Non-parametric and Distribution-free Approaches

Question 1

How do you find the Kaplan-Meier estimate? (method not formula)

Answer 1

Multiply 1-dj/nj for all t up to and including the required t (essentially product of the survival probabilities

Question 2

Confidence interval for KM estimate

Answer 2

S(t) * ( 1 + 1.96 * sqrt( var(s(t) ) )

note Var(s(t)) formula will be given in exam if required

Question 3

Give the formula for the Breslow estimator

Answer 3

Shat = exp ( - sum (dj / nj) )

Question 4

What is a p-value

Answer 4

Probability you reject H0 when H0 is true

Question 5

Do you want the p-value to be big or small

Answer 5

small

Question 6

What is the power of a test

Answer 6

probability you reject H0 when H0 is false

Question 7

Do you want power to be big or small

Answer 7

big

Question 8

What does the log-rank test do?

Answer 8

Performs a statistical test of the difference in survival times been two groups

Question 9

Give the formulae for di, Yi, e1i, and v1i

Answer 9

di = d1i + d2i
Yi = Y1i + Y2i
e1i = (Y1i / Yi ) * di
v1i = (Y1i / Yi) * (1 - (Y1i / Yi) ) * ( (Yi - di)/(Yi - 1) ) * di

Question 10

Log-rank test statistic generally

Answer 10

(O - E)^2 / Var(O - E)

Question 11

Log-rank using d1i, e1i and v1i

Answer 11

[ sum(d1i) - sum(e1i) ]^2 / v1i