Stephen and I recently presented a pair of papers to the Institute and Faculty of Actuaries: Richards & Macdonald (2024) and Macdonald & Richards (2024). In these papers we encourage actuaries to use continuous-time models in their work. But where does that leave discrete-time?
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The World Health Organization (WHO) makes available a one-page checklist for use by surgical teams. The WHO claims that this checklist has made "significant reduction in both morbidity and mortality" and is "now used by a majority of surgical providers around the world". For example, the checklist is used by surgical teams in NHS England.
In Richards & Macdonald (2024) we advocate that actuaries use the Kaplan-Meier estimate of the survival curve. This is not just because it is an excellent visual communication tool, but also because it is a particularly useful data-quality check.
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In a recent blog, I looked at the most fundamental unit of observation in a mortality study, namely an individual life. But is there such a thing as a fundamental unit of modelling mortality? In Macdonald & Richards (2024) we argue that there is, namely an infinitesimal Bernoulli trial based on the mortality hazard.
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In Macdonald & Richards (2024), Angus and I continue our long-standing advocacy for using individual records for mortality analysis, rather than grouped counts of lives. One argument in our paper is that the individual life is the most irreducible unit of observation in mortality analysis. After all, any group can be disaggregated into individuals, but further subdivision would just be dismemberment.
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In a (much) earlier blog, Angus introduced the product-integral representation of the survival function:
\[{}_tp_x = \prod_0^t(1-\mu_{x+s}ds),\qquad(1)\]
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A common approach to teaching students about mortality is to view survival as a Bernoulli trial over one year. This view proposes that, if a life alive now is aged \(x\), whether the life dies in the coming year is a Bernoulli trial with the probability of death equal to \(q_x\). With enough observations, one can estimate \(\hat q_x\), which is the basis of the life tables historically used by actuaries.
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On 29th August 2024 Professor Angus S. Macdonald and Dr. Stephen J. Richards will give a joint seminar on contemporary mortality modelling, in principle and in practice. Attendance is free and pre-registration is not required.
The seminar will take place at 11:45hrs in Room T.01 in the Colin Maclaurin building at Heriot-Watt's Riccarton campus. See also the campus map for location and parking.
The Institute and Faculty of Actuaries (IFoA) is hosting a meeting on contemporary mortality modelling on 24th October 2024. Booking details can be found on the IFoA website.
Longevitas is pleased to announce that the Government Actuary’s Department has licensed the Longevitas survival-modelling software. Further details can be found in the press release.
