Unformatted text preview: tion between z1 and any of the remaining
Assume that z1 has K possible values.
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
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
2 Alternatively, plot ln[H2O (t )] − ln[H1O (t )], · · · , and
ˆ KO (t )] − ln[H1O (t )] versus t .
This corresponds to plotting the expression above
If the assumption holds, each curve shoul...
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- Three '14
- Survival analysis, cox regression model