Module 3: (Cox Reg) Semi-Para Models Flashcards
Why Cox regression?
So we can model separate factors, eg weight, height, age etc
What does vector Z hold;
the data about the person, eg weight, age, smoking status
What does λ0(t) represent?
The baseline hazad function.
HF when all the Z numbers are 0
Expression for the hazard function under the cox model
λ0(t) * exp( ∑j=1 p βjZij )
If β is +ve then….
Hazard rate (instant chance of death) increases with the jth covariate.
Does magnitude of β matter?
No, because of scaling.
What does proportionality of hazard rates mean broadly;
The hazard rates for different individuals are proportional for any t. Ie they’ve curved but paralell lines.
What is partial likelihood estimation used for
Estimating the β values
What 2 assumptions does partial likelihood estimation rely on?
- Non-informative censoring
- Lives are independent
What does the function R(tj) tell us?
The set of the label of all lives who are still alive at tj-
What are the two cases of partial likelihood regression we consider?
- Deaths cannot occur simaltaneously
- They can
Properties of β under MLE estimation (2)
- βhat is asymptotically unbiased.
- It asymptotically follows a multivariate normat distribution.
What 2 tests can we use to determine significance of covariates?
- Likelihood ratio test
- Wald test
What H0 will we set in our covariate significance testing?
We will introduce an extra set of q β’s and test if they all =0
Likelihood ratio test statistic
-2 [log Lp - log Lp+q]
