Dana-Farber Cancer Institute and the Harvard School of Public Health, Boston, MA, USA
Received 12 July 2002; accepted 3 April 2003
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Abstract |
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Key words: breast cancer, clinical trials, mammography, mathematical models
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Introduction |
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There have been eight randomised clinical trials evaluating the benefit of mammography, physical examinations or their combination in diagnosing asymptomatic breast cancer. These are often referred to as the HIP trial [1], the Malmö study [2], the Swedish Two-County studies [3, 4], the Stockholm study [5, 6], the Gothenburg study [7], the Edinburgh study [8, 9] and the two Canadian studies (NBSS-1 and -2 [10, 11]).
Some of these trials have been severely criticised by Gøstzche and Olsen [12, 13]. They raised serious doubts about the evidence showing mortality benefit for early detection. The criticism dealt with the quality of the trials. Recently, Nyström et al. [14] updated the analysis for nearly all of the trials carried out in Sweden and responded to the Gøtzsche and Olsen criticisms. The updated analysis showed a mortality benefit for early detection of breast cancer.
These screening trials are difficult to implement compared with therapeutic trials. They require a large number of subjects, as the eligibility requirement is that subjects are disease-free. Long-term follow-up, in the neighbourhood of 1015 years, is necessary to have sufficient numbers of breast cancer deaths to adequately compare mortality. Compliance is a major issue in these trials. Women are randomised to receive (or not receive) invitations to have special examinations. A significant proportion may not respond to the initial invitation. Even those starting an early detection examination schedule may not attend all scheduled examinations. Furthermore, subjects randomised to the usual care (control) group may independently seek mammogram examinations.
It is doubtful whether there will be future clinical trials initiated to further evaluate mammography. Such trials may not be feasible due to ethical, compliance and resource issues. In addition, because minimum follow-up is likely to be a decade, during that time advances in detection modality may make the intervention being compared obsolete.
Here we present a probability model that predicts breast cancer mortality as a function of both the characteristics of the case finding process and the detection modalities. In many fields of science and technology, models are used for prediction when experiments cannot be carried out. One of the objectives of the modelling is to predict outcomes when input variables are changed. We believe that many unanswered questions about breast cancer early detection may be answered with our model.
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Model description |
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All models make assumptions. Our two major assumptions are: (i) breast cancer is a progressive disease; and (ii) potential benefit from early detection arises because of a stage shift. The progressive disease assumption implies that the disease stage never becomes more favourable with delay in diagnosis. The stage-shift assumption means that screen-detected cases have a distribution of disease stages that have more favourable prognosis compared with usual care. Furthermore, the shift in the stage distribution is greater than could be expected from length-biased sampling. An ancillary assumption is that ultimate survival depends on stage of diagnosis, treatment and age, but is independent of mode of detection.
The input variables for the model are: age-specific incidence, survival conditional on stage, age of diagnosis and treatment, stage distribution at diagnosis, mode of detection and screening variables (pattern of screening, sensitivity and stage shift). Many of these variables may depend on chronological time. The variables associated with patterns of screening can be obtained from the early detection clinical trials. The other variables (incidence, survival and usual care stage distribution) can be obtained from population databases such as SEER.
One important implication of the model is that a reduction in mortality will only occur if there is a stage shift in exam-detected cases. The model can compare changes in mortality rates, for example screening versus no screening, different screening schedules, effect of changes in sensitivity and effect of advances in treatment.
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Application of the model to early detection trials |
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We assumed that breast cancer progresses from no disease (or disease that cannot be detected) to preclinical disease to clinical disease. The sojourn time in the preclinical state was assumed to follow an exponential distribution with an age-dependent mean. The sensitivity of the examinations (mammograms, clinical examinations or a combination) was also assumed to be age dependent. Numerical values for the mean sojourn time in the preclinical state and the sensitivity of the examinations were obtained from the early detection trials. For example, the Swedish Two-County studies reported that the mean sojourn times in the preclinical stage ranged from 1.25 years in 40- to 49-year-old women to 3.9 years in 60- to 69-year-old women. The sensitivity of mammograms also varied from 60% in younger women to 86% in older women. Our model requires age-specific incidence probabilities and transition probabilities from no disease to preclinical stage that would be unaffected by screening. The SEER database for 19731982 was used to estimate these probabilities. This time period was selected because early detection programmes would minimally affect these parameters.
In addition, we assumed that the process by which early detection changes prognosis is by a stage shift. Table 1 summarises the stage shifts reported in the early detection trials. The stage shift is expressed as a proportion of cases with positive nodes or with stage IIIV disease.
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The Edinburgh and HIP studies used both mammograms and physical examinations as screening modalities. The model predicted a mortality reduction of 11% after 14 years of follow-up time for the Edinburgh study. The prediction is within the reported 95% confidence limits. The HIP trial reported a 30% mortality reduction for cases diagnosed within 5 years of study entry and 10 years of follow-up time. (No confidence limits were supplied with this estimate.) However, the model predicted a 3.3% mortality reduction. The Canadian studies (NBSS-1, NBSS-2) included physical examinations in the control groups. The studies were designed to assess the additional benefit of mammography. Our model predicted little additional benefit of mammography.
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Discussion |
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The model predictions may be further improved. In the absence of detailed compliance information, we assumed a 100% compliance rate for both intervention and control groups. The model did not take into account competing risks, which may be important in predictions for older women. US SEER data were used for survival. Comparable Swedish data may be more appropriate to predict outcomes for the Swedish trials. The characterisation of disease stage can be made more detailed using estrogen receptor status, number of positive nodes, tumour size, etc.
The model can be used to guide public health programmes. It may be applied to evaluate the potential benefit of different screening strategies as a function of age and risk status. Inputting improved sensitivities and longer lead times can assess advances in early detection modalities. Advances may be due to technological innovations or finding breast cancer markers. These issues are all-important but are unlikely to be settled by future clinical trials. Finally, we remark that our model is a general model for evaluating early detection programmes and can be applied to other chronic diseases.
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Acknowledgements |
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Note added in proof |
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Footnotes |
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References |
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