A HYBRID LIKELIHOOD ALGORITHM FOR RISK MODELING

The risk of radiation-induced cancer is assessed through the follow-up of large cohorts, such as atomic bomb survivors or underground miners who have been occupationally exposed to radon and its decay products. The models relate to the dose, age and time dependence of the excess tumour rates, and they contain parameters that are estimated in terms of maximum likelihood computations. The computations are performed wit h the software package EPICURE, which contains the two main options of person-by person regression or of Poisson regression with grouped dat a. The Poisson regression is most frequently employed. but there are c ertain models that require an excessive number of cells when grouped d ata are used. One example involves computations that account explicitl y for the temporal distribution of continuous exposures, as they occur with underground miners. In past work such models had to be approxima ted, but it is shown here that they can be treated explicitly in a sui tably reformulated person-by person computation of the likelihood. The algorithm uses the familiar partitioning of the log-likelihood into t wo terms, L(1), and L(0). The first term, L(1), represents the contrib ution of the 'events' (tumours). It needs to be evaluated in the usual way, but constitutes no computational problem. The second term, L(0), represents the event-free periods of observation. It is, in its usual form, unmanageable for large cohorts. However, it can be reduced to a simple form, in which the number of computational steps is independen t of cohort size. The method requires less computing time and computer memory, but more importantly it leads to more stable numerical result s by obviating the need for grouping the data. The algorithm may be mo st relevant to radiation risk modelling, but it can facilitate the mod elling of failure-time data in general.