ALTA ALTA Standard Folio Data PPH-Weibull: Difference between revisions

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Solving for the parameters that maximize Eqn. (PH LKV) will yield the parameters for the PH-Weibull model. Note that for  <math>\beta </math>  = 1, Eqn. (PH LKV) becomes the likelihood function for the PH-exponential model, which is similar to the original form of the proportional hazards model proposed by Cox [28].
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Note that the likelihood function given by Eqn. (GLL-LK) is very similar to the likelihood function for the proportional hazards-Weibull model given by Eqn. (PH LKV). In particular, the shape parameter of the Weibull distribution can be included in the regression coefficients of Eqn. (13) as follows:
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<math>{{a}_{i,PH}}=-\beta \cdot {{a}_{i,GLL}}</math>
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where:
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• <math>{{a}_{i,PH}}</math>  are the parameters of the PH model.
 
• <math>{{a}_{i,GLL}}</math>  are the parameters of the general log-linear model.
 
In this case, the likelihood functions given by Eqns. (PH LKV) and (GLL-LK) are identical. Therefore, if no transformation on the covariates is performed, the parameter values that maximize Eqn. (GLL-LK) also maximize the likelihood function for the proportional hazards-Weibull (PHW) model with parameters given by Eqn. (GLL Parameters). Note that for  <math>\beta </math>  = 1 (exponential life distribution), Eqns. (PH LKV) and (GLL-LK) are identical, and  <math>{{a}_{i,PH}}=-{{a}_{i,GLL}}.</math>
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Latest revision as of 19:55, 8 July 2015

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