A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening

Use of the AHP methodology in system dynamics: Modelling and simulation for health technology assessments to determine the correct prosthesis choice for hernia diseases

Health technology assessments (HTAs) are often difficult to conduct because of the decisive procedures of the HTA algorithm, which are often complex and not easy to apply. Thus, their use is not always convenient or possible for the assessment of technical requests requiring a multidisciplinary approach. This paper aims to address this issue through a multi-criteria analysis focusing on the analytic hierarchy process (AHP). This methodology allows the decision maker to analyse and evaluate different alternatives and monitor their impact on different actors during the decision-making process. However, the multi-criteria analysis is implemented through a simulation model to overcome the limitations of the AHP methodology. Simulations help decision-makers to make an appropriate decision and avoid unnecessary and costly attempts. Finally, a decision problem regarding the evaluation of two health technologies, namely, the evaluation of two biological prostheses for incisional infected hernias, will be analysed to assess the effectiveness of the model.

Diversity of model approaches for breast cancer screening: a review of model assumptions by The Cancer Intervention and Surveillance Network (CISNET) Breast Cancer Groups

The National Cancer Institute-sponsored Cancer Intervention and Surveillance Network program on breast cancer is composed of seven research groups working largely independently to model the impact of screening and adjuvant therapy on breast cancer mortality trends in the US from 1975 to 2000. Each of the groups has chosen a different modeling methodology without purposeful attempt to be in contrast with each other. The seven groups have met biannually since November 2000 to discuss their methodology and results. This article investigates the differences in methodology. To facilitate this comparison, each of the groups submitted a description of their model into a uniformly structured web based ‘model profiler’. Six of the seven models simulate a preclinical natural history that cannot be observed directly with parameters estimated from published evidence concerning screening and therapy effects. The remaining model regards published evidence on intervention effects as prior information and updates that with information from the US population in a Bayesian type analysis. In general, the differences between the models appear to be small, particularly among the models driven by natural history assumptions. However, we demonstrate that such apparently small differences can have a large impact on surveillance of population trends. We describe a systematic approach to evaluating differences in model assumptions and results, as well as differences in modeling culture underlying the differences in model structure and parameters.

Simulation models in population breast cancer screening: A systematic review

The aim of this review was to critically evaluate published simulation models for breast cancer screening of the general population and provide a direction for future modeling. A systematic literature search was performed to identify simulation models with more than one application. A framework for qualitative assessment which incorporated model type; input parameters; modeling approach, transparency of input data sources/assumptions, sensitivity analyses and risk of bias; validation, and outcomes was developed. Predicted mortality reduction (MR) and cost-effectiveness (CE) were compared to estimates from meta-analyses of randomized control trials (RCTs) and acceptability thresholds. Seven original simulation models were distinguished, all sharing common input parameters. The modeling approach was based on tumor progression (except one model) with internal and cross validation of the resulting models, but without any external validation. Differences in lead times for invasive or non-invasive tumors, and the option for cancers not to progress were not explicitly modeled. The models tended to overestimate the MR (11-24%) due to screening as compared to optimal RCTs 10% (95% CI - 2-21%) MR. Only recently, potential harms due to regular breast cancer screening were reported. Most scenarios resulted in acceptable cost-effectiveness estimates given current thresholds. The selected models have been repeatedly applied in various settings to inform decision making and the critical analysis revealed high risk of bias in their outcomes. Given the importance of the models, there is a need for externally validated models which use systematical evidence for input data to allow for more critical evaluation of breast cancer screening.

Tumor size as a recommendable variable for accuracy of the prognostic prediction of gastric cancer: a retrospective analysis of 1,521 patients

BACKGROUND

It is still controversial whether tumor size (Ts) should be considered an important indicator for evaluation the prognosis of gastric cancer (GC). The purpose of this study was to elucidate the prognostic prediction superiority of Ts in the large-scale cohort of GC patients.

METHODS

Data from 1,521 patients who underwent the curative resection were analyzed for demonstration the prognostic value of Ts. In addition, a tumor size-node-metastasis (TsNM) classification system was proposed to evaluate the comparative superiorities of the prognostic prediction of GC patients.

RESULTS

With the univariate and multivariate analyses, Ts was identified as an independently prognostic predictor of GC patients, as was T stage. Ts was demonstrated to have smaller Akaike information criterion and Bayesian Information Criterion values within the Cox regression analyses than shown by T stage, which represented the optimum prognostic stratification. TsNM classification was also found to be competent for accurately prognostic evaluation of GC patients. The matched case-control logistic regression showed that TsNM classification could provide very powerful discriminations of patients' overall survival, compared with TNM classification. Additionally, Ts stage was found to enhance the survival discriminations in patients with certain clinicopathological characteristics, including male gender, T4a stage, N0 stage, diffuse type of Lauren classification, or age ≤60 years.

CONCLUSIONS

Ts should be recommended as an important clinicopathologic variable to enhance the accuracy of the prognostic prediction of GC clinical patients.

Effects of menopausal hormonal therapy on occult breast tumors

An estimated 7% of 40-80 year old women dying of unrelated causes harbor occult breast tumors at autopsy. These lesions are too small to be detected by mammography, a method which requires tumors to be approximately 1cm in diameter to be diagnosed. Tumor growth rates, as assessed by "effective doubling times" on serial mammography range from 10 to >700 days with a median of approximately 200 days. We previously reported two models, based on iterative analysis of these parameters, to describe the biologic behavior of undiagnosed, occult breast tumors. One of our models is biologically based and includes parameters of a 200 day effective doubling time, 7% prevalence of occult tumors in the 40-80 aged female population and a detection threshold of 1.16 cm and the other involves computer based projections based on age related breast cancer incidence. Our models facilitate interpretation of the Women's Health Initiative (WHI) and anti-estrogen prevention studies. The biologically based model suggests that menopausal hormone therapy with conjugated equine estrogens plus medroxyprogesterone acetate (MPA) in the WHI trial primarily promoted the growth of pre-existing, occult lesions and minimally initiated de novo tumors. The paradoxical reduction of breast cancer incidence in women receiving estrogen alone is consistent with a model that this hormone causes apoptosis in women deprived of estrogen long term as a result of the cessation of estrogen production after the menopause. Understanding of the kinetics of occult tumors suggests that breast cancer "prevention" with anti-estrogens or aromatase inhibitors represents early treatment rather than a reduction in de novo tumor formation. Our in vivo data suggest that the combination of a SERM, bazedoxifene (BZA), with conjugated equine estrogen (CEE) acts to block maturation of the mammary gland in oophorectomized, immature mice. This hormonal combination is defined by the generic term, tissue selective estrogen complex or TSEC. Xenograft studies with the BZA/CEE combination show that it blocks the growth of occult, hormone dependent tumors in nude mice. These pre-clinical data suggest that the BZA/CEE TSEC combination may prevent the growth of occult breast tumors in women. Based on the beneficial effects of this TSEC combination on symptoms and fracture prevention in menopausal women, the combination of BZA/CEE might be used as a means both to treat menopausal symptoms and to prevent breast cancer. This article is part of a Special Issue entitled 'CSR 2013'.

Risk of developing breast cancer by utilizing Gail model

The Gail model has been widely used to quantify an individual woman's risk of developing breast cancer by using important clinical parameters, usually for clinical counselling purposes or to determine eligibility for mammography and genetic tests. The aim of the present study was to estimate the five-year and lifetime breast cancer risk among women in Rasht, Iran. In this cross-sectional study, 314 women were evaluated at Alzahra Women Hospital in 2007. Participants were ≥35 years of age without a history of breast cancer. Risk estimation was performed using the computerized Gail model. A five-year risk >1.66% was considered high-risk; 5.1% of women were high-risk. The mean five-year breast cancer risk was 0.8% (SD±1). Mean breast cancer risk up to the age of 90 years (lifetime risk) was 9.0% (SD±3.9%); 16.2% of the participants had a five-year risk higher than the average woman of the same age, and 18.2% had the same risk. Also for the lifetime risk, 11.1% of the women had higher risk and 1.6% had the same risk as the average woman. Routine use of the Gail model is recommended for identifying women at high average risk for increasing the survival of women from breast cancer.

Calibration methods used in cancer simulation models and suggested reporting guidelines

Increasingly, computer simulation models are used for economic and policy evaluation in cancer prevention and control. A model's predictions of key outcomes, such as screening effectiveness, depend on the values of unobservable natural history parameters. Calibration is the process of determining the values of unobservable parameters by constraining model output to replicate observed data. Because there are many approaches for model calibration and little consensus on best practices, we surveyed the literature to catalogue the use and reporting of these methods in cancer simulation models. We conducted a MEDLINE search (1980 through 2006) for articles on cancer-screening models and supplemented search results with articles from our personal reference databases. For each article, two authors independently abstracted pre-determined items using a standard form. Data items included cancer site, model type, methods used for determination of unobservable parameter values and description of any calibration protocol. All authors reached consensus on items of disagreement. Reviews and non-cancer models were excluded. Articles describing analytical models, which estimate parameters with statistical approaches (e.g. maximum likelihood) were catalogued separately. Models that included unobservable parameters were analysed and classified by whether calibration methods were reported and if so, the methods used. The review process yielded 154 articles that met our inclusion criteria and, of these, we concluded that 131 may have used calibration methods to determine model parameters. Although the term 'calibration' was not always used, descriptions of calibration or 'model fitting' were found in 50% (n = 66) of the articles, with an additional 16% (n = 21) providing a reference to methods. Calibration target data were identified in nearly all of these articles. Other methodological details, such as the goodness-of-fit metric, were discussed in 54% (n = 47 of 87) of the articles reporting calibration methods, while few details were provided on the algorithms used to search the parameter space. Our review shows that the use of cancer simulation modelling is increasing, although thorough descriptions of calibration procedures are rare in the published literature for these models. Calibration is a key component of model development and is central to the validity and credibility of subsequent analyses and inferences drawn from model predictions. To aid peer-review and facilitate discussion of modelling methods, we propose a standardized Calibration Reporting Checklist for model documentation.

Breast cancer tumor growth estimated through mammography screening data

Introduction

Knowledge of tumor growth is important in the planning and evaluation of screening programs, clinical trials, and epidemiological studies. Studies of tumor growth rates in humans are usually based on small and selected samples. In the present study based on the Norwegian Breast Cancer Screening Program, tumor growth was estimated from a large population using a new estimating procedure/model.

Methods

A likelihood-based estimating procedure was used, where both tumor growth and the screen test sensitivity were modeled as continuously increasing functions of tumor size. The method was applied to cancer incidence and tumor measurement data from 395,188 women aged 50 to 69 years.

Results

Tumor growth varied considerably between subjects, with 5% of tumors taking less than 1.2 months to grow from 10 mm to 20 mm in diameter, and another 5% taking more than 6.3 years. The mean time a tumor needed to grow from 10 mm to 20 mm in diameter was estimated as 1.7 years, increasing with age. The screen test sensitivity was estimated to increase sharply with tumor size, rising from 26% at 5 mm to 91% at 10 mm. Compared with previously used Markov models for tumor progression, the applied model gave considerably higher model fit (85% increased predictive power) and provided estimates directly linked to tumor size.

Conclusion

Screening data with tumor measurements can provide population-based estimates of tumor growth and screen test sensitivity directly linked to tumor size. There is a large variation in breast cancer tumor growth, with faster growth among younger women.

Estimating the growth rates of primary lung tumours from samples with missing measurements

A method to estimate the population variability in tumour growth rate using incomplete data was developed. We assume exponential growth and lognormal distribution for the parameter of the growth curve. Estimates of growth rate obtained based on the cases with two measurements, one of which is obtained retrospectively, are biased towards lower growth rate. For the data sets where two measurements are available for some tumours and only one measurement for others (which means that no tumour was seen in retrospect for those cases), several approaches were developed that can eliminate or substantially reduce the bias. The relative error of the best estimates, as assessed by simulation, rarely exceeds 20 per cent. We found that the results of application of our estimation procedures to chest X-ray screening data agree well with the expectations.

Simulation modeling of change to breast cancer detection age eligibility recommendations in Ontario, 2002-2021

PURPOSE

The purpose of this project was to demonstrate the development and use of a decision support tool based on simulation modeling of breast cancer screening to evaluate the implications for the provision of health services and the economic impact of extending routine radiographic screening for breast cancer to women in the 40-49 age group between 2002 and 2021.

METHODS

The main method was computer simulation with a Markov model that used published estimates of population size by age group, breast cancer prevalence and incidence, screening program participation rate, sensitivity and specificity of the screening test and diagnostic test, stage transition probabilities, directed diagnosis rates and costs.

FINDINGS

The model predicted that changes to age eligibility requirements would result in the detection of an additional 6610 women with breast cancer in Ontario requiring treatment, at an additional cost of 795 Canadian per case. These costs include those related to screening, diagnosis and initial treatment and apply to the 20-year period.

CONCLUSIONS

The model provided a useful decision support tool for those planning and implementing breast cancer screening programs.

Recent translational research: computational studies of breast cancer

The combination of mathematics – queen of sciences – and the general utility of computers has been used to make important inroads into insight-providing breast cancer research and clinical aids. These developments are in two broad areas. First, they provide useful prognostic guidelines for individual patients based on historic evidence. Second, by suggesting numeric tumor growth laws that are correlated to clinical parameters, they permit development of biologically relevant theories and comparison with patient data to help us understand complex biologic processes. These latter studies have produced many new ideas that are testable in clinical trials. In this review we discuss these developments from a clinical perspective, and ask whether and how they translate into useful tools for patient treatment.