Parametric Models and Estimation

Question 1

Give the De Moivre hazard function?

Answer 1

h(t) = 1 / (w-t)

Question 2

Give the weibull hazard function

Answer 2

h(t) = a * t(a-1)

Question 3

Give the Gopertz hazard function

Answer 3

h(t) = Bc^t

Question 4

Give the integrated hazard of the Gompertz function

Answer 4

-(c^t) * (-B / ln(c) )

Question 5

What is the asymptotic variance of the MLE

Answer 5

• 1 / E( d^2l / dθ^2)

Question 6

How do you linearise an exponential distribution? POSSIBLE EXAM LEARN HOW TO DO

Answer 6

plot - log( S(t) ) against t

Question 7

How do you linearise a weibull distribution? POSSIBLE EXAM LEARN HOW TO DO

Answer 7

plot log(−log(Sˆ(t)) against log(t)

Question 8

How do you linearise a Gompertz distribution? POSSIBLE EXAM LEARN HOW TO DO

Answer 8

plot of log(−log(Sˆ(t)) against t

Question 9

How do you linearise a log-logistic distribution? POSSIBLE EXAM LEARN HOW TO DO

Answer 9

plot log( S(t) / 1 - S(t) ) against log(t)

Question 10

Give the log linear model and explain the constant c

Answer 10

S0(t) = S1(t/c)

If c<1 covariate group age faster than reference group

Question 11

Give the proportional hazard model

Answer 11

S1(t) = S0(t) ^λ

Question 12

Give the proportional odds model

Answer 12

λlogit( 1 - S1(t) ) = logit ( 1 - S0(t) ) - log(λ)