# GLMs in Life Assurance - using an Expected "framework"

#### NielDaniels

##### New Member
I work in Life Assurance and the GLM concept is fairly new to us. To date, we have analysed our mortality experience in the following way

- Define an Expected mortality table (this might be a standard published table - or an internal table derived from a prior analysis)
- This table might (for example) vary just by Age and Sex
- Then investigate mortality data by deriving an expected (number of lives * expected mortality rate)
- Compare Actual deaths to Expected
- Analyse experience
- We might want to investigate (for example) how experience varies by policy size (larger policies typically have lighter experience because they are from better socio-economic groups)
- But our analysis of how mortality varies by policy size would be a simple one-way analysis

So now we are introducing GLMs. We can throw the same dataset above into R and can investigate the effect of Age, Sex and PolicySize. R returns that all three factors are significant (as we'd expect).

But, what I want to do is use the old approach (of having an Expected mortality table) and apply that within a GLM environment. So I want to derive an Expected number of deaths and then analyse how Actual compares to Expected using GLM tools.

So what's my question then ? There are 2 !!

Firstly, I don't know the best way to get an expected table into the calculation. Do I simply derive my Expected and then do a GLM <- glm(Deaths / Expected ~ offset(log(exposure) + PolicySize, family = Poisson) and perhaps add Age and Sex into the fit to see if there is residual variance there ?? Or is there some other more subtle method ?

Secondly, and more importantly, I lose a key output of the fitting process if I do this - ie I no longer get told if Age or Sex are significant - because I have factored them out by putting them into the Expected. R will return that both Age and Sex are NOT significant factors - but we know that they are. We are being told that they are not - simply because there is not much RESIDUAL variance. So we are not getting an overly helpful response. So what I want is to get all the useful GLM info - but using my expected mortality table as a framework

Thnaks in advance for any help that people can provide