Information Matrix

Different countries have different mortality characteristics, and this is true even where countries have similar levels of wealth and development.  However, different countries also have shared mortality characteristics, and one of these is seasonal variation. 

Stephen's earlier blog explained the origin of the very useful result relating the life-table survival probability \({}_tp_x\) and the hazard rate \(\mu_{x+t}\), namely:

\[ {}_tp_x = \exp \left( - \int_0^t \mu_{x+s} \, ds \right). \qquad (1) \]

To complete the picture, we add the assumption that the future lifetime of a person now aged \(x\) is a random variable, denoted by \(T_x\), and the connection with expression (1) which is:

To talk informally about a concept, we need only give it a recognisable name. For example, we use the label "medical error" and we all know what is meant - or at least we think we do.

As with anything that must combine reliable data with hard maths and sound judgement, forecasting mortality is difficult.

A basic result in probability theory is that the variance of the sum of two random variables is not necessarily the same as the sum of their variances.

In previous posts we have looked at problems with the quality and reliability of cause-of-death data and a list of hurdles for mortality projections based on such data.  One other issue is that of detail.

In civil engineering, no building can be sounder than the foundation on which it rests.  A similar comment applies to statistical analysis, which is obviously limited by the quality of the underlying data. 

I have written several times about the challenges in creating mortality projections based on cause-of-death data.  Those interested in the details can consult my recent paper published in a special edition of the British Actuarial Journal. 

With the exception of dressmaking, bias is generally undesirable. This is particularly the case when projecting future mortality rates for reserving for pension liabilities. 

Stephen has written about the challenges in using population cause-of-death data for mortality analysis and forecasting. Another potential source of data is computerised patient records such as the General Practice Research Database (GPRD).