hw5 - under Section 1.10(a Fit a Weibull model to this data...

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HW 5 for Stat 4930/6934 - Fall 2003 Due October 29, 2003 Reading in text for this assignment Chapters 5 and 6 1. (4930) Consider the the accelerated failure time model, log ( T ) = μ + β 0 x + σ±, where S ± ( ± ) = 1 1+exp( ± ) . Show that this implies that T follows a log-logistic distribution. Express the parameters ( μ, β, σ ) in terms of the parameters of the log-logistic, ( θ, β, κ ) and give the form of the standard errors for ( θ, β, κ ) in terms of the covariance matrix of ( μ, β, σ ). 2. (6934) Consider the the accelerated failure time model, log ( T ) = μ + β 0 x + σ±, where S ± ( ± ) = 1 1+exp( ± ) . This induces a log-logistic distribution on T . Show that this model implies proportional odds, i.e., S i ( t ) 1 - S i ( t ) = exp( - κη i ) S 0 ( t ) 1 - S 0 ( t ) where η i = β 0 x and S i and S 0 are the survival functions for T . 3. Consider the bone marrow transplant data described in class and given at www.biostat.mcw.edu/homepgs
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Unformatted text preview: / under Section 1.10. (a) Fit a Weibull model to this data including the covariates disease type, graft type, and an interaction. Find the maximum likelihood estimates for the baseline hazard parameters λ and γ and the regression coefficients of the PH model. (b) Compute the standard errors of these parameters using the multivariate delta-method. (c) Find the mle for the median survival for all four groups and compare. 4. Repeat parts a), and c) from the previous exercise using the log-logistic model. Which model do you prefer? Explain. Feel free to use evidence from graphical checks and by appropriate comparisons of the log likelihood....
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