or progression towards or away from remission. If larger values of 𝑋 correspond to a state of worse depression, a patient is in the GENDEP study as their depression status is above a clinical threshold. Following the path from randomisation, the patient would be determined to be in remission when their level falls below the threshold, 𝐴, Defined here to be a score of 10 or less on the MADRS (Xxxxxx, Xxxx et al. 2002, Xxxxxx, Himmerich et al. 2003). The time it takes for 𝑋(𝑡) to move from randomisation, 𝑡0, to remission, 𝑡𝐴, is the individual’s time to remission. Since 𝑋(𝑡) is a stochastic process, the individual’s time to remission will be a random variable with characteristics dependent on the statistical properties of 𝑋(𝑡). The stochastic process is comparable to a physical diffusion process. As time passes, the patient’s depression level fluctuates randomly about a trend, shown by the straight line, and at some point the patient’s depression reaches the threshold and they are deemed to be in remission. There are many factors which may influence the depression level to deviate from its expected path which could be compared to the movement of a molecule colliding with other molecules. Therefore, this process is Brownian motion with drift. Formally, it is characterised as a Wiener diffusion process that exhibits drift from an initial level at randomisation, towards an absorbing barrier at level 𝐴. The first passage time to the absorbing barrier follows an IG distribution (Cox and Xxxxxx 1977). For 𝑋(𝑡) to be a Wiener process it must satisfy the following conditions (Xxxxxxxx 1975):
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