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.

The cost-effectiveness of risk-stratified breast cancer screening in the UK

BACKGROUND

There has been growing interest in the UK and internationally of risk-stratified breast screening whereby individualised risk assessment may inform screening frequency, starting age, screening instrument used, or even decisions not to screen. This study evaluates the cost-effectiveness of eight proposals for risk-stratified screening regimens compared to both the current UK screening programme and no national screening.

METHODS

A person-level microsimulation model was developed to estimate health-related quality of life, cancer survival and NHS costs over the lifetime of the female population eligible for screening in the UK.

RESULTS

Compared with both the current screening programme and no screening, risk-stratified regimens generated additional costs and QALYs, and had a larger net health benefit. The likelihood of the current screening programme being the optimal scenario was less than 1%. No screening amongst the lowest risk group, and triannual, biennial and annual screening amongst the three higher risk groups was the optimal screening strategy from those evaluated.

CONCLUSIONS

We found that risk-stratified breast cancer screening has the potential to be beneficial for women at the population level, but the net health benefit will depend on the particular risk-based strategy.

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.

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.

Long-term effects of the interruption of the Dutch breast cancer screening program due to COVID-19: A modelling study

Due to COVID-19, the Dutch breast cancer screening program was interrupted for three months with uncertain long-term effects. The aim of this study was to estimate the long-term impact of this interruption on delay in detection, tumour size of screen-detected breast cancers, and interval cancer rate. After validation, the micro-simulation model SiMRiSc was used to calculate the effects of interruption of the breast cancer screening program for three months and for hypothetical interruptions of six and twelve months. A scenario without interruption was used as reference. Outcomes considered were tumour size of screen-detected breast cancers and interval cancer rate. Women of 55-59 and 60-64 years old at time of interruption were considered. Uncertainties were estimated using a sensitivity analysis. The three-month interruption had no clinically relevant long-term effect on the tumour size of screen-detected breast cancers. A 19% increase in interval cancer rate was found between last screening before and first screening after interruption compared to no interruption. Hypothetical interruptions of six and twelve months resulted in larger increases in interval cancer rate of 38% and 78% between last screening before and first screening after interruption, respectively, and an increase in middle-sized tumours in first screening after interruption of 26% and 47%, respectively. In conclusion, the interruption of the Dutch screening program is not expected to result in a long-term delay in detection or clinically relevant change in tumour size of screen-detected cancers, but only affects the interval cancer rate between last screening before and first screening after interruption.

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.

Assessment of the Benefits and Cost-Effectiveness of Population-Based Breast Cancer Screening in Urban China: A Model-Based Analysis

BACKGROUND

To decrease the burden of breast cancer (BC), the Chinese government recently introduced biennial mammography screening for women aged 45-70 years. In this study, we assess the effectiveness and cost-effectiveness of implementing this programme in urban China using a micro-simulation model.

METHODS

The 'Simulation Model on radiation Risk and breast cancer Screening' (SiMRiSc) was applied, with parameters updated based on available data for the Chinese population. The base scenario was biennial mammography screening for women aged 45-70 years, and this was compared to a reference population with no screening. Seven alternative scenarios were then simulated by varying the screening intervals and participant ages. This analysis was conducted from a societal perspective. The discounted incremental cost-effectiveness ratio (ICER) was compared to a threshold of triple the gross domestic product (GDP) per life years gained (LYG), which was 30 785 USD/LYG. Univariate sensitivity analyses were conducted to evaluate model robustness. In addition, a budget impact analysis was performed by comparing biennial screening with no screening at a time horizon of 10 years.

RESULTS

Compared with no screening, the base scenario was cost-effective in urban China, giving a discounted average cost-effectiveness ratio (ACER) of 17 309 USD/LYG. The model was most sensitive to the cost of mammography per screen, followed by mean size of self-detected tumours, mammographic breast density and the cumulative lifetime risk of BC. The efficient frontier showed that at a threshold of 30 785 USD/LYG, the base scenario was the optimal scenario with a discounted ICER of 25 261 USD/LYG. Over 10 years, screening would incur a net cost of almost 38.1 million USD for a city with 1 million citizens.

CONCLUSION

Compared to no screening, biennial mammography screening for women aged from 45-70 is cost-effective in urban China.

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.

Overdiagnosis of invasive breast cancer in population-based breast cancer screening: A short- and long-term perspective

BACKGROUND

Overdiagnosis of invasive breast cancer (BC) is a contentious issue.

OBJECTIVE

The aim of this paper is to estimate the overdiagnosis rate of invasive BC in an organised BC screening program and to evaluate the impact of age and follow-up time.

METHODS

The micro-simulation model SiMRiSc was calibrated and validated for BC screening in Flanders, where women are screened biennially from age 50 to 69. Overdiagnosis rate was defined as the number of invasive BC that would not have been diagnosed in the absence of screening per 100,000 screened women during the screening period plus follow-up time (which was set at 5 years and varied from 2 to 15 years). Overdiagnosis rate was calculated overall and stratified by age.

RESULTS

The overall overdiagnosis rate for women screened biennially from 50 to 69 was 20.1 (95%CI: 16.9-23.2) per 100,000 women screened at 5-year follow-up from stopping screening. Overdiagnosis at 5-year follow-up time was 12.9 (95%CI: 4.6-21.1) and 74.2 (95%CI: 50.9-97.5) per 100,000 women screened for women who started screening at age 50 and 68, respectively. At 2- and 15-year follow-up time, overdiagnosis rate was 98.5 (95%CI: 75.8-121.3) and 13.4 (95%CI: 4.9-21.9), respectively, for women starting at age 50, and 297.0 (95%CI: 264.5-329.4) and 34.2 (95%CI: 17.5-50.8), respectively, for those starting at age 68.

CONCLUSIONS

Sufficient follow-up time (≥10 years) after screening stops is key to obtaining unbiased estimates of overdiagnosis. Overdiagnosis of invasive BC is a larger problem in older compared to younger women.

Development and evaluation of a method for tumor growth simulation in virtual clinical trials of breast cancer screening

Purpose: Image-based analysis of breast tumor growth rate may optimize breast cancer screening and diagnosis by suggesting optimal screening intervals and guide the clinical discussion regarding personalized screening based on tumor aggressiveness. Simulation-based virtual clinical trials (VCTs) can be used to evaluate and optimize medical imaging systems and design clinical trials. This study aimed to simulate tumor growth over multiple screening rounds. Approach: This study evaluates a preliminary method for simulating tumor growth. Clinical data on tumor volume doubling time (TVDT) was used to fit a probability distribution ("clinical fit") of TVDTs. Simulated tumors with TVDTs sampled from the clinical fit were inserted into 30 virtual breasts ("simulated cohort") and used to simulate mammograms. Based on the TVDT, two successive screening rounds were simulated for each virtual breast. TVDTs from clinical and simulated mammograms were compared. Tumor sizes in the simulated mammograms were measured by a radiologist in three repeated sessions to estimate TVDT. Results: The mean TVDT was 297 days (standard deviation, SD, 169 days) in the clinical fit and 322 days (SD, 217 days) in the simulated cohort. The mean estimated TVDT was 340 days (SD, 287 days). No significant difference was found between the estimated TVDTs from simulated mammograms and clinical TVDT values ( p > 0.5 ). No significant difference ( p > 0.05 ) was observed in the reproducibility of the tumor size measurements between the two screening rounds. Conclusions: The proposed method for tumor growth simulation has demonstrated close agreement with clinical results, supporting potential use in VCTs of temporal breast imaging.

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.

Cost-effectiveness of abbreviated-protocol MRI screening for women with mammographically dense breasts in a national breast cancer screening program

Introduction

Magnetic resonance imaging (MRI) has shown the potential to improve the screening effectiveness among women with dense breasts. The introduction of fast abbreviated protocols (AP) makes MRI more feasible to be used in a general population. We aimed to investigate the cost-effectiveness of AP-MRI in women with dense breasts (heterogeneously/extremely dense) in a population-based screening program.

Methods

A previously validated model (SiMRiSc) was applied, with parameters updated for women with dense breasts. Breast density was assumed to decrease with increased age. The base scenarios included six biennial AP-MRI strategies, with biennial mammography from age 50–74 as reference. Fourteen alternative scenarios were performed by varying screening interval (triennial and quadrennial) and by applying a combined strategy of mammography and AP-MRI. A 3% discount rate for both costs and life years gained (LYG) was applied. Model robustness was evaluated using univariate and probabilistic sensitivity analyses.

Results

The six biennial AP-MRI strategies ranged from 132 to 562 LYG per 10,000 women, where more frequent application of AP-MRI was related to higher LYG. The optimal strategy was biennial AP-MRI screening from age 50–65 for only women with extremely dense breasts, producing an incremental cost-effectiveness ratio of € 18,201/LYG. At a threshold of € 20,000/LYG, the probability that the optimal strategy was cost-effective was 79%.

Conclusion

Population-based biennial breast cancer screening with AP-MRI from age 50–65 for women with extremely dense breasts might be a cost-effective alternative to mammography, but is not an option for women with heterogeneously dense breasts.

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AP-MRI can be cost-effective for screening women with extremely dense breast.

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The more frequent the use of AP-MRI, the more life years will be gained.

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Biennial AP-MRI for women with extremely dense breast up to age 65 is optimal.

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.

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.

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.