Uncertainty of AIDS incubation time and its effects on back-calculation estimates

Estimating the variance of cancer prevalence from population-based registries

Cancer prevalence is the proportion of people in a population diagnosed with cancer in the past and still alive. One way to estimate prevalence is via population-based registries, where data on diagnosis and life status of all incidence cases occurring in the covered population are collected. In this paper, a method to estimate the complete prevalence and its variance from population-based registries is presented. In order to obtain unbiased estimates of the complete prevalence, its calculation can be thought as made by three steps. Step 1 counts the incidence cases diagnosed during the period of registration and still alive. Step 2 estimates the expected number of survivors among cases lost to follow-up. Step 3 estimates the complete prevalence by taking into account cases diagnosed before the start of registration. The combination of steps 1+2 is defined as the counting method, to estimate the limited duration prevalence; step 3 is the completeness index method, to estimate the complete prevalence. For early established registries, steps 1+2 are more important than step 3, because observation time is long enough to include all past diagnosed cases still alive in the prevalence data. For more recently established registries, step 3 is by far the most critical because a large part of prevalence might have been diagnosed before the period of registration (Corazziari I, Mariotto A, Capocaccia R. Correcting the completeness bias of observed prevalence. Tumori 1999; 85: 370-81). The work by Clegg LX, Gail MH, Feuer EJ. Estimating the variance of disease-prevalence estimates from population-based registries. Biometrics 2002; 55: 1137-44. considers the problem of the variability of the estimated prevalence up to step 2. To our knowledge, no other work has considered the variability induced by correcting for the unobserved cases diagnosed before the period of registration, crucial to estimate the prevalence in recent registries. An analytic approach is considered to calculate the variance of step 3. A unified expression for the variance of the prevalence allowing for steps 1 through 3 is obtained. Some applications to cancer data are presented.

Estimating cancer incidence using a Bayesian back-calculation approach

We propose a Bayesian hierarchical model for the calculation of incidence counts from mortality data by a convolution equation that expresses mortality through its relationship with incidence and the survival probability density. The basic idea is to use mortality data together with an estimate of the survival distribution from cancer incidence to cancer mortality to reconstruct the numbers of individuals who constitute previously incident cases that give rise to the observed pattern of cancer mortality. This model is novel because it takes into account the uncertainty from the survival distribution; thus, a Bayesian-mixture cure model for survival is introduced. Furthermore, projections are obtained starting from a Bayesian age-period-cohort model. The main advantage of the proposed approach is its consideration of the three components of the model: the convolution equation, the survival mixture cure model and the age-period-cohort projection within a directed acyclic graph model. Furthermore, the estimation are obtained through the Gibbs sampler. We applied the model to cases of women with stomach cancer using six age classes [15-45], [45-55], [55-65], [65-75], [75-85] and [85-95] and validated it by using data from the Tuscany Cancer Registry. The model proposed and the program implemented are convenient because they allow different cancer disease to be analysed because the survival time is modelled by flexible distributions that are able to describe different trends.