a.List two graphical methods that can be used to assess the proportional hazard

Question

a.List two graphical methods that can be used to assess the proportional hazard assumption of the Cox model.

b.The log-rank test is equivalent to : A. Wald test B. Likelihood ratio test C. Score test for the log-relative risk in the Cox model (circle one).

c.Why martingale residual is right skewed?

d.List four types of residuals and describe how would you use them to do model diagnostics.

e.Describe, in details, on how to use the forward selection of covariates to build a Cox model using the p-value criterion.

f.List two graphical methods that can be used to assess the proportional hazard assumption of the Cox model.

g.Describe, in details, on how to use the forward selection of covariates to build a Cox model using the AIC criterion.

Explanation / Answer

Ans a ) List of two grphical methods :

a) Plot the survival curve based on the cox model and kaplan-meier estimates for theeach group.(Departure of the two KM estimator provides the evidence that the daviation from assumption of prarortional hazad model.)

b) Plot of the estimated cummulative hazard vs number of failures. ( If curves are not linear that they are roughly as close to the angle 45degree line as under praportionality, then the hazards are not praportional.)

Ans b) Under the assumption of praportional hazards, the log rank test is used to test null hypothesis that the log of hazard ratio is equal to zero.

The log rank test is equivalent to the partial likelihood score test of cox for the praportional hazards regression model and this test is asymptotically equivalent to the Wald test when we use the maximum partial likelihood estimator of the log of hazard ratio.

so ths option C is correct.

ans g)

AIC Crireria for Cox model :

Since under the cox model, the partial likelihood should be used in forming the AIC.

This turns out to be the case , because the partial likelihood possesses the properties of a classical likelihood , that is in terms of 2nd order Taylor expansion that was used in the proof of classic AIC ( partial likehood as a profile likelihood).

So

AIC= -2pl(y|B^(y) +2p,

where pl() is the log partial likelihood and p is the dimension of B

Interpretation:

1)the partial likelihood does not exactly correspond to the density function, it has to be viewed via the profile likelihood.

And the model is choosen with minimum AIC.

Ans e) forword selection method for model building:

F orwor selection method is the simplest method for model building. in this method we add variable to the model one at a time.At each step, each variable that is not already in the model. we cal add variable in the model so that, the P- value of that variable is below some pre-set level.

and the pre-set value is set above theconvential 0.05 level at say 0.10 or 0.15 because the exploratory nature of this method.

we start the variable whis is most significant in the initial analysis,and we keep continuing adding the variable untill none of the remaining variables are "singnificant" when it is added to the model.

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