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13_AS_3_lec_a

# 4245 actuarial statistics module 3 semi parametric

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Unformatted text preview: tion between z1 and any of the remaining covariates. Assume that z1 has K possible values. ˆ Fit a Cox model stratiﬁed on each value of z1 , and let HgO (t ) be the estimated cumulative baseline hazard rate in the g th (g = 1, 2, · · · , K ) stratum. So we have K models which should be ‘proportional’ for the assumption to be valid with respect to covariate z1 . 41/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Diagnostics for the Cox regression model Graphical diagnostic tools 1 ˆ ˆ ˆ Plot ln[H1O (t )], ln[H2O (t )], · · · , and ln[HKO (t )] versus t . the ratio of any two should be of the form ln e β1 z1,g1 = β1 (z1,g1 − z1,g2 ), e β1 z1,g2 (where z1,g1 and z1,g2 are the respective possible outcomes for z1 ), which does not depend on t Hence, if the assumption holds, these curves should be approximately parallel. ˆ ˆ 2 Alternatively, plot ln[H2O (t )] − ln[H1O (t )], · · · , and ˆ KO (t )] − ln[H1O (t )] versus t . ˆ ln[H This corresponds to plotting the expression above If the assumption holds, each curve shoul...
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