Identification of the Fraction of Indolent Tumors and Associated Overdiagnosis in Breast Cancer Screening Trials

Abstract

It is generally accepted that some screen-detected breast cancers are overdiagnosed and would not progress to symptomatic cancer if left untreated. However, precise estimates of the fraction of nonprogressive cancers remain elusive. In recognition of the weaknesses of overdiagnosis estimation methods based on excess incidence, there is a need for model-based approaches that accommodate nonprogressive lesions. Here, we present an in-depth analysis of a generalized model of breast cancer natural history that allows for a mixture of progressive and indolent lesions. We provide a formal proof of global structural identifiability of the model and use simulation to identify conditions that allow for parameter estimates that are sufficiently precise and practically actionable. We show that clinical follow-up after the last screening can play a critical role in ensuring adequately precise identification of the fraction of indolent cancers in a stop-screen trial design, and we demonstrate that model misspecification can lead to substantially biased estimates of mean sojourn time. Finally, we illustrate our findings using the example of Canadian National Breast Screening Study 2 (1980-1985) and show that the fraction of indolent cancers is not precisely identifiable. Our findings provide the foundation for extended models that account for both in situ and invasive lesions.

Modeling the overdetection of screen‐identified cancers in population‐based cancer screening with the Coxian phase‐type Markov process

“…Moreover, while the Davidov and Zelen model features a good mathematical algorithm, it may be computationally intractable when overdetection is not only limited to one‐jump processes, but allows a finite Markov process. This similar circumstance is also noted in the work of Ryser et al, which is another valuable modeling approach for capturing the proportion of overdetection from progressive cases still remaining in the PCDP using the mixture model. To render a modeling approach that efficiently uses information about detection modes and that is amenable to estimation, we propose a generalized Coxian phase‐type Markov process to separate the latent multistate pathway for progressive PCDP from the latent multistate pathway for nonprogressive PCDP, while making an allowance for the sensitivity of screening tools to provide a useful way to consider progressive vs nonprogressive cancers at a population‐based level.…”

“…In contrast to the Ryser's method, which used the mixture model to capture the proportion of indolent cancers, our method can accommodate the age‐dependent proportion of nonprogressive cancers. In our model, we used two continuous‐time Markov processes that allow for age‐dependent nonprogressive rates, which are critical for cancers with low progressive rates and a late age of onset, such as prostate cancer.…”

“…For breast cancer screening with mammography, some studies have reported 5%‐10% overdetection, whereas others have estimated up to 50% overdetection. The discrepancy between these findings is mainly due to the failure to consider lead time in population‐based service screening programs, particularly when the follow‐up time in these programs is not sufficiently long . As lead time is unobservable, it is imperative to consider the use of a statistical model to separate overdetected cases from early detected cases gained with lead time.…”

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

“…Thus, additional pressure data do not carry information about the non-influential parameters. If the model has structural unidentifiabilities, subsequent predictions are unreliable, and can lead to spurious diagnoses or sub-optimal treatments [ 50 , 51 ]. For this reason, it is imperative that in our exponential radius-dependent models, the entire expression χ ( f 1 , f 2 , f 3 ) in equation ( 3.5 ) is interpreted, and not the individual parameters, f 1 , f 2 , f 3 .…”

Breast cancer screening and overdiagnosis

“…Overdiagnosis is estimated by counting simulated invasive screen‐detected cancers that would not have become symptomatic before death. Recent extended models also accommodate for nonprogressive lesions and enable precise quantification of the fraction of indolent cancers in settings such as stop‐screen trials 18 . Results of recent modelling of overdiagnosis are illustrated thereafter from Sweden 19,20 and from Australia (http://www.policy1.org/models/breast).…”