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Unformatted text preview: rds assumption for a given covariate
Z1 after adjusting for all other relevant covariates
Write the covariate vector (p -dimension) as Z = (z1 , Z2 ),
where Z2 represents the remaining p − 1 covariates.
Assume no interaction 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 – Week 4: The 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
ˆKO (t )] − ln[H1O (t )] versus t .
This corresponds to plotting the expression above
If the assumption holds, each curve should be roughly
42/45 Actuarial Statistics – Week 4: The Cox Regression Model
Diagnostics for the Cox regression model Example Comparing the diﬀerence in disease-free survival between patients
given an autologous (auto) and allogeneic (allo) bone marrow
transplant for acute leukemia. There is only a single covariate Z
taking a value 1 if the patient has an auto transplant and 2 if the
patient had an allo transplant.
We will consider two plots:
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- Three '14