Evaluation by Markov chain models of a non-randomised breast cancer screening programme in women aged under 50 years in Sweden

Likelihood function for estimating parameters in multistate disease process with Laplace-transformation-based transition probabilities

Multistate statistical models are often used to characterize the complex multi-compartment progression of the disease such as cancer. However, the derivation of multistate transition kernels is often involved with the intractable convolution that requires intensive computation. Moreover, the estimation of parameters pertaining to transition kernel requires the individualized time-stamped history data while the traditional likelihood function forms are constructed. In this paper, we came up with a novel likelihood function derived from Laplace transformation-based transition probabilities in conjunction with Expectation-Maximization algorithm to estimate parameters. The proposed method was applied to two large population-based screening data with only aggregated count data without relying on individual time-stamped history data.

Precision Science on Incidence and Progression of Early-Detected Small Breast Invasive Cancers by Mammographic Features

The aim was to evaluate how the inter-screening interval affected the performance of screening by mammographic appearances. This was a Swedish retrospective screening cohort study with information on screening history and mammography features in two periods (1977-1985 and 1996-2010). The pre-clinical incidence and the mean sojourn time (MST) for small breast cancer allowing for sensitivity by mammographic appearances were estimated. The percentage of interval cancer against background incidence (I/E ratio) was used to assess the performance of mammography screening by different inter-screening intervals. The sensitivity-adjusted MSTs (in years) were heterogeneous with mammographic features, being longer for powdery and crushed stone-like calcifications (4.26, (95% CI, 3.50-5.26)) and stellate masses (3.76, (95% CI, 3.15-4.53)) but shorter for circular masses (2.65, (95% CI, 2.06-3.55)) in 1996-2010. The similar trends, albeit longer MSTs, were also noted in 1977-1985. The I/E ratios for the stellate type were 23% and 32% for biennial and triennial screening, respectively. The corresponding figures were 32% and 43% for the circular type and 21% and 29% for powdery and crushed stone-like calcifications, respectively. Mammography-featured progressions of small invasive breast cancer provides a new insight into personalized quality assurance, surveillance, treatment and therapy of early-detected breast cancer.

The challenge of evaluating annual mammography screening for young women with a family history of breast cancer

It has been recommended that women aged 40–49 years with a significant family history of breast cancer should be offered annual mammography screening ( http://www.nice.org.uk ). An observational study known as FH01 ( http://www.screeningservices.org/btw/fh01/index.asp ) is evaluating this policy in a cohort of 6000 women at moderately increased risk of breast cancer due to family history. The main aims are to assess the likely impact on breast cancer mortality and cost-effectiveness. Measuring these outcomes is challenging in an environment where a randomized trial is not feasible and there is no natural comparison group. In this paper, we present some approaches to estimating effectiveness and the planned analyses. These involve comparison of disease stage and likely consequent breast cancer mortality in the cohort offered screening with that estimated in the absence of screening. The estimation uses observed outcomes in external populations and estimated outcomes for the hypothetical situation where screening had not taken place.

Using Simulation to Model and Validate Invasive Breast Cancer Progression in Women in the Study and Control Groups of the Canadian National Breast Screening Studies I and II

BACKGROUND

Modeling breast cancer progression and the effect of various risk is helpful in deciding when a woman should start and end screening, and how often the screening should be undertaken.

METHODS

We modeled the natural progression of breast cancer using a hidden Markov process, and incorporated the effects of covariates. Patients are women aged 50-59 (older) and 40-49 (younger) years from the Canadian National Breast Screening Studies. We included prevalent cancers, estimated the screening sensitivities and rates of over-diagnosis, and validated the models using simulation.

RESULTS

We found that older women have a higher rate of transition from a healthy to preclinical state and other causes of death but a lower rate of transition from preclinical to clinical state. Reciprocally, younger women have a lower rate of transition from a healthy to preclinical state and other causes of death but a higher rate of transition from a preclinical to clinical state. Different risk factors were significant for the age groups. The mean sojourn times for older and younger women were 2.53 and 2.96 years, respectively. In the study group, the sensitivities of the initial physical examination and mammography for older and younger women were 0.87 and 0.81, respectively, and the sensitivity of the subsequent screens were 0.78 and 0.53, respectively. In the control groups, the sensitivities of the initial physical examination for older and younger women were 0.769 and 0.671, respectively, and the sensitivity of the subsequent physical examinations for the control group aged 50-59 years was 0.37. The upper-bounds for over-diagnosis in older and younger women were 25% and 27%, respectively.

CONCLUSIONS

The present work offers a basis for the better modeling of cancer incidence for a population with the inclusion of prevalent cancers.

Quantifying the natural history of breast cancer

Background:

Natural history models of breast cancer progression provide an opportunity to evaluate and identify optimal screening scenarios. This paper describes a detailed Markov model characterising breast cancer tumour progression.

Methods:

Breast cancer is modelled by a 13-state continuous-time Markov model. The model differentiates between indolent and aggressive ductal carcinomas in situ tumours, and aggressive tumours of different sizes. We compared such aggressive cancers, that is, which are non-indolent, to those which are non-growing and regressing. Model input parameters and structure were informed by the 1978–1984 Ostergotland county breast screening randomised controlled trial. Overlaid on the natural history model is the effect of screening on diagnosis. Parameters were estimated using Bayesian methods. Markov chain Monte Carlo integration was used to sample the resulting posterior distribution.

Results:

The breast cancer incidence rate in the Ostergotland population was 21 (95% CI: 17–25) per 10 000 woman-years. Accounting for length-biased sampling, an estimated 91% (95% CI: 85–97%) of breast cancers were aggressive. Larger tumours, 21–50 mm, had an average sojourn of 6 years (95% CI: 3–16 years), whereas aggressive ductal carcinomas in situ took around half a month (95% CI: 0–1 month) to progress to the invasive ⩽10 mm state.

Conclusion:

These tumour progression rate estimates may facilitate future work analysing cost-effectiveness and quality-adjusted life years for various screening strategies.

Standardized breast cancer mortality rate compared to the general female population of Iran

INTRODUCTION

Breast cancer is the most common cancer in women. Improvements of early diagnosis modalities have led to longer survival rates. This study aimed to determine the 5, 10 and 15 year mortality rates of breast cancer patients compared to the normal female population.

MATERIALS AND METHODS

The follow up data of a cohort of 615 breast cancer patients referred to Iranian Breast Cancer Research Center (BCRC) from 1986 to 1996 was considered as reference breast cancer dataset. The dataset was divided into 5 year age groups and the 5, 10 and 15 year probability of death for each group was estimated. The annual mortality rate of Iranian women was obtained from the Death Registry system. Standardized mortality ratios (SMRs) of breast cancer patients were calculated using the ratio of the mortality rate in breast cancer patients over the general female population.

RESULTS

The mean age of breast cancer patients at diagnosis time was 45.9 (±10.5) years ranging from 24-74. A total of 73, 32 and 2 deaths were recorded at 5, 10 and 15 years, respectively, after diagnosis. The SMRs for breast cancer patients at 5, 10 and 15 year intervals after diagnosis were 6.74 (95% CI, 5.5- 8.2), 6.55 (95%CI, 5-8.1) and 1.26 (95%CI, 0.65-2.9), respectively.

CONCLUSION

Results showed that the observed mortality rate of breast cancer patients after 15 years from diagnosis was very similar to expected rates in general female population. This finding would be useful for clinicians and health policy makers to adopt a beneficial strategy to improve breast cancer survival. Further follow-up time with larger sample size and a pooled analysis of survival rates of different centres may shed more light on mortality patterns of breast cancer.

Parameter estimates for invasive breast cancer progression in the Canadian National Breast Screening Study

Background:

The aim of screening is to detect a cancer in the preclinical state. However, a false-positive or a false-negative test result is a real possibility.

Methods:

We describe invasive breast cancer progression in the Canadian National Breast Screening Study and construct progression models with and without covariates. The effect of risk factors on transition intensities and false-negative probability is investigated. We estimate the transition rates, the sojourn time and sensitivity of diagnostic tests for women aged 40–49 and 50–59.

Results:

Although younger women have a slower transition rate from healthy state to preclinical, their screen-detected tumour becomes evident sooner. Women aged 50–59 have a higher mortality rate compared with younger women. The mean sojourn times for women aged 40–49 and 50–59 are 2.5 years (95% CI: 1.7, 3.8) and 3.0 years (95% CI: 2.1, 4.3), respectively. Sensitivity of diagnostic procedures for older women is estimated to be 0.75 (95% CI: 0.55, 0.88), while women aged 40–49 have a lower sensitivity (0.61, 95% CI: 0.42, 0.77). Age is the only factor that affects the false-negative probability. For women aged 40–49, ‘age at entry', ‘history of breast disease' and ‘families with breast cancer' are found to be significant for some of the transition rates. For the age-group 50–59, ‘age at entry', ‘history of breast disease', ‘menstruation length' and ‘number of live births' are found to affect the transition rates.

Conclusion:

Modelling and estimating the parameters of cancer progression are essential steps towards evaluating the effectiveness of screening policies. The parameters include the transition rates, the preclinical sojourn time, the sensitivity, and the effect of different risk factors on cancer progression.

Validation of a modelling approach for estimating the likely effectiveness of cancer screening using cancer data on prevalence screening and incidence

PURPOSE

This study aims to validate a biostatistical approach to predict the likely effectiveness of screening in reducing advanced disease in the absence of data on incident screen and interval cancers.

METHODS

We derived the predicted relative reduction in advanced stage disease following screening from the expected proportion of advanced disease following screening and the observed proportion of advanced disease detected clinically among the controls. We compared the predicted estimates to those observed in a randomised trial.

RESULTS

Using our method, the predicted estimates of relative reduction in node positive breast cancer following screening were comparable to the observed estimates for the age groups 50-59 and 60-69 in the screening study (predicted 32% vs. observed 40% (p=0.274) and predicted 34% vs. observed 45% (p=0.068), respectively). However, for the age groups 40-49 and 70-74 the predicted values were overestimates of the likely effectiveness of screening compared to the observed values (predicted 38% vs. observed 16% (p=0.014) and predicted 34% vs. observed 0% (p=0.001), respectively).

CONCLUSION

When the number of cancer cases is more than hundred, the method of prediction using only prevalence screen data may be accurate. Where cancers are less common, for example in small populations or young age groups, further data from interval cancers or incidence screens may be necessary.

Multi-state Markov models in cancer screening evaluation: a brief review and case study

This work presents a brief overview of Markov models in cancer screening evaluation and focuses on two specific models. A three-state model was first proposed to estimate jointly the sensitivity of the screening procedure and the average duration in the preclinical phase, i.e. the period when the cancer is asymptomatic but detectable by screening. A five-state model, incorporating lymph node involvement as a prognostic factor, was later proposed combined with a survival analysis to predict the mortality reduction associated with screening. The strengths and limitations of these two models are illustrated using data from French breast cancer service screening programmes. The three-state model is a useful frame but parameter estimates should be interpreted with caution. They are highly correlated and depend heavily on the parametric assumptions of the model. Our results pointed out a serious limitation to the five-state model, due to implicit assumptions which are not always verified. Although it may still be useful, there is a need for more flexible models. Over-diagnosis is an important issue for both models and induces bias in parameter estimates. It can be addressed by adding a non-progressive state, but this may provide an uncertain estimation of over-diagnosis. When the primary goal is to avoid bias, rather than to estimate over-diagnosis, it may be more appropriate to correct for over-diagnosis assuming different levels in a sensitivity analysis. This would be particularly relevant in a perspective of mortality reduction estimation.

A natural history model of stage progression applied to breast cancer

Invasive breast cancer is commonly staged as local, regional or distant disease. We present a stochastic model of the natural history of invasive breast cancer that quantifies (1) the relative rate that the disease transitions from the local, regional to distant stages, (2) the tumour volume at the stage transitions and (3) the impact of symptom-prompted detection on the tumour size and stage of invasive breast cancer in a population not screened by mammography. By symptom-prompted detection, we refer to tumour detection that results when symptoms appear that prompt the patient to seek clinical care. The model assumes exponential tumour growth and volume-dependent hazard functions for the times to symptomatic detection and stage transitions. Maximum likelihood parameter estimates are obtained based on SEER data on the tumour size and stage of invasive breast cancer from patients who were symptomatically detected in the absence of screening mammography. Our results indicate that the rate of symptom-prompted detection is similar to the rate of transition from the local to regional stage and an order of magnitude larger than the rate of transition from the regional to distant stage. We demonstrate that, in the even absence of screening mammography, symptom-prompted detection has a large effect on reducing the occurrence of distant staged disease at initial diagnosis.

The relation of breast cancer staging to screening protocol compliance: a computer simulation study

A computer model based on relational database techniques was used to analyze the relationship between staging and population compliance to a breast cancer screening protocol. Stage distribution data permitted estimates of compliance to the protocol. This relationship followed the equation y=5.83e-2.44x where y was compliance and x was disease stage. Application of this equation to SEER and NCDB data estimated that the levels of compliance never exceeded 16 percent. Results indicated increasing clinical Stage IV disease as population compliance decreased. As the clinical staging increased there was increased sub-clinical Stage IV disease. With regular screening, simulation suggested that mortality would decrease.

DCIS, cytokeratins, and the theory of the sick lobe

We postulate that ductal carcinoma in situ (DCIS), and consequently breast carcinoma in general, is a lobar disease, as the simultaneously or asynchronously appearing, often multiple, in situ tumor foci are localized within a single lobe. Although the whole lobe is sick, carrying some form of genetic instability, the malignant transformation of the epithelial cells may appear localized to a part or different parts of the sick lobe at the same time or with varying time difference. It may be confined to terminal ductal lobular units (TDLUs), to ducts or both. The malignant transformation is often associated with aberrant branching and/or aberrant lobularization within the sick lobe. Involvement of a single individual TDLU or of a group of adjacent TDLUs generates a unifocal lesion. Multifocal lesions appear if distant TDLUs are involved. Diffuse growth pattern in DCIS indicates involvement of the larger ducts. The extent of the involved area in multifocal or diffuse cases varies considerably. Diffuse growth pattern with or without evidence of aberrant arborisation within the sick lobe seems to characterize a subgroup of DCIS with unfavourable prognosis. In this paper, we discuss the anatomical, embryological and pathological background of the theory of the sick lobe and present supporting evidence from modern radiological breast imaging, long-term follow-up studies and from our own series of 108 DCIS cases.

Bayesian evaluation of breast cancer screening using data from two studies

The mean sojourn time (the duration of the period during which a cancer is symptom free but potentially detectable by screening) and the screening sensitivity (the probability that a screen applied to a cancer in the preclinical screen detectable period will result in a positive diagnosis) are two important features of a cancer screening programme. Little data from any single study are available on the potential effectiveness of mammographic screening for breast cancer in women with a family history of the disease, despite this being an important public health issue. We develop a method of estimation, from two separate studies, of the two parameters, assuming that transition from no disease to preclinical screen detectable disease, and from preclinical disease to clinical disease, are Poisson processes. Estimation is performed by a Markov chain Monte Carlo algorithm. The method is applied to the synthesis of two studies of mammographic screening in women with a family history of breast cancer, one in Manchester and one in Kopparberg, Sweden.

Routine follow-up examinations in breast cancer patients have minimal impact on life expectancy: a simulation study

BACKGROUND

Little is known about the effects of routine follow-up examinations on life expectancy in cancer patients. Lately, the benefits of follow-up examinations have been debated, which has given rise to less extensive, though still frequent, follow-up strategies. In this study, a simulation model was applied to evaluate the impact of different follow-up strategies on life expectancy in breast cancer patients.

MATERIALS AND METHODS

A five-state Markov chain model was developed, with which various follow-up strategies with regard to frequency and elaborateness were simulated. Calculations were based on a hypothetical population of breast cancer patients treated with curative intent. Medical aspects were studied, such as life expectancy and the proportion of patients who died from breast cancer. Social and psychological aspects and quality of life were not taken into account. Data from the literature were used to estimate the parameters needed for the model.

RESULTS

The gain in life expectancy with standard follow-up compared to no follow-up examination, was about 2 months in breast cancer patients aged 50 years treated with curative intent. The percentage of patients who died from breast cancer was 45.4% with standard follow-up, versus 45.8% without follow-up. In older women, the gain was even less. Sensitivity analyses showed that the effects on life expectancy were robust.

CONCLUSIONS

Our model showed that standard follow-up had minimal impact on the prognosis of breast cancer patients. It may be unnecessary to continue standard follow-up by medical specialists after the end of the surveillance period of the primary therapy, provided that the patients continue to have easy access to health care facilities in the case of symptoms or concern. However, future research is needed to study quality of life aspects of follow-up.