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

Abstract

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 cancerspecific survival curves should be interpreted. We also propose an approach for correcting survival comparisons for the length bias.

Mammographic sensitivity as a function of tumor size: A novel estimation based on population-based screening data

“…The differences between our model and the other models could be also explored from data perspective. Specifically, to estimate the tumor size distribution, we used relatively new data from 2004 to 2009, while Weedon-Fekjaer et al estimated the parameters of the function by using screening data from 1995 to 2002 [10], and Isheden et al and Abrahamsson et al used same data from 1993 to 1995 [12,13]. As mammography detectability has been improved over time [38], and the modern mammography is able to detect more tumors at smaller size, a higher sensitivity at smaller size and also an overall lower sensitivity was observed in our study.…”

“…In their studies, the sensitivity was estimated simultaneously with a continuous growth model utilizing breast cancer screening data, and back-calculation methods were used to estimate tumor size at screening from tumor size distributions of clinically detected tumors. Inspired by this approach, Swedish researchers estimated the sensitivity not only based on tumor size, but also breast density [12,13]. What is remarkable about the findings of their studies is that the sensitivity is 100% for tumors varying in size from 15 to 20 mm and over.…”

A natural history and copula-based joint model for regional and distant breast cancer metastasis

“…The five-year risks of distant metastasis counting time from the earlier diagnosis are represented as grey dots in the subplots of Figure 3 ; these five-year risks are, however, of course, not directly comparable to the five-year risks counting time from when the tumour reached 15 mm. To correct for what is essentially lead-time bias (note that lead time is defined as the time between the early diagnosis, e.g., because of screening, and the time that cancer would have been otherwise diagnosed through symptoms 31 – 33 ) we calculated five-year risks from the time the tumour reached 15 mm. These estimates are represented as black triangles in Figure 3 ; these represent the proportions that should be interpreted (we however keep the naive estimates as a reminder of the importance of incorporating lead time in interpreting early detection in studies of screening).…”

Correspondence on‘Haemodynamic phenotypes and survival in patients with systemic sclerosis: the impact of the new definition of pulmonary arterial hypertension’

“…This can be performed by subtracting an estimate of the lead time bias obtained in a multistate model with simple-possibly unrealistic-assumptions, 5 or more complex models of the mPAP measurement process, akin to the use of tumour growth models in cancer screening. 6 Models adjusted for the age, and/or calendar-matched population can also allow to overcome this potential problem.…”