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Given a covariate Z, suppose that the log survival time Y follows a linear model with a logistic error distribution, that is, Y = ln(X) = μ + βΖ + σ W where the pdf of W is given by eu f(w) = (1 + ewy,
(a) For an individual with covariate Z, find the conditional survival function of the survival time X, given Z, namely, S(x |Z). (b) The odds that an individual will die prior to time x is expressed by 1- Sa lZ)l/S(a |Z). Compute the odds of death prior to time x for this model. (c) Consider two individuals with different covariate values. Show that, for any time x, the ratio of their odds of death is independent of x. The log logistic regression model is the only model with this property
math   Statistics-And-Probability   
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