Estimating screening test sensitivity and tumour progression using tumour size and time since previous screening

Random effects models of tumour growth for investigating interval breast cancer

In Nordic countries and across Europe, breast cancer screening participation is high. However, a significant number of breast cancer cases are still diagnosed due to symptoms between screening rounds, termed "interval cancers". Radiologists use the interval cancer proportion as a proxy for the screening false negative rate (ie, 1-sensitivity). Our objective is to enhance our understanding of interval cancers by applying continuous tumour growth models to data from a study involving incident invasive breast cancer cases. Building upon previous findings regarding stationary distributions of tumour size and growth rate distributions in non-screened populations, we develop an analytical expression for the proportion of interval breast cancer cases among regularly screened women. Our approach avoids relying on estimated background cancer rates. We make specific parametric assumptions concerning tumour growth and detection processes (screening or symptoms), but our framework easily accommodates alternative assumptions. We also show how our developed analytical expression for the proportion of interval breast cancers within a screened population can be incorporated into an approach for fitting tumour growth models to incident case data. We fit a model on 3493 cases diagnosed in Sweden between 2001 and 2008. Our methodology allows us to estimate the distribution of tumour sizes at the most recent screening for interval cancers. Importantly, we find that our model-based expected incidence of interval breast cancers aligns closely with observed patterns in our study and in a large Nordic screening cohort. Finally, we evaluate the association between screening interval length and the interval cancer proportion. Our analytical expression represents a useful tool for gaining insights into the performance of population-based breast cancer screening programs.

Influence of mammographic density and compressed breast thickness on true mammographic sensitivity: a cohort study

Understanding the detectability of breast cancer using mammography is important when considering nation-wide screening programmes. Although the role of imaging settings on image quality has been studied extensively, their role in detectability of cancer at a population level is less well studied. We wish to quantify the association between mammographic screening sensitivity and various imaging parameters. Using a novel approach applied to a population-based breast cancer screening cohort, we specifically focus on sensitivity as defined in the classical diagnostic testing literature, as opposed to the screen-detected cancer rate, which is often used as a measure of sensitivity for monitoring and evaluating breast cancer screening. We use a natural history approach to model the presence and size of latent tumors at risk of detection at mammography screening, and the screening sensitivity is modeled as a logistic function of tumor size. With this approach we study the influence of compressed breast thickness, x-ray exposure, and compression pressure, in addition to (percent) breast density, on the screening test sensitivity. When adjusting for all screening parameters in addition to latent tumor size, we find that percent breast density and compressed breast thickness are statistically significant factors for the detectability of breast cancer. A change in breast density from 6.6 to 33.5% (the inter-quartile range) reduced the odds of detection by 61% (95% CI 48-71). Similarly, a change in compressed breast thickness from 46 to 66 mm reduced the odds by 42% (95% CI 21-57). The true sensitivity of mammography, defined as the probability that an examination leads to a positive result if a tumour is present in the breast, is associated with compressed breast thickness after accounting for mammographic density and tumour size. This can be used to guide studies of setups aimed at improving lesion detection. Compressed breast thickness-in addition to breast density-should be considered when assigning complementary screening modalities and personalized screening intervals.

Tumour Growth Models of Breast Cancer for Evaluating Early Detection-A Summary and a Simulation Study

With the advent of nationwide mammography screening programmes, a number of natural history models of breast cancers have been developed and used to assess the effects of screening. The first half of this article provides an overview of a class of these models and describes how they can be used to study latent processes of tumour progression from observational data. The second half of the article describes a simulation study which applies a continuous growth model to illustrate how effects of extending the maximum age of the current Swedish screening programme from 74 to 80 can be evaluated. Compared to no screening, the current and extended programmes reduced breast cancer mortality by 18.5% and 21.7%, respectively. The proportion of screen-detected invasive cancers which were overdiagnosed was estimated to be 1.9% in the current programme and 2.9% in the extended programme. With the help of these breast cancer natural history models, we can better understand the latent processes, and better study the effects of breast cancer screening.

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

The few existing statistical models of breast cancer recurrence and progression to distant metastasis are predominantly based on multi-state modelling. While useful for summarising the risk of recurrence, these provide limited insight into the underlying biological mechanisms and have limited use for understanding the implications of population-level interventions. We develop an alternative, novel, and parsimonious approach for modelling latent tumour growth and spread to local and distant metastasis, based on a natural history model with biologically inspired components. We include marginal sub-models for local and distant breast cancer metastasis, jointly modelled using a copula function. Different formulations (and correlation shapes) are allowed, thus we can incorporate and directly model the correlation between local and distant metastasis flexibly and efficiently. Submodels for the latent cancer growth, the detection process, and screening sensitivity, together with random effects to account for between-patients heterogeneity, are included. Although relying on several parametric assumptions, the joint copula model can be useful for understanding - potentially latent - disease dynamics, obtaining patient-specific, model-based predictions, and studying interventions at a population level, for example, using microsimulation. We illustrate this approach using data from a Swedish population-based case-control study of postmenopausal breast cancer, including examples of useful model-based predictions.

A unifying framework for continuous tumour growth modelling of breast cancer screening data

The aim of the current article is to present theory that can help unify continuous growth approaches for modelling breast cancer tumour growth based on human data. We present a framework that has three main features: a general likelihood function to account for patient specific screening regiments; stable disease assumptions describing tumour population dynamics; and mathematical models describing tumour growth, individual variation in tumour growth, a hazard for symptomatic detection, and screening test sensitivity. The framework is able to incorporate any random effects distributions for the tumour growth rate parameter, any hazard functions for symptomatic tumour detection, as well as any monotonously increasing function for the tumour growth model. Based on a sample of 1902 incident breast cancer cases with data on mammography screening, we show how the framework can be used to estimate tumour growth based on different growth functions.

Estimating Distributions of Breast Cancer Onset and Growth in a Swedish Mammography Screening Cohort

BACKGROUND

In recent years, biologically motivated continuous tumor growth models have been introduced for breast cancer screening data. These provide a novel framework from which mammography screening effectiveness can be studied.

METHODS

We use a newly developed natural history model, which is unique in that it includes a carcinogenesis model for tumor onset, to analyze data from a large Swedish mammography cohort consisting of 65,536 participants, followed for periods of up to 6.5 years. Using patient data on age at diagnosis, tumor size, and mode of detection, as well as screening histories, we estimate distributions of patient's age at onset, (inverse) tumor growth rates, symptomatic detection rates, and screening sensitivities. We also allow the growth rate distribution to depend on the age at onset.

RESULTS

We estimate that by the age of 75, 13.4% of women have experienced onset. On the basis of a model that accounts for the role of mammographic density in screening sensitivity, we estimated median tumor doubling times of 167 days for tumors with onset occurring at age 40, and 207 days for tumors with onset occurring at age 60.

CONCLUSIONS

With breast cancer natural history models and population screening data, we can estimate latent processes of tumor onset, tumor growth, and mammography screening sensitivity. We can also study the relationship between the age at onset and tumor growth rates.

IMPACT

Quantifying the underlying processes of breast cancer progression is important in the era of individualized screening.

Estimating latent, dynamic processes of breast cancer tumour growth and distant metastatic spread from mammography screening data

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.

Random effects models of lymph node metastases in breast cancer: quantifying the roles of covariates and screening using a continuous growth model

We recently described a joint model of breast cancer tumor size and number of affected lymph nodes, which conditions on screening history, mammographic density, and mode of detection, and can be used to infer growth rates, time to symptomatic detection, screening sensitivity, and rates of lymph node spread. The model of lymph node spread can be estimated in isolation from measurements of tumor volume and number of affected lymph nodes, giving inference identical to the joint model. Here, we extend our model to include covariate effects. We also derive theoretical results in order to study the role of screening on lymph node metastases at diagnosis. We analyze the association between hormone replacement therapy (HRT) and breast cancer lymph node spread, using data from a case-control study designed specifically to study the effects of HRT on breast cancer. Using our method, we estimate that women using HRT at time of diagnosis have a 36% lower rate of lymph node spread than nonusers (95% confidence interval [CI] =(8%,58%)). This can be contrasted with the effect of HRT on the tumor growth rate, estimated here to be 15% slower in HRT users (95% CI = (-34%,+7%)). For screen-detected cancers, we illustrate how lead time can relate to lymph node spread; and using symptomatic cancers, we illustrate the potential consequences of false negative screens in terms of lymph node spread.

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

Background

Instead of a single value for mammographic sensitivity, a sensitivity function based on tumor size more realistically reflects mammography’s detection capability. Because previous models may have overestimated size-specific sensitivity, we aimed to provide a novel approach to improve sensitivity estimation as a function of tumor size.

Methods

Using aggregated data on interval and screen-detected cancers, observed tumor sizes were back-calculated to the time of screening using an exponential tumor growth model and a follow-up time of 4 years. From the observed number of detected cancers and an estimation of the number of false-negative cancers, a model for the sensitivity as a function of tumor size was determined. A univariate sensitivity analysis was conducted by varying follow-up time and tumor volume doubling time (TVDT). A systematic review was conducted for external validation of the sensitivity model.

Results

Aggregated data of 22,915 screen-detected and 10,670 interval breast cancers from the Dutch screening program were used. The model showed that sensitivity increased from 0 to 85% for tumor sizes from 2 to 20 mm. When TVDT was set at the upper and lower limits of the confidence interval, sensitivity for a 20-mm tumor was 74% and 93%, respectively. The estimated sensitivity gave comparable estimates to those from two of three studies identified by our systematic review.

Conclusion

Derived from aggregated breast screening outcomes data, our model’s estimation of sensitivity as a function of tumor size may provide a better representation of data observed in screening programs than other models.

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Mammographic sensitivity is a key indicator of screening effectiveness.

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Previous model using logistic function might overestimate size-specific sensitivity.

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Our model showed that sensitivity increased from 0 to 85% for tumor sizes from 2 to 20 mm.

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Our model may provide a better representation of data observed in screening programs.

Is mammography screening beneficial: An individual-based stochastic model for breast cancer incidence and mortality

The benefits of mammography screening have been controversial, with conflicting findings from various studies. We hypothesize that unmeasured heterogeneity in tumor aggressiveness underlies these conflicting results. Based on published data from the Canadian National Breast Screening Study (CNBSS), we develop and parameterize an individual-based mechanistic model for breast cancer incidence and mortality that tracks five stages of breast cancer progression and incorporates the effects of age on breast cancer incidence and all-cause mortality. The model accurately reproduces the reported outcomes of the CNBSS. By varying parameters, we predict that the benefits of mammography depend on the effectiveness of cancer treatment and tumor aggressiveness. In particular, patients with the most rapidly growing or potentially largest tumors have the highest benefit and least harm from the screening, with only a relatively small effect of age. However, the model predicts that confining mammography to populations with a high risk of acquiring breast cancer increases the screening benefit only slightly compared with the full population.

Statistical models of tumour onset and growth for modern breast cancer screening cohorts

Historically, multi-state Markov models have been used to study breast cancer incidence and mammography screening effectiveness. In recent years, more biologically motivated continuous tumour growth models have emerged as alternatives. However, a number of challenges remain for these models to make use of the wealth of information available in large mammography cohort data. In particular, methodology is needed to address random left truncation and individual, asynchronous screening. We present a comprehensive continuous random effects model for the natural history of breast cancer. It models the unobservable processes of tumour onset, tumour growth, screening sensitivity, and symptomatic detection. We show how the unknown model parameter values can be jointly estimated using a prospective cohort with diagnostic data on age and tumour size at diagnosis, and individual screening histories. We also present a microsimulation study calibrated to population breast cancer incidence data, and to data on mode of detection and tumour size. We highlight the importance of adjusting for random left truncation, derive tumour doubling time distributions for screen-detected and interval cancers, and present results concerning the relationship between tumour presence time and age at diagnosis.

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.

Joint models of tumour size and lymph node spread for incident breast cancer cases in the presence of screening

Continuous growth models show great potential for analysing cancer screening data. We recently described such a model for studying breast cancer tumour growth based on modelling tumour size at diagnosis, as a function of screening history, detection mode, and relevant patient characteristics. In this article, we describe how the approach can be extended to jointly model tumour size and number of lymph node metastases at diagnosis. We propose a new class of lymph node spread models which are biologically motivated and describe how they can be extended to incorporate random effects to allow for heterogeneity in underlying rates of spread. Our final model provides a dramatically better fit to empirical data on 1860 incident breast cancer cases than models in current use. We validate our lymph node spread model on an independent data set consisting of 3961 women diagnosed with invasive breast cancer.

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

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.

Modelling breast cancer tumour growth for a stable disease population

Statistical models of breast cancer tumour progression have been used to further our knowledge of the natural history of breast cancer, to evaluate mammography screening in terms of mortality, to estimate overdiagnosis, and to estimate the impact of lead-time bias when comparing survival times between screen detected cancers and cancers found outside of screening programs. Multi-state Markov models have been widely used, but several research groups have proposed other modelling frameworks based on specifying an underlying biological continuous tumour growth process. These continuous models offer some advantages over multi-state models and have been used, for example, to quantify screening sensitivity in terms of mammographic density, and to quantify the effect of body size covariates on tumour growth and time to symptomatic detection. As of yet, however, the continuous tumour growth models are not sufficiently developed and require extensive computing to obtain parameter estimates. In this article, we provide a detailed description of the underlying assumptions of the continuous tumour growth model, derive new theoretical results for the model, and show how these results may help the development of this modelling framework. In illustrating the approach, we develop a model for mammography screening sensitivity, using a sample of 1901 post-menopausal women diagnosed with invasive breast cancer.

Translation of research results to simple estimates of the likely effect of a lung cancer screening programme in the United Kingdom

Background:

There is considerable interest in the possibility of provision of lung cancer screening services in many developed countries. There is, however, no consensus on the target population or optimal screening regimen.

Methods:

In this paper, we demonstrate the use of published results on lung cancer screening and natural history parameters to estimate the likely effects of annual and biennial screening programmes in different risk populations, in terms of deaths prevented and of human costs, including screening episodes, further investigation rates and overdiagnosis.

Results:

Annual screening with the UK Lung Screening Study eligibility criteria was estimated to result in 956 lung cancer deaths prevented and 457 overdiagnosed cancers from 330 000 screening episodes. Biennial screening would result in 802 lung cancer deaths prevented and 383 overdiagnosed cancers for 180 000 screening episodes.

Interpretation/conclusion:

The predictions suggest that the intervention effect could justify the human costs. The evidence base for low-dose CT screening for lung cancer pertains almost entirely to annual screening. The benefit of biennial screening is subject to additional uncertainty but the issue merits further empirical research.

A statistical model of breast cancer tumour growth with estimation of screening sensitivity as a function of mammographic density

Understanding screening sensitivity and tumour progression is important for designing and evaluating screening programmes for breast cancer. Several approaches for estimating tumour growth rates have been described, some of which simultaneously estimate (mammography) screening sensitivity. None of the continuous tumour growth modelling approaches has incorporated mammographic density, although it is known to have a profound influence on mammographic screening sensitivity. We describe a new approach for estimating breast cancer tumour growth which builds on recently described continuous tumour growth models and estimates mammographic screening sensitivity as a function of tumour size and mammographic density.

Modelling the overdiagnosis of breast cancer due to mammography screening in women aged 40 to 49 in the United Kingdom

INTRODUCTION

Overdiagnosis of breast cancer due to mammography screening, defined as the diagnosis of screen-detected cancers that would not have presented clinically in a women's lifetime in the absence of screening, has emerged as a highly contentious issue, as harm caused may question the benefit of mammographic screening. Most studies included women over 50 years old and little information is available for younger women.

METHODS

We estimated the overdiagnosis of breast cancer due to screening in women aged 40 to 49 years using data from a randomised trial of annual mammographic screening starting at age 40 conducted in the UK. A six-state Markov model was constructed to estimate the sensitivity of mammography for invasive and in situ breast cancer and the screen-detectable mean sojourn time for non-progressive in situ, progressive in situ, and invasive breast cancer. Then, a 10-state simulation model of cancer progression, screening, and death, was developed to estimate overdiagnosis attributable to screening.

RESULTS

The sensitivity of mammography for invasive and in situ breast cancers was 90% (95% CI, 72 to 99) and 82% (43 to 99), respectively. The screen-detectable mean sojourn time of preclinical non-progressive and progressive in situ cancers was 1.3 (0.4 to 3.4) and 0.11 (0.05 to 0.19) years, respectively, and 0.8 years (0.6 to 1.2) for preclinical invasive breast cancer. The proportion of screen-detected in situ cancers that were non-progressive was 55% (25 to 77) for the first and 40% (22 to 60) for subsequent screens. In our main analysis, overdiagnosis was estimated as 0.7% of screen-detected cancers. A sensitivity analysis, covering a wide range of alternative scenarios, yielded a range of 0.5% to 2.9%.

CONCLUSION

Although a high proportion of screen-detected in situ cancers were non-progressive, a majority of these would have presented clinically in the absence of screening. The extent of overdiagnosis due to screening in women aged 40 to 49 was small. Results also suggest annual screening is most suitable for women aged 40 to 49 in the United Kingdom due to short cancer sojourn times.