A Model for Reporting Delays
Summary
This blog demonstrates that the practice can also be justified theoretically in the survival modelling framework, although the choice of six months as the cut-off remains an empirical matter. We make our model a MPP by assuming that when a transition \(dN^{12}(t+z)=1\) occurs, we observe \(Z\) (which is equivalent to learning the value of \(T_x\)). If \(dN^{12}(t+z)=1\), the contribution to the likelihood of the jump and the mark is: which is equal to the joint probability of the jump and the observed mark: (Of course, this joint probability also admits the decomposition: but this has no useful interpretation in the survival models framework. • Contributions to the likelihood arising from censored observations include the occupancy probability \({}_wp_x^{01}\) in such a way that it cannot be factorized out, and the exponent involves \(N^{12}(w)\) instead of \(N^{01}(w)\). This analysis does not, of course, tell us how much of the most recent data to discard, but Stephens blog suggests that six months is an acceptable rule-of-thumb.
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