Smoothing and forecasting mortality rates Iain D Currie 1 , Maria Durban 2 and Paul HC Eilers 3 1 Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, UK 2 Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid, Edificio Torres Quevedo, Leganes, Madrid, Spain 3 Department of Medical Statistics, Leiden University Medical Center, Leiden, The Netherlands Abstract: The prediction of future mortality rates is a problem of fundamental importance for the insurance and pensions industry. We show how the method of P-splines can be extended to the smoothing and forecasting of two-dimensional mortality tables. We use a penalized generalized linear model with Poisson errors and show how to construct regression and penalty matrices appropriate for two- dimensional modelling. An important feature of our method is that forecasting is a natural consequence of the smoothing process. We illustrate our methods with two data sets provided by the Continuous Mortality Investigation Bureau, a central body for the collection and processing of UK insurance and pensions data. Key words: forecasting; mortality; overdispersion; P-splines; two dimensions Data and software link available from: http:==stat.uibk.ac.at=SMIJ Received September 2003; revised July 2004; accepted August 2004 1 Introduction The modelling and projecting of disease incidence and mortality rates is a problem of fundamental importance in epidemiology and population studies generally, and for the insurance and pensions industry in particular. Human mortality has improved substan- tially over the last century, but this manifest benefit has brought with it additional stress in support systems for the elderly, such as healthcare and pension provision. For the insurance and pensions industry, the pricing and reserving of annuities depends on three things: stock market returns, interest rates and future mortality rates. Likewise, the return from savings for the policyholder depends on the same three factors. In the most obvious way, increasing longevity can only be regarded as a good thing for the policyholder; a less welcome consequence is that annual income from annuities will be reduced. In this article, we consider one of these three factors: the prediction of mortality rates. We have been provided with data sets from two classes of UK insurance business, and we will use these to illustrate our approach to the smoothing and projecting of mortality rates. Address for correspondence: Iain D Currie, Department of Actuarial Mathematics and Statistics, Heriot- Watt University, Edinburgh EH14 4AS, UK. E-mail: i.d.currie@hw.ac.uk Statistical Modelling 2004; 4: 279–298 # Arnold 2004 10.1191=1471082X04st080oa