Cox Proportional Hazard Regression

Question 1

What does log rank test do?

Answer 1

Tests if survival curves as the same for both groups.

Question 2

How do we test for confounders in survival curve?

Answer 2

Cox proportional hazard regression model. The log rank test is a crude association.

Question 3

What is the hazard rate ratio?

Answer 3

Estimates the hazard of one group compared to another.

Question 4

What is an assumption of the hazard rate ratio?

Answer 4

Proportional hazards: the difference between hazard in one group compared to another is constant over time.

Question 5

What is the equation for the Cox proportional hazards regression model?

Answer 5

h(t|X) = ho(t)e ^ (betaX)

Question 6

What do the pieces in a Cox regression model mean?

Answer 6

h(t|x) = Ho(t)e ^ (betaX)

h models the hazard
t is time
X is a given value of X
Ho(t) is the baseline hazard

Question 7

How is hazard modelled in a Cox regression model?

Answer 7

As a rate.

At time, t, for values of X.

Hazard is a function of time for some covariate X

Question 8

What is H0 in Cox model?

Answer 8

Baseline hazard when all coviariates = 0.

Question 9

What is E ^ βX in a Cox model?

Answer 9

E ^ β is the natural log of the hazard ratio; compares ratio by one unit in the value of X.
Difference in two groups at any point in time.

Question 10

What is beta in Cox model?

Answer 10

Represents the log hazard ratio of the outcome associated with a one unit change in X1.

Question 11

Give an example of log hazard.

Answer 11

21 leukemia pxs in placebo and 21 in treatment.
Outcome: time to cancer reccurence.
X1 is treatmentment group
X2 is log of while blood cell count.

Question 12

What is a model with those parameters with white blood cell as confounder?

Answer 12

h(t|x=1) = h0(t) * e^beta1(rx) + beta2*logwbc)

Question 13

What is a model with log wbc as effect modifier?

Answer 13

h(t|x=1) = h0(t) * e^beta1(rx) + beta2(logwbc) + beta3(rx*logwbc).

Question 14

What is e^beta1 for the following equation: h(t|x1=1) = ho(t) * e^beta1(rx=1)+beta2(logwbc=0)+beta3(rx=1*logwbc=0)?

Answer 14

e^beta1 is the log hazard ratio of time to cancer reccurence with a one unit change in X1 at fixed values of X2 and X3.

Question 15

What does the parameter estiamate of hazard show?

Answer 15

Hazard ratio comparing treatment to placebo group adjusting for log of wbc. Need to have e^rx estimate.

Question 16

What does Wald statistic say about hazard ratio?

Answer 16

Null: Hazard = 1
or
Beta = 0

Question 17

What is the code for hazard ratio?

Answer 17

proc phreg data = ander;
model survt*status (0) = rx logwbc /rl;
run;

survt is time to reccurence
status (0) is censoring variable
rl asks for confidence intervals around hazard ratio.