Contribution of Early Detection and Adjuvant Treatments to Breast Cancer Mortality Reduction in Catalonia, Spain

Background Reductions in breast cancer (BC) mortality in Western countries have been attributed to the use of screening mammography and adjuvant treatments. The goal of this work was to analyze the contributions of both interventions to the decrease in BC mortality between 1975 and 2008 in Catalonia. Methodology/Principal Findings A stochastic model was used to quantify the contribution of each intervention. Age standardized BC mortality rates for calendar years 1975–2008 were estimated in four hypothetical scenarios: 1) Only screening, 2) Only adjuvant treatment, 3) Both interventions, and 4) No intervention. For the 30–69 age group, observed Catalan BC mortality rates per 100,000 women-year rose from 29.4 in 1975 to 38.3 in 1993, and afterwards continuously decreased to 23.2 in 2008. If neither of the two interventions had been used, in 2008 the estimated BC mortality would have been 43.5, which, compared to the observed BC mortality rate, indicates a 46.7% reduction. In 2008 the reduction attributable to screening was 20.4%, to adjuvant treatments was 15.8% and to both interventions 34.1%. Conclusions/Significance Screening and adjuvant treatments similarly contributed to reducing BC mortality in Catalonia. Mathematical models have been useful to assess the impact of interventions addressed to reduce BC mortality that occurred over nearly the same periods.


NATURAL HISTORY OF BREAST CANCER AND VARIABLES OF THE MATHEMATICAL MODEL
The goal of this Appendix is to provide the values of the inputs of the model and further details of the mathematical equations in order to facilitate the understanding of the main assumptions.
The following Figure A1 shows a simplified scheme of the natural history of the progressive model of breast cancer (BC). The model considers four states: the undetectable or disease free state S 0 ; the pre-clinical state, S p , where the disease is asymptomatic but may be detected by screening mammography; the symptomatic disease state, S c , where BC may detected by usual care; and the state S d , which indicates death caused by BC. The model defines ∆ and ∆ as the transition probabilities between S 0 and S p and between S p and S c during an age interval , ∆ where I is the incidence rate function. Figure 1 also shows the ages at which each of the transitions happens, x, and y.

BREAST CANCER INCIDENCE MODEL
Population data on BC incidence, in areas where screening mammography has been used, is affected by early detection. Screening increases incidence rates by age. On the one hand, age at diagnosis decreases as a result of advancing BC diagnosis (lead time). On the other hand, screening may cause overdiagnosis when it detects tumors which would never have been diagnosed during a lifetime without screening. The model developed by Lee and Zelen (LZ model) considers as an input the incidence of the background group, which corresponds to the incidence, by age, in the absence of screening [1]. Then depending on the level of use of mammography the model estimates the number of women that will be diagnosed with BC, taking into account the background incidence, the periodicity of the screening exams, the sensitivity of the screening exams, and the sojourn time in the preclinical state of BC. For this reason, it was necessary to estimate BC incidence in the absence of screening. Reference [2] details the methods we used to estimate the background incidence, which can be summarized as: a) Estimating an age-cohort Poisson regression model for the observed incidence. The explanatory variables for this model were age at diagnosis and cohort characteristics. Cohort characteristics were completed fertility rate (CFR), percentage of women that used mammography at age 50 (PM50), and year of birth (YB). The model provided the expected BC incidence rate using the following expressions .
. b) BC incidence in the absence of screening, by cohort of birth, was derived from the Poisson model described in a) when considering that the proportion of women having periodic mammograms at age 50 (PM50) was zero. The incidence rates in absence of screening are lower than the observed ones. Non-progressive disease is not included in the estimated incidence rates.
3. TRANSITIONS FROM S 0 TO S P AND FROM S P TO S C Since the transition from S 0 to S p is not observed, the transition probabilities, , can not be estimated directly. Lee and Zelen showed that the, transition rates can be derived from the S p S c age-specific incidence rates, , and of the sojourn time in S p , [3]. Let be the probability density function (pdf) of the sojourn time in S p , which was assumed to be exponential. For the estimation of , incidence data was grouped by age. Let the th age interval be defined as , where 5 ∆. And let be the BC incidence rate for an age group of five years. The transition rate function was estimated recursively using the formulas ∆ 1 ∆ For the first age interval, 0 and for successive age intervals where is the mean sojourn time in S p and 1/ . Values of the mean sojourn time in S p for different age groups are 2 for 40 yrs., 6 0.2 for 40,50 yrs., and 4 for 50 yrs. [1]. Young women usually have BC that progress faster than BC in older women.
Survival is measured from the time of clinical diagnosis in the symptomatic cases and from the estimated time of clinical diagnosis in the screen detected cases. In the LZ model the survival function adjusts for the lead time in the following way. In the LZ model, the exam-detected, interval, and clinical cases all have the origin for which survival is measured at the time of clinical diagnosis. Consequently, there is an implied "guarantee time" for disease-specific survival, that is, the cases diagnosed earlier would have been alive at the time the disease would have been clinically diagnosed. This guarantee time which corresponds to the lead-time is a random variable and is incorporated into the model equations.
In a previous work we derived twenty five BC survival pdfs by age (five age groups) and stage (I,II-, II+,III or IV) at diagnosis for the period prior to the introduction of BC screening and adjuvant treatments 1980-89 [4].
The is a mixture of five pdfs weighted by the probability of being diagnosed at stage at age ( | ). One of the assumptions of the model is that the screen-diagnosed cases may have a stage shift towards a more favorable prognosis relative to the distribution of stages with usual care (see [1] for further details). Using the expression | | | the BC survival pdfs for the Background ( ) and the Screening scenarios were obtained. For the Screening scenarios we differentiated between screen-detected ( , ) and interval cases ( , ), where the subindexes a and b refer to annual and biennial periodicities, respectively. The corresponding stage distributions for each of the survival functions can be found in Table S1. The BC survival pdf for the Adjuvant treatment scenario is a mixture of the g weighted by | which corresponds to is the probability of receiving treatment at calendar year for a woman diagnosed at age , then | , | | | Note that the stage distribution for adjuvant treatments is the same than for the Background. The where obtained from Mariotto et al. [5,6], who modeled the adjuvant treatment dissemination. The benefit of tamoxifen was applied to the percentage of women with estrogen receptor positive BC. Percentages were of 63% (<50 yrs.), 77% (50-69 yrs.) and 85% (≥70 yrs.) (see [1] for more details). Finally, to obtain the BC survival pdfs for the scenario that incorporates Both Adjuvant treatments+Screening we followed the same steps as we did for . The difference was that, instead of using the Background stage distribution, , we used each of the stage distributions associated with screening (screen detected and interval cases for annual and biennial screening), thus obtaining the survival functions , , and .

PROBABILITY OF DYING OF BREAST CANCER,
).
The probability of dying of BC, , at age for birth cohort for the Background scenario was estimated as: where is the probability of surviving to year for birth cohort for women from the general population.
Equation (1) was also used to estimate the probability of death for the Only adjuvant treatments scenario, using the survival pdfs that include the treatment effect. For the Background scenario we used the Background pdf while in the Only adjuvant treatments we used the pdf that include the benefits of tamoxifen and multiagent chemotherapy and takes into account their dissemination usage conditioned to the period of diagnosis.
The estimation of the probability of dying of BC in the scenarios that include the Screening benefit is more complex. The full set of equations can be found in [7]. To illustrate it, the next two equations show the probabilities of BC death for women that had only one exam at age . The probability of BC death for screendetected cases was estimated as: The , is the sensitivity of the mammography exam, which depends on the woman's age and the calendar year at which the mammogram was performed. The values used in the model are shown in Table S3 and were obtained from [1].
The probability of dying of BC for interval cases was estimated as: Equation (3) has two components: the first refers to women that were in the preclinical state at the time that the exam was performed but the result of the exam was negative (false negative cases); and the second refers to women that entered the preclinical state after the first exam at age (true interval cases).
When estimating probabilities of BC death for women that had more mammographic exams, the false positive results may take place at any of the previous exams.
The equations that allow estimation of the probability of BC death have the same expression for annual or biennial screening periodicities, with the difference in the survival functions. Each screening periodicity has an associated survival function that takes into account the corresponding distribution of disease stages at diagnosis. Survival functions associated with annual screening are for screen detected cases and for interval cases; for biennial periodicity, survival functions are for screen detected cases and for interval cases.
The scenario that combines Both adjuvant treatments and screening is estimated using the same equations as the Only screening scenario. The survival pdfs incorporate the benefits of adjuvant treatments and the stage distribution of screen detected and interval cases for annual and biennial screening: , , and .

DISSEMINATION OF SCREENING MAMMOGRAPHY
The proportions of women who were having periodic mammographies for early detection in Catalonia by and birth cohort was estimated in [8] following a mixed effects model: The is the horizontal asymptote as age increases, indicates the age value at which approximately half of the population is receiving periodic mammograms, and indicates the difference in years between the age at which 3/4 of the population are receiving periodic mammograms and the age .
The parameters and were estimated as fixed effects and the parameter as random effect. Parameter values can be found in [8]. Finally, based on results from a previous publication [8], the probability of receiving annual screening was estimated as 0.637 and the probability of receiving biennial screening was estimated as 0.363 .