Prediction of the future number of cancer cases is of great interest to society. The classical approach is to use the age-period-cohort model for making cancer incidence predictions. We made an empirical comparison of different versions of this model, using data from cancer registries in the Nordic countries for the period 1958-1997. We have applied 15 different methods to 20 sites for each sex in Denmark, Finland, Norway and Sweden. Median absolute value of the relative difference between observed and predicted numbers of cases for these 160 combinations of site, sex and country was calculated. The medians varied between 10.4 per cent and 15.3 per cent in predictions 10 years ahead, and between 15.1 per cent and 32.0 per cent for 20 year predictions. We have four main conclusions: (i) projecting current trends worked better than assuming that future rates are equal to present rates; (ii) the method based on the multiplicative APC model often overestimated the number of cancer cases due to its exponential growth over time, but using a power function to level off this growth improved the predictions; (iii) projecting only half of the trend after the first 10 years also gave better long-term predictions; (iv) methods that emphasize trends in the last decade seem to perform better than those that include earlier time trends.

Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet.

The effectiveness of highly active antiretroviral treatment lasted for at least four and a half years and increased after the first two calendar years. The problem of less effectiveness among HIV-diagnosed intravenous drug users should be addressed by the health authorities.