The Inverse Gaussian distribution Sample Clauses

The Inverse Gaussian distribution as a depression remission model In this application of the threshold model, the health status of each patient with respect to depression is assumed to follow a latent stochastic process, 𝑋(𝑡), where 𝑡 denotes time measured from randomisation. The initial health status of the subject at baseline is 𝑋(0) = 𝑐 > 0. The mean rate of change of depression status over the interval is denoted by µ. Remission occurs when the depression status process decreases to the threshold level, denoted 𝐴, which is taken as an absorbing boundary or threshold for the process. If µ > 0 then the remission endpoint is not assured because the process would tend to drift away from the threshold. If µ < 0 there is a tendency to drift towards the remission threshold, moreover if µ ≤ 0 it can be shown that remission will occur in some finite time with probability one (Xxxxxxxx 1979). Study withdrawal would cause a right censored observation. The IG model has several characteristics of its distribution that make it an attractive model for the remission process. At any one point in time a complete description of patient’s depression status would be complex, including details regarding symptoms, prognosis, history, comorbidity etc. A simple picture could be a map of depression status on to a single scale, where 𝑋 denotes the level of a patient’s depression status on this scale at time 𝑡, so 𝑋(𝑡) is the path of the patient’s depression
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