Week 4 Lecture Slides (1)

2 alternatively plot lnh2o t lnh1o t and ko

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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 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 – Week 4: The 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 ˆKO (t )] − ln[H1O (t )] versus t . ˆ ln[H This corresponds to plotting the expression above If the assumption holds, each curve should be roughly constant. 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: ˆ 1 (11....
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