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

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.

Evaluating cancer screening programs using survival analysis

The main purpose of cancer screening programs is to provide early treatment to patients that are diagnosed with cancer on a screening test, thus increasing their chances of survival. To test this hypothesis directly, one should compare the survival of screen-detected cases to the survival of their counterparts not included to the program. In this study, we develop a general notation and use it to formally define the comparison of interest. We explain why the naive comparison between screen-detected and interval cases is biased and show that the total bias that arises in this case can be decomposed as a sum of lead time bias, length time bias, and bias due to overdetection. With respect to the estimation, we show what can be estimated using existing methods. To fill in the missing gap, we develop a new nonparametric estimator that allows us to estimate the survival of the control group, that is, the survival of cancer cases that would be screen-detected among those not included to the program. By joining the proposed estimator with existing methods, we show that the contrast of interest can be estimated without neglecting any of the biases. Our approach is illustrated using simulations and empirical data.

Novel predictions of invasive breast cancer risk in mammography screening cohorts

Mammography screening programs are aimed at reducing mortality due to breast cancer by detecting tumors at an early stage. There is currently interest in moving away from the age-based screening programs, and toward personalized screening based on individual risk factors. To accomplish this, risk prediction models for breast cancer are needed to determine who should be screened, and when. We develop a novel approach using a (random effects) continuous growth model, which we apply to a large population-based, Swedish screening cohort. Unlike existing breast cancer prediction models, this approach explicitly incorporates each woman's individual screening visits in the prediction. It jointly models invasive breast cancer tumor onset, tumor growth rate, symptomatic detection rate, and screening sensitivity. In addition to predicting the overall risk of invasive breast cancer, this model can make separate predictions regarding specific tumor sizes, and the mode of detection (eg, detected at screening, or through symptoms between screenings). It can also predict how these risks change depending on whether or not a woman will attend her next screening. In our study, we predict, given a future diagnosis, that the probability of having a tumor less than (as opposed to greater than) 10-mm diameter, at detection, will be, on average, 2.6 times higher if a woman in the cohort attends their next screening. This indicates that the model can be used to evaluate the short-term benefit of screening attendance, at an individual level.

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.

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.