2. A Cox proportional hazards model was used to study losses from two groups. Group
1 has $z = 0$ and group 2 has $z = 1$. A sample of size three is taken from each group.
Group 1: 275, 325, 520
Group 2: 215, 250, 300
(a) Assume the baseline survival function is $S_0(x) = (200/x)^\alpha$, $x > 200$, $\alpha > 0$.
Determine the maximum likelihood estimates of the baseline parameter $\alpha$ and
the coefficient $\beta$ of the covariate $z$.
[20 marks]
(b) Obtain an estimating equation for the covariate coefficient using the partial likelihood method (no need to solve the equation).
[20 marks]