A time-dependent Markov model was used to compare hypothetic populations of women, one followed clinically without screening and the others underwent different screening mammography policies. The structure of the model, which is presented in Figure 1, is similar to other models already used in the evaluation of breast cancer screening programs, such as MISCAN [3,4] and MICROLIFE . The difference between ourmodel and the reported models is in the breast cancer classification approach. While the majority of other models use tumor size as the classification criterion, a simplified TNM (Tumor Node Metastasis Classification) cancer stage  of breast cancers was used in our model. The model characterizes the natural history of the disease as having four preclinical stages when breast cancer can be detected by screening but shows no clinical symptoms. Approximately 60% of the invasive breast cancers are assumed not to be preceded by ductal carcinoma in situ (DCIS), which is screen-detectable and from which a 65% progression to invasive cancer is assumed . The invasive stages are defined as follows. In the localized stage of breast cancer, neither regional node involvement nor distant metastases are found (T1-3 and N0, M0 after TNM Classification). The regional stage includes tumors classified as T3 and T4 and/or regional node metastases (N1), if no metastases in distant lymph nodes or organs (M0) are found. The disease with metastases in distant nodes or organs is classified as distant stage (M1) .
Figure 1. Structure of the model for breast cancer screening with the possible courses of the disease. The dashed lines correspond to transitions possible only by screening policies. The state “death from other causes” which can be attained from all other states is not shown. DCIS, ductal carcinoma in situ.
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The transitions to clinically diagnosed local, regional, and distant states are governed by the rate of the incidence, clinical-stage distribution data, and sojourn time. In the case of early detection by screening, the women enter the corresponding screen-detected DCIS, local, regional, or distant states. The state “false positives” refers to women with positive screening examination in whom no breast cancer is found at further invasive assessment. The two absorbing end-states of the model are death from breast cancer and death from other causes.
The cohort simulation approach with a cycle length of 1 week was used for running the Markov model [8,9], which was developed with the SAS System for Windows Release 8.02 (SAS Institute Inc., Cary, NC, USA) . The cycle length of 1 week was chosen to enable the modeling of the sojourn times and treatment durations with sufficient precision. Breast cancer incidence, mammography sensitivity, mortality, and breast cancer relative survival were modeled as time-dependent transition probabilities.
The perspective for the evaluation was that of health-care sector and the time horizon covered the full lifetime of the patients from age 40 years onward. A discount rate of 3% for costs and effects was applied to the analyses, in accordance with recommendations from the Panel on Cost Effectiveness in Health and Medicine . All costs are expressed in 2004 European euros. Throughout the modeling process, the principles of good practice for decision analytic modeling in health-care evaluation were followed, as proposed by the ISPOR Task Force on Good Research Practices-Modeling Studies .
All data regarding age-dependent cancer incidence, clinical-stage distribution, treatments, and survival were obtained from the Cancer Registry of Slovenia . Because of the introduction of preventive mammography examinations (though unorganized) in the early 1990s and consequently the slight shift of clinical-stage distribution toward the earlier stages of breast cancer, the database for the time period of 1980–1990 was used for estimating a clinical-stage distribution of breast cancer. In that period, 41% of breast cancers were detected in the local stage, 47% in the regional stage, and the remaining 12% in the distant stage. The database for the period 1999–2001 was used for the estimation of age-dependent incidence. The incidence in this period is slightly higher than it was in the period 1980–1990; here the assumption was made that the effect of unorganized screening on higher incidence is negligible in respect to the effect of higher risk factors in recent years, which are consequences of less healthy lifestyle, lower fertility rates, lower average number of children, higher age at first birth, and higher awareness of the disease .
The survival of women with preclinical stages of breast cancer, of women with screen-detected DCIS, and of women with false positive results was assumed to be equal to the survival of women with no breast cancer. Although this assumption is obvious for women with false positive results, the choice for the same assumption in the other two women groups needs further comment. It was reported that operational removal of DCIS cures at least 98% of lesions  and that the 5-year mortality because of DCIS is 1% , which justifies this assumption also for screen-detected DCIS. The determination of survival of women with preclinical stages of breast cancer is quite problematical if not impossible. One possible way to justify the assumption is by comparing the number of women that died because of the breast cancer and the number of women in which the breast cancer was registered only on the death certificate. The number of women, in which breast cancer was registered only on a death certificate represents only approximately 1% to 2% of incidence of breast cancer and only 2% to 4% of deaths because of breast cancer . The assumption is further justified by the fact that the durations of the preclinical stages are quite short when compared to the durations in the clinical stages.
Stage-specific relative mortality from breast cancer (i.e., the proportion of women that die because of breast cancer after specific period) was obtained in the following manner. A relative 1–7 years survival of breast cancer patients (i.e., the proportion of women with breast cancer alive after specific period) diagnosed in the period 1991–1995 was subtracted from the relative survival of the general population (i.e., the proportion of women alive after specific period) in corresponding age groups. Because the obtained relative stage-specific mortality was quite similar among different ages at diagnosis, it was assumed to be independent of age at diagnosis.
Various patterns of stage-specific treatments were taken from the Cancer Registry of Slovenia for the same groups of women that were included in the relative survival calculation, to properly estimate the effect of treatment on survival. Treatments consisted of four basic interventions: surgery, hormonal therapy, radiotherapy, and chemotherapy. For screen-detected DCIS, surgery with no further treatment was presumed .
One of the key assumptions of the screening, and hence of this model, is that mammography makes it possible to capture a sizable amount of cancer cases that would otherwise have gone undetected until the appearance of clinical symptoms. The model thereby needs to incorporate an estimate of sojourn time, that is, the period when the cancer is screen-detectable but shows no clinical symptoms. We assumed a value of 3 to 7 years with a mean of 5 years [8,15] for DCIS and a value of 2 to 3 years with a mean of 2.5 years [16–18] for invasive carcinoma in preclinical local stage. The sojourn time in preclinical regional and in preclinical distant states was estimated from the approximate growth rates of tumors. Approximately one half of the breast cancers in the Cancer Registry of Slovenia have a defined TNM stage from which approximate tumor sizes were calculated for local, regional, and distant carcinomas. Then the cancer cells' doubling times from 60 to 180 days were presumed to obtain the ranges for a sojourn time of 0.36 to 1.08 years and 0.35 to 1.04 years for regional and distant stages, respectively; this method was adopted from Michaelson et al.  and Kopans et al. .
The assumed sensitivity of the mammography is 86.7% for ages between 40 and 49 years, 93.6% for ages between 50 and 59 years, 94.1% for ages between 60 and 69 years, and 91.2% for ages 70 years and older . Based on the results from mass screening in other countries, a reasonable estimate of the attendance is 75%  and the estimate of the recall rate is 7% [22,23]. About 20% of the women who are recalled for additional diagnostic procedures undergo invasive diagnostic procedures such as fine-needle aspiration and surgical biopsy. The remaining 80% undergo noninvasive imaging (further mammography, ultrasound) and clinical examination [22,23]. Diagnostic procedures for clinically detected breast cancers include noninvasive (mammography, ultrasound, clinical examination) and invasive techniques (fine-needle aspiration, surgical biopsy).
The costs for mammography examination, the costs for diagnostic interventions for clinically detected breast cancer, the costs for invasive and noninvasive diagnostics at recall, and the costs for treatment interventions were obtained from the Institute of Oncology Ljubljana .
In order to capture the difference in mortality and morbidity due to screening, health improvement was measured in quality-adjusted life-years (QALYs). QALYs for treatment and the corresponding durations of treatments were obtained from the literature . The quality of life for DCIS, local and regional breast cancers after treatment was weighted according to the treatment interventions. The quality of life for distant cancer was weighted with 0.515 .
The quality of life for women with false positive result was also reduced according to the diagnostic duration and QALY weight . In the case of death from breast cancer, a terminal illness lasting 1 month with QALY weight of 0.288 was taken into account .
Different screening policies were considered with respect to the following eligibility criteria: age at the beginning of the screening, age at the end of the screening, and the interval between two screenings. All possible combinations of starting ages 40, 45 and 55 years, ending ages 65, 70, 75 and 80 years, and screening intervals of 1, 2 and 3 years were considered, thus giving 36 different screening policies, listed in Table 1.
Table 1. List of screening policies taken into consideration and their labeling in the article
Currently, only opportunistic screening activity takes place in Slovenia. Because there is no register of the women that underwent such screening, the extent of screening would be difficult to estimate suitably. Therefore, the present situation was omitted from the analysis and the “null option” chosen for screening policies was the no-screen option.
Probabilistic Sensitivity Analysis
Probability distributions were defined for all the model parameters except for breast cancer incidence and the cost of mammography examination, as the incidence of breast cancer has been quite constant in recent years and the cost of mammography examination is fixed. Beta distributions were fitted using the method of moments  with mean and standard error drawn from the literature to represent the uncertainties surrounding probabilities (attendance, recall rate, proportion of invasive diagnostics, sensitivities, clinical-stage distribution, and progression from DCIS) and QALYs. A negative exponential function was fitted to stage-specific breast cancer relative mortality, and fitted parameter's distributions were used to describe the distributions of relative mortality at specific times after the diagnosis. In order to gain distributions of costs for chemotherapy, hormonal therapy, radiotherapy, and surgery, an approximate number of patients for various subtypes of each of the four treatment interventions (i.e., various types of chemotherapy, hormonal therapy, radiotherapy, and surgery) along with treatment costs were obtained from the Institute of Oncology Ljubljana. Log-normal distributions were fitted to different treatment costs and, in a similar manner, log-normal distributions were fitted to costs for invasive and noninvasive diagnostic examinations and for examinations after clinically detected breast cancer. Finally, a log-normal distribution was assumed for sojourn times to assure that generated times were all positive.
The net benefit framework was used for analyzing the results from probabilistic sensitivity analysis to derive cost-effectiveness acceptability curves (CEACs) for each screening policy at different values of willingness to pay per QALY (λ) [28,29]. The policies with the highest expected net benefits (i.e., the policies of choice) at different λ's were plotted on CEACs in the form of cost-effectiveness acceptability frontier .