Abstract
We propose a framework for jointly modelling tumour size at diagnosis and time to distant metastatic spread, from diagnosis, based on latent dynamic sub-models of growth of the primary tumour and of distant metastatic detection. The framework also includes a sub-model for screening sensitivity as a function of latent tumour size. Our approach connects post-diagnosis events to the natural history of cancer and, once refined, may prove useful for evaluating new interventions, such as personalised screening regimes. We evaluate our model-fitting procedure using Monte Carlo simulation, showing that the estimation algorithm can retrieve the correct model parameters, that key patterns in the data can be captured by the model even with misspecification of some structural assumptions, and that, still, with enough data it should be possible to detect strong misspecifications. Furthermore, we fit our model to observational data from an extension of a case-control study of post-menopausal breast cancer in Sweden, providing model-based estimates of the probability of being free from detected distant metastasis as a function of tumour size, mode of detection (of the primary tumour), and screening history. For women with screen-detected cancer and two previous negative screens, the probabilities of being free from detected distant metastases 5 years after detection and removal of the primary tumour are 0.97, 0.89 and 0.59 for tumours of diameter 5, 15 and 35 mm, respectively. We also study the probability of having latent/dormant metastases at detection of the primary tumour, estimating that 33% of patients in our study had such metastases.