Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 32 / 4 / b / Solution

Within month two, each individual contributes only the time spent at risk between times one and two. There are $104-6-1=97$ complete one-month contributions. The six event contributions are $0.08,0.16,0.22,0.50,0.63,0.72$, and the censored contribution is $0.69$. ConsequentlyThe month-specific likelihood factor in a piecewise-exponential survival model is ${\theta }_2^6{e}^{-{\theta }_2{T}_2}$, givingThe eight individuals no longer at risk at time one contribute no month-two exposure. Using either all 112 individuals or all 104 as full-month observations would give the wrong denominator.