Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 34 / 3 / a / Solution

Assume independent individuals and independent censoring, with the censoring law not involving the event-rate parameters. If $T_j$ is the survival time and $C_j$ its censoring time, we observe $x_j=\min (T_j,C_j)$ and $v_j=1_{\{T_j\le C_j\}}$. The exponential distribution givesAn observed event contributes $f_j(x_j)$, while a right-censored observation contributes $S_j(x_j)$, because it only says the event has not occurred by $x_j$. Multiplying these survival likelihood contributions and omitting censoring factors independent of the parameters givesWithout independent censoring the censoring factors cannot generally be discarded in this way.