We analyse the stochasticity in mortality data from the USA, the UK and Sweden, and in particular to which extent mortality rates are explained by systematic variation, due to various risk factors, and random noise. We formalise this in terms of a mixed regression model with a logistic link function, and decomposethe variance of the observations into three parts: binomial risk, the variance due to random mortality variation in a finite population, systematic risk explained by the covariates and unexplained systematic risk, variance that comes from real changes in mortality rates, not captured by the covariates. The fraction of unexplained variance caused by binomial risk provides a limit in terms of the resolution that can be achieved by a model. This can be used as a model selection tool for selecting the number of covariates and regression parameters of the deterministic part of the regression function, and for testing whether unexplained systematic variation should be explicitly modelled or not. We use a two-factor model with ageand calendar year as covariates, and perform the variance decomposition for a simple model with a linear time trend on the logit scale. The population size turns out to be crucial, and for Swedish data, the simple model works surprisingly well, leaving only a small fraction of unexplained systematic risk, whereas for the UK and the USA, the amount of unexplained systematic risk is larger, so that more elaborate models might work better.
Springer Publishing Company, 2014. 199-222 p.