Breast cancer tumour growth modelling for studying the association of body size with tumour growth rate and symptomatic detection using case-control 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.

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 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.

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.

Radiological audit of interval breast cancers: Estimation of tumour growth rates

INTRODUCTION

This multicentre, retrospective study aimed to establish correlation between estimated tumour volume doubling times (TVDT) from a series of interval breast cancers with their clinicopathological features. The potential impact of delayed diagnosis on prognosis was also explored.

MATERIALS AND METHODS

Interval cancers, where screening mammograms demonstrated changes that were retrospectively classified as either uncertain or suspicious, were reviewed from five screening units within the UK NHS Breast Screening Programme (NHSBSP). Data collected included the time interval between screening mammogram and cancer diagnosis, the size of the initial mammographic abnormality and of the subsequent cancer, demographics, mammographic density and tumour biology. We estimated volume doubling times and the estimated change in size and node status, which would have followed if these cancers had been detected at the previous screen.

RESULTS

306 interval cancers meeting the inclusion criteria were identified. Average time from screening to diagnosis was 644 days (SD 276 days). 19% were diagnosed in the first twelve months, 42% in the subsequent twelve months and 39% thereafter. Overall average estimated TVDT was 167 days (95% CI 151-186). Significant differences were noted with age (p = 0.01), grade (p < 0.001) and ER status (p < 0.001) with women under 60, grade 3 cancers and ER negative cancers having shorter TVDTs. HER2 positive tumours had shorter doubling times than HER2 negative, but this difference was not statistically significant. It was estimated that diagnosing these cancers at the previous screen would have increased ten-year survival from 82% to 86%.

CONCLUSION

High grade, ER negativity and younger age were associated with shorter durations of TVDT. The role of HER2 status on interval cancer growth rate requires further assessment. It is likely that the delayed diagnosis of interval cancers confers a 4% reduction in ten-year survival.

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.

Long-term prognostic implications of risk factors associated with tumor size: a case study of women regularly attending screening

Background

Breast cancer prognosis is strongly associated with tumor size at diagnosis. We aimed to identify factors associated with diagnosis of large (> 2 cm) compared to small tumors, and to examine implications for long-term prognosis.

Methods

We examined 2012 women with invasive breast cancer, of whom 1466 had screen-detected and 546 interval cancers that were incident between 2001 and 2008 in a population-based screening cohort, and followed them to 31 December 2015. Body mass index (BMI) was ascertained after diagnosis at the time of study enrollment during 2009. PD was measured based on the contralateral mammogram within 3 years before diagnosis. We used multiple logistic regression modeling to examine the association between tumor size and body mass index (BMI), mammographic percent density (PD), or hormonal and genetic risk factors. Associations between the identified risk factors and, in turn, the outcomes of local recurrence, distant metastases, and death (153 events in total) in women with breast cancer were examined using Cox regression. Analyses were carried out according to mode of detection.

Results

BMI and PD were the only factors associated with tumor size at diagnosis. For BMI (≥25 vs. < 25 kg/m²), the multiple adjusted odds ratios (OR) were 1.37 (95% CI 1.02–1.83) and 2.12 (95% CI 1.41–3.18), for screen-detected and interval cancers, respectively. For PD (≥20 vs. < 20%), the corresponding ORs were 1.72 (95% CI 1.29–2.30) and 0.60 (95% CI 0.40–0.90). Among women with interval cancers, those with high BMI had worse prognosis than women with low BMI (hazard ratio 1.70; 95% CI 1.04–2.77), but PD was not associated with the hazard rate. Among screen-detected cancers, neither BMI nor PD was associated with the hazard rate.

Conclusions

In conclusion, high BMI was associated with the risk of having a tumor larger than 2 cm at diagnosis. Among women with interval cancer, high BMI was associated with worse prognosis. We believe that women with high BMI should be especially encouraged to attend screening.

Electronic supplementary material

The online version of this article (10.1186/s13058-018-0962-6) contains supplementary material, which is available to authorized users.

E-Science technologies in a workflow for personalized medicine using cancer screening as a case study

Objective

We provide an e-Science perspective on the workflow from risk factor discovery and classification of disease to evaluation of personalized intervention programs. As case studies, we use personalized prostate and breast cancer screenings.

Materials and Methods

We describe an e-Science initiative in Sweden, e-Science for Cancer Prevention and Control (eCPC), which supports biomarker discovery and offers decision support for personalized intervention strategies. The generic eCPC contribution is a workflow with 4 nodes applied iteratively, and the concept of e-Science signifies systematic use of tools from the mathematical, statistical, data, and computer sciences.

Results

The eCPC workflow is illustrated through 2 case studies. For prostate cancer, an in-house personalized screening tool, the Stockholm-3 model (S3M), is presented as an alternative to prostate-specific antigen testing alone. S3M is evaluated in a trial setting and plans for rollout in the population are discussed. For breast cancer, new biomarkers based on breast density and molecular profiles are developed and the US multicenter Women Informed to Screen Depending on Measures (WISDOM) trial is referred to for evaluation. While current eCPC data management uses a traditional data warehouse model, we discuss eCPC-developed features of a coherent data integration platform.

Discussion and Conclusion

E-Science tools are a key part of an evidence-based process for personalized medicine. This paper provides a structured workflow from data and models to evaluation of new personalized intervention strategies. The importance of multidisciplinary collaboration is emphasized. Importantly, the generic concepts of the suggested eCPC workflow are transferrable to other disease domains, although each disease will require tailored solutions.

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.