Continuous tumour growth models, lead time estimation and length bias in breast cancer screening studies.

Comparisons of survival times between screen-detected and symptomatically detected breast cancer cases are subject to lead time and length biases. Whilst the existence of these biases is well known, correction procedures for these are not always clear, as are not the interpretation of these biases. In this paper we derive, based on a recently developed continuous tumour growth model, conditional lead time distributions, using information on each individual's tumour size, screening history and percent mammographic density. We show how these distributions can be used to obtain an individual-based (conditional) procedure for correcting survival comparisons. In stratified analyses, our correction procedure works markedly better than a previously used unconditional lead time correction, based on multi-state Markov modelling. In a study of postmenopausal invasive breast cancer patients, we estimate that, in large (>12 mm) tumours, the multi-state Markov model correction over-corrects five-year survival by 2-3 percentage points. The traditional view of length bias is that tumours being present in a woman's breast for a long time, due to being slow-growing, have a greater chance of being screen-detected. This gives a survival advantage for screening cases which is not due to the earlier detection by screening. We use simulated data to share the new insight that, not only the tumour growth rate but also the symptomatic tumour size will affect the sampling procedure, and thus be a part of the length bias through any link between tumour size and survival. We explain how this has a bearing on how observable breast cancer-specific survival curves should be interpreted. We also propose an approach for correcting survival comparisons for the length bias.