Semi-parametric Survival Modelling

Question 1

What is the cox-proportional hazard model?

Answer 1

h(t, x) = h0(t) * ψ(x ; B)

Question 2

What are the three choices for ψ?

Answer 2

exp( - B^(T) * x ) = log linear
1 +B^(T) * x = linear
ln( 1 + exp( - B^(T) * x ) ) = logisitic

Question 3

How do you find the joint probability function?

Answer 3

product [ ψ(ij) / sum(k in R(tj)) ψ(k) ]

R(tj) is the risk set at time tj

Question 4

Given two groups, what is ψ(x) given by?

Answer 4

1 if individual is in group 1

exp(β) if individual is in group 2

Question 5

Give the likelihood for β given two groups

Answer 5

product ( exp( βxi ) / sum(k in R(tj) exp(βxj) )

Question 6

Formula for time dependent covariates?

Answer 6

h(t) = h0(t) * exp( β * x(t) )

Question 7

Formula for time dependent coefficients?

Answer 7

β(t) = ax + blog(t) * x

Question 8

What is the difference between time dependent coefficients and covariates?

Answer 8

Coefficient means β’s change with time, covariates mean x’s change with time