Fitting Bivariate Intensity Functions, with an Application to Modelling Delays in Reporting Acquired Immune Deficiency Syndrome

When estimating the incidence of acquired immune deficiency syndrome (AIDS), reporting delays can result in serious underestimation of recent diagnoses. Various bivariate intensity functions for non-homogeneous Poisson processes in the plane can be fitted as log-linear models. This is illustrated by application to such reporting delay data. It is shown that (quasi-)stationary models seriously overestimate recent AIDS diagnoses for England and Wales, and that a non-stationary model is more appropriate.