By Cancer Rose, November 27, 2021

The decision aid describes the number of cancers, the number of deaths from cancer, and the number of false alarms estimated in 2 cohorts of 2,000 women starting at age 50:

- One cohort participates in organized screening until age 59 and has 5 screening mammograms (at age 50, 52, 54, 56, and 58)

- The other cohort does not participate (0 screening mammograms).

The calculations are based on:

- French epidemiological data available (in October 2021) on the Santé Publique France website ^{1,2}

- An assumption of 65% of the women concerned getting screened (50% through organized screening + 15% through screening on individual initiative). This hypothesis is consistent with the figures announced by INCa ^{3}

- A hypothesis of overdiagnosis representing 20% of cancers detected in a population of screened women. This hypothesis is in the middle of the range of published values and is compatible with the range of values accepted by INCa (1 to 20%) ^{4}

- An assumption of a 15% reduction in mortality through screening. This assumption is in the middle of the range of published values and is consistent with the range of values accepted by the INCa (15 to 21%)^{4}

__1-Estimation of the number of cancers__

__1-Estimation of the number of cancers__

The epidemiological data used are presented in the table below extracted from reference 1.

The incidences shown above are expressed as the number of breast cancers per 100,000 women.

For 2.000 women, we have :

- for women aged 50-54:

285.1*2000/100000 = 5.702 cancers / 2.000 women

- for women aged 55-59:

273.1*2000/100000 = 5.462 cancers / 2,000 women

In a cohort of 2,000 women, we would observe:

5.702 cancers when the cohort is 50 years old

5.702 cancers when the cohort is 51 years old

5.702 cancers when the cohort is 52 years old

5.702 cancers when the cohort is 53 years old

5.702 cancers when the cohort is 54 years old

5.462 cancers when the cohort is 55 years old

5.462 cancers when the cohort is 56 years old

5.462 cancers when the cohort is 57 years old

5.462 cancers when the cohort is 58 years old

5.462 cancers when the cohort is 59 years old

This means a total of 55.82 cancers (rounded to 56)

This incidence, cumulated over 10 years, of 56 cancers per 2,000 women corresponds to a cohort representative of the French population. This population comprises screened women and women who are not getting screened.

In other words, the 56 cancers are the sum of cancers that affect women who get screened + cancers that affect women who do not get screened.

This can be expressed as 56 = P_{D}*C_{D} + P_{N}*C_{N}

where C_{D} = cumulative incidence of cancer in women who are screened

C_{N } = cumulative incidence of cancers in women who are not screened

P_{D} = proportion of women who are screened

P_{N} = proportion of women who are not screened

With our assumption of 65% of women being screened: P_{D} = 0.65 and P_{N} = 0.35.

We therefore have: 56 = 0,65*C_{D }+ 0,35*C_{N }(equation 1)

With our hypothesis of 20% overdiagnosis of cancer among women who are screened, we have: overdiagnosis = C_{D} - C_{N }= 0,2*C_{D } d'où C_{N} = 0,8*C_{D} (equation 2)

Combining equations 2 and 1, we obtain: 56 = 0,65*C_{D} + 0,35*0,8*C_{D } soit : 56 = 0,65*C_{D} + 0,28*C_{D}

hence : 56 = 0,93*C_{D} hence : C_{D} = 56/0,93 = 60,22 and : C_{N} = 0,8*C_{D} = 0,8*60,22 = 48,18

**In summary:**

- the number of expected cancers in the screened cohort can be estimated at 60

- the number of expected cancers in the non-screened cohort can be estimated at 48

- the number of overdiagnoses in the screenedcohort can be estimated at 12.

**2- Estimating the number of deaths**

The epidemiological data used are presented in the table below taken from reference 2.

The data for women aged 50 and 60 allows us to draw Graph 1 below.

This graph suggests that survival tends to stabilize at around 70% over time. Therefore, the lethality associated with breast cancer can be estimated at approximately 30% (by lethality, we mean the proportion of women with breast cancer who will die).

To have at least 20 years of hindsight in 2018, the data come from cancers diagnosed before 1998, therefore, before the organized screening. We can therefore consider that this 30% lethality concerns unscreened women.

The number of deaths in the unscreened cohort can be estimated by applying this 30% case fatality rate to the 48 breast cancers expected in this cohort.

Thus: number of deaths among women not screened = 48*0.3 = 14.4 (rounded to 14)

Assuming a 15% reduction in mortality in the screening cohort, the number of deaths in this cohort equals 85% of the number of deaths in the unscreened cohort.

Thus: number of deaths in the screening cohort = 14.4*0.85 = 12.24 (rounded to 12)

**In summary:**

- The expected number of breast cancer deaths in the unscreened cohort can be estimated at 14

- the number of breast cancer deaths expected in the screening cohort can be estimated at 12

- the number of breast cancer deaths prevented by screening can be estimated at 2.

__3- Sensitivity analysis__

__3- Sensitivity analysis__

The assumption of 65% of women being screened is questionable. A sensitivity analysis, using a proportion of women being screened ranging from 50% to 90%, in 10% increments, gives the following results.

There is slight variation in the results, particularly in overdiagnosis estimates and avoided deaths.

The assumption of a 30% case fatality in women not being screened is also questionable. A sensitivity analysis, re-running the calculation with a case fatality ranging from 10% to 50% in 5% increments, gives the results below.

The estimate of deaths is sensitive to the value chosen for the case fatality. In particular, with the problem of rounding, an underestimation of the case fatality, even a modest one (30% rather than 35%), could lead to underestimating the deaths prevented.

However, this underestimation is unlikely because the epidemiological data correspond to cancers diagnosed more than 20 years ago. The therapeutic progress made since then suggests that our estimate of 30% is more likely to be overestimated than underestimated.

__4-Two other decision aids__

__4-Two other decision aids__

The hypotheses used for the frequency of overdiagnosis (20%) and the reduction in mortality (15%) correspond to median hypotheses and are compatible with the ranges accepted by the INCa. However, it is interesting to look at the outcome of the decision aid based on other assumptions.

Decision aid with assumptions favorable to screening: overdiagnosis = 10% - reduction in mortality = 25%.

Decision-aid with unfavorable assumptions for screening: overdiagnosis = 40% - mortality reduction = 5%.

**Références**

- Defossez G, Le Guyader‑Peyrou S, Uhry Z, Grosclaude P, Colonna M, Dantony E, et al.
*Estimations*. Saint‑Maurice (Fra) : Santé publique France, 2019. 372p.

nationales de l’incidence et de la mortalité par cancer en France métropolitaine entre 1990 et 2018. Volume 1 – Tumeurs solides

https://www.santepubliquefrance.fr/maladies-et-traumatismes/cancers/cancer-du-sein/documents/enquetes-etudes/survie-des-personnes-atteintes-de-cancer-en-france-metropolitaine-1989-2018-sein - Molinié F, Trétarre B, Arveux P, Woronoff A-S, Lecoffre C, Lafay L et al.
*Survie des personnes atteintes de cancer en France métropolitaine 1989-2018 – Sein*. Boulogne-Billancourt : Institut national du cancer, septembre 2020, 12 p.

https://www.santepubliquefrance.fr/maladies-et-traumatismes/cancers/cancer-du-sein/documents/enquetes-etudes/survie-des-personnes-atteintes-de-cancer-en-france-metropolitaine-1989-2018-sein - https://www.e-cancer.fr/Professionnels-de-sante/Depistage-et-detection-precoce/Depistage-du-cancer-du-sein/Le-programme-de-depistage-organise
- https://www.e-cancer.fr/Professionnels-de-sante/Depistage-et-detection-precoce/Depistage-du-cancer-du-sein/Les-reponses-a-vos-questions

__5-Number of positive screenings__

__5-Number of positive screenings__

Source: "Indicateurs nationaux de performance du programme de dépistage du cancer du sein sur la période 2017-2018. Updated July 12, 2021. Open access on the Santé Publique France website - https://psite.santepubliquefrance.fr/ Last access on September 17, 2021.

During 2017-2018:

- among women aged 50 to 54, 1,131,008 screenings were performed (N01)

- In women aged 55-59, 1,043,554 screenings were performed (N01)

Calculation of what happens to 2000 women aged 50 who start screening without having had any mammograms before and who continue for 10 years, i.e. 5 screening cycles

**Number of positive screenings (N05)**

A cohort of 2,000 women aged 50 years and exposed to screening for 10 years:

"number of positive L1 or L2 screens before the assessment"

(N05) / number of women screened (N01) x 2,000

50 years old, Initial screening 50-54

23,310 / 150,107 x 2000 = 311 positive tests.

Remaining 2000 - 311 = 1689 women without a positive test.

52 years old, subsequent screening 50-54 years

42,351 / 526,619 x 1689 = 136 positive tests.

Remaining 1689 - 136 = 1553 women without positive test results

54 years old, subsequent screening 50-54 range

42,351 / 526,619 x 1553 = 125 positive tests.

Remain 1553 - 125 = 1428 women without positive test results

56 years old, subsequent screening 55-59

68 566 / 943 696 x 1428 = 104 positive tests

Remain 1428 - 104 = 1324 women without positive test results

58 years old, subsequent screening 55-59

68,566 / 943,696 x 1324 = 96 positive tests.

Remain 1324 - 96 = 1228 women without positive test results

**Number of women with at least one positive test after 5 cycles (10 years): 2000 - 1228 = 772**

**This number was rounded to 770 to avoid giving a false impression of accuracy and precision.**

__6-Number of interval cancers__

__6-Number of interval cancers__

**Source** : Exbrayat C. et coll. "Sensibilité et spécificité du programme de dépistage organisé du cancer du sein à partir des données de cinq départements français, 2002-2006" BEH 2012 ; (35-36-37) : 404-406.

As of November 2011, there is no more comprehensive or recent French data to our knowledge.

In this study of 5 French departments from 2002 to 2006, there were:

414,432 mammograms resulting in 3082 screened cancers plus 638 interval cancers.

The percentage of interval cancers among all breast cancers is therefore :

638 / (3082 + 638) = 638 / 3720 = 17,15 %

Out of 60 cancers, we have 60 x 17.5/100 = 10.29 interval cancers, rounded to 10.

**- - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -**

__7-Number of true positives__

__7-Number of true positives__

Since there are 60 breast cancers, of which 10 are interval cancers, the number of true positive cancers detected by mammography is 60 - 10 = 50.

__ - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -__

__8-Number of non-overdiagnosed cancers detected__

__8-Number of non-overdiagnosed cancers detected__

Since there are 12 overdiagnosed cancers (20% of 60), the number of true positive non-overdiagnosed cancers detected by mammography is 50 - 12 = 38.

__9-Number of false positives__

__9-Number of false positives__

Since there are 770 positive screenings, of which 50 are true positives, there are 770 - 50 = 720 false positives.

__10-Number of women who had at least one biopsy__

__10-Number of women who had at least one biopsy__

Source:

File: "tableaux de l'ensemble des indicateurs nationaux pour les années 2017 et 2018 cumulées, déclinés par rang published on July 12, 2021. Last access on November 27, 2021.

"Number of surgical biopsies or tumor resection performed (N10)

+ Number of micro or macro biopsies performed (N11)

(N10+N11) / number of women screened (N01) x 2,000

50 years old, initial screening 50-54

N10 + N11 = 1863 + 3711 = 5574

5574 / 150 107 x 2000 = 74 biopsies

Remaining 2000 - 74 = 1926 women without biopsy

52 years old, subsequent screening 50-54 years

N10 + N11 = 3335 + 6330 = 9665

9665 / 526 619 x 1926 = 35 biopsies

Remaining 1926 - 35 = 1891 women without biopsy

54 years old, subsequent screening 50-54

N10 + N11 = 3335 + 6330 = 9665

9665 / 526 619 x 1891 = 35 biopsies

Remaining 1891 - 35 = 1856 women without biopsy

56 years old, subsequent screening 55-59

N10 + N11 = 6438 + 10659 = 17097

17097 / 943 696 x 1856 = 34 biopsies

Remaining 1856 - 34 = 1822 women without biopsy

58 years old, subsequent screening 55-59

N10 + N11 = 6438 + 10659 = 17097

17097 / 943 696 x 1822 = 33 biopsies

Remaining 1822 - 33 = 1789 women without biopsy

**Number of women with at least one biopsy after 5 cycles (10 years):**

**2000 - 1789 = 211 rounded to 210. Of these 210 biopsies, 50 resulted in cancer diagnoses, and therefore there are 210 - 50 = 160 biopsies for women who had a false positive.**

__Estimation of deaths due to overdiagnosis - Dr. V. Robert__

__Estimation of deaths due to overdiagnosis - Dr. V. Robert__

Overdiagnosis is treated in the same way as progressive breast cancer. They, therefore, generate unnecessary treatments (= overtreatments). Like all treatments, overtreatment leads to side effects, some of which can be fatal. This is particularly true of radiotherapy, which can cause lung cancer or heart complications.

It is therefore indisputable that overdiagnosis and its treatment cause deaths. However, it is impossible to quantify these deaths precisely in the absence of reliable epidemiological data.

All clinical trials concluded that there is no significant difference in overall mortality (all causes) between women who are screened and those who are not screened.

This finding can be interpreted in 3 ways:

- either there is no difference in overall mortality. In this case, the breast cancer deaths prevented by screening have to be compensated by an equivalent excess of deaths from other causes. Applied to our cohort of 2,000 screened women, this means that the 2 breast cancer deaths prevented are compensated by an excess of 2 deaths from other causes due to the 12 overdiagnoses.
- or there is a decrease in overall mortality among screened women, which does not appear statistically significant due to a lack of power in the clinical trials. At most, this decrease in overall mortality could be equal to the decrease in breast cancer mortality. This assumes that there are no excess deaths from other causes. Applied to our cohort of 2,000 screened women, this means that there are 2 breast cancer deaths avoided and 0 deaths due to overdiagnosis.

- or there is an increase in overall mortality in screened women, which does not appear to be statistically significant because of a lack of power in clinical trials. In this case, deaths due to overdiagnosis must outnumber breast cancer deaths prevented by screening. Applied to our cohort of 2,000 screened women, this means that the 12 overdiagnoses should account for more than 2 deaths. More than 2 deaths per 12 overdiagnoses means that overdiagnosis would cause death in more than 17% of cases. Due solely to side effects, such high case fatality seems unlikely. We do not support this hypothesis.

**In summary:** It is not possible to quantify precisely the deaths due to the 12 overdiagnoses, but it is likely that these deaths are between 0 and 2.

__Deaths from screening and overdiagnosis__ - Dr. J. Doubovetzky

__Deaths from screening and overdiagnosis__

Randomized controlled trials have not shown a statistically significant decrease in the number of deaths due to screening. Neither have epidemiological studies (historical or geographic comparisons).

Since the introduction of screening, there has been an overall decrease in breast cancer mortality, but this is mainly attributed to improved treatment and reduction of certain risks (e.g., "preventive" hormonal treatments for menopausal disorders).

As long as it is not demonstrated that screening decreases mortality, it is normal to include the lack of mortality decrease in the assumptions.

Plausible explanatory hypotheses support this view.

There are many potentially fatal adverse effects of screening mammography and overdiagnosis. Unfortunately, these adverse events have never been thoroughly evaluated, so their mortality is not quantifiable.

These potentially fatal adverse effects include:

- The direct effects of ionizing radiation from mammography. To estimate them, we rely on indirect data such as the data from Hiroshima, the impact of the former X-ray monitoring of tuberculosis patients, or even the historical treatment of dermatological diseases by radiation. Linear mathematical models are used, which are known to be wrong.

- Suicides, cardiovascular deaths, and road accidents following the announcement of a cancer diagnosis. Their existence is demonstrated for the first two but not quantified. It is probable for the third. As far as we know, this risk is all the higher when cancer in question is perceived as serious (which is what the pro-screening campaigns contribute to). But we don't have precise figures.

- Anesthetic and infectious complications of biopsies and surgical treatments (known, poorly quantified)

- Cardiac and cancerous complications of over-treatment with radiotherapy.

- Adverse effects of treatments. For example, the undesirable effects of heart failure treatments due to overdiagnosis of radiotherapy. Or the undesirable effects of psychiatric treatments linked to anxiety and depression secondary to overdiagnosis (for example, rhythm disorders secondary to antidepressants by prolongation of the QT interval, or falls or accidents linked to benzodiazepines, partially overlapping with the previous item). These effects have been demonstrated but not quantified. They also depend on prescribing habits, which vary from country to country...

While each of these numbers may seem small, no one can assess the total impact of these adverse events. Any assessment of "I think it is a lot" or "I think it is not a lot" is purely subjective. The only true expression of this risk is "between zero and equivalent to the benefit." Or even more. Some authors have made calculations and projections that the mortality due to the adverse effects of screening and overtreatment would be greater than the gain in mortality made possible by mammography.

For example, Professor Baum estimated that for every life saved by screening, between 1 and 3 lives would be shortened by the adverse effects of overdiagnosis ([1]).

Therefore, the range we have chosen (0 to 2 deaths due to adverse effects of screening and overdiagnosis) is reasonable.

[1]Baum M "Harms from breast cancer screening outweigh benefit if death caused by treatment is included" Br Med J 2013; 346: f385. Doi: 10.1136/BMJ.f385