Department of Radiology, John H Stroger Jr Hospital of Cook County, 1901 West Harrison Street, Chicago, IL, 60612-9985, USA

Department of Veterinary and Biomedical Sciences, University of Nebraska, PO Box 148, Clay Center, NE, 68933, USA

Abstract

Background

We analyzed the claim "mammography saves lives" by calculating the life-saving absolute benefit of screening mammography in reducing breast cancer mortality in women ages 40 to 65.

Methods

To calculate the absolute benefit, we first estimated the screen-free absolute death risk from breast cancer by adjusting the Surveillance, Epidemiology and End Results Program 15-year cumulative breast cancer mortality to account for the separate effects of screening mammography and improved therapy. We calculated the absolute risk reduction (reduction in absolute death risk), the number needed to screen assuming repeated screening, and the survival percentages without and with screening. We varied the relative risk reduction from 10%–30% based on the randomized trials of screening mammography. We developed additional variations of the absolute risk reduction for a screening intervention, including the average benefit of a single screen, as well as the life-saving proportion among patients with earlier cancer detection.

Results

Because the screen-free absolute death risk is approximately 1% overall but rises with age, the relative risk reduction from repeated screening mammography is about 100 times the absolute risk reduction between the starting ages of 50 and 60. Assuming a base case 20% relative risk reduction, repeated screening starting at age 50 saves about 1.8 (overall range, 0.9–2.7) lives over 15 years for every 1000 women screened. The number needed to screen repeatedly is 1000/1.8, or 570. The survival percentage is 99.12% without and 99.29% with screening. The average benefit of a single screening mammogram is 0.034%, or 2970 women must be screened once to save one life. Mammography saves 4.3% of screen-detectable cancer patients' lives starting at age 50. This means 23 cancers must be found starting at age 50, or 27 cancers at age 40 and 21 cancers at age 65, to save one life.

Conclusion

The life-saving absolute benefit of screening mammography increases with age as the absolute death risk increases. The number of events needed to save one life varies depending on the prospective screening subset or reference class. Less than 5% of women with screen-detectable cancers have their lives saved.

Background

Under ideal conditions, a woman participates in screening mammography after deciding that the potential benefit (increasing the length and quality of her life), considering the limitations, outweighs the expected harms and opportunity cost (time and money)

Furthermore, the components of informed medical decision-making regarding screening are not universally accepted

Because popular claims such as "All women of the appropriate age should be screened" are often linked with the mantra "good quality screening mammography saves lives"

Methods

Absolute benefit defined

Absolute risk is defined as the probability of a particular event occurring over a specified period

The second statistic, the number needed to treat to prevent one injury, is simply the reciprocal of the frequency form of the reduction in absolute risk

When the event is a death, the intervention causes a life-saving absolute benefit that reduces an absolute death risk. The absolute risk reduction equals the relative

Absolute death risk

The first step in calculating the life-saving absolute benefit is to estimate the absolute death risk from breast cancer. Returning to the automobile example, assume both restraint use (seat belts) and vehicle improvements (anti-lock brakes) contributed to a reduction in the annual automobile accident absolute death risk over the last 2 decades since the promotion of seat belt use. To calculate the absolute benefit of seat belts, RADR = RRR *

For breast cancer, we need to subtract the benefit of improved breast cancer treatment from the prescreening absolute death risk to get a new screen-free absolute death risk of breast cancer. Fortunately, these data are now available. Based on computer modeling, Berry et al estimated that screening mammography has been responsible for 46% (range 28%–65%) of the 30 percent breast cancer mortality reduction from 1975–2000, with the remaining 54% (range 35%–72%) due to therapy

Fletcher and Harris previously used the cumulative probability of breast cancer death to present absolute death risk

Therefore, to estimate the current therapy but screen-free absolute death risk, we first needed to calculate a risk difference = H - L, with H = higher 1980 prescreen death risk and L = lower 2004 current death risk. We started with the SEER 1978–1980 death risk per 1000 women including both DCIS and invasive cancer, e.g. for age 40 H = 5.95 (95% confidence interval (CI) 5.71–6.19). We subtracted the 2002–2004 death risk, L = 3.73 (95% CI 3.64–3.81), to obtain the risk difference or mortality improvement, H - L = 2.22. The 95% CI is 1.96–2.48 using Monte Carlo resampling. We multiplied the risk difference by the fraction attributable to therapy or 0.54. We then subtracted this therapy benefit (0.54 * 2.22 = 1.20) from the 1978–1980 death risk to obtain a new screen-free absolute death risk, e.g. 5.95 – 1.20 = 4.75 at age 40. We calculated the range (4.30–5.32) by using interval analysis.

Reduction in absolute death risk

With the new screen-free absolute death risk from breast cancer, we can calculate the life-saving absolute benefit of screening knowing the RRR since RADR =

Average benefit

The RRR from the analyses of the screening trials is due to women undergoing multiple or repeated screening mammograms over a median period of about 6 years. To estimate the number of mammogram examinations needed to save one life, the NNSR needs to be multiplied by the median average number of screening rounds of 4.25 (range 2–9)

Life-saving proportions

We also estimated the fraction or proportion of women with life-saving mammography in the two following groups: those who will develop cancer, and those who can have their cancer detected by screening mammography. The numerator of the life-saving proportion (LSP) is the screen-free absolute death risk multiplied by the RRR. The denominator is the SEER 2002–2004 cumulative 15-year probability of developing cancer, multiplied by the chance of having that cancer detected (mammography sensitivity), or the cumulative cancer detection rate (CCDR). Therefore, the LSP = RADR/CCDR. We assumed a cumulative sensitivity of 80% for repeated mammography over the period of screening

Life-saving percentages

We can summarize our results by converting the life-saving absolute benefit of mammography in the various screening subsets that we have analyzed into the life-saving percentage of events in each subset. These prospective subsets or reference classes

To simplify our results, we also generated scatter plots of death risk and development risk versus age in Excel (Microsoft, Redmond WA). We determined the best-fitting trend line by simple linear regression as defined by the highest coefficient of variation (R^{2}).

Results

Absolute death risk

Figure ^{2 }+ 5.63AGE - 129.6]/1000, R^{2 }= .99. The absolute death risk varies between 0.475% at age 40 to 1.274% at age 65. The best-fit equation = [-0.006AGE^{2 }+ 0.96AGE - 23.9]/1000, R^{2 }= .99. Between the starting ages of 40 and 55 (1.05%), the absolute death risk over 15 years more than doubles. Between the ages of 50 (0.883%) and 60 (1.177%), the absolute death risk is about 1%.

The life-saving absolute benefit or reduction in absolute death risk from repeated screening mammography according to age

**The life-saving absolute benefit or reduction in absolute death risk from repeated screening mammography according to age**. Data are from the Surveillance, Epidemiology, and End Results (SEER) Program including women ages 40 to 65 in five-year age increments. The first column in each age group shows the 2002–2004 cumulative 15-year development risk for breast cancer for average women. The 1978–1980 cumulative 15-year absolute death risk from breast cancer (2^{nd }column) is higher than the 2002–2004 death risk (3^{rd }column) due to screening effects and better therapy. We multiplied plausible values for relative risk reduction (RRR) of 10% to 30% from repeated screening by the screen-free absolute death risk (4^{th }column) to achieve estimates of the reduction in absolute death risk (RADR) from repeated screening (5^{th }to 9^{th }columns). The RADR is the same as the life-saving absolute benefit or absolute risk reduction. Starting at age 50 and 20% RRR, the RADR is 1.8/1000. The numerator is the same as lives saved per 1000 women screened. Between the starting ages of 40 and 55, the life-saving absolute benefit from mammography more than doubles, corresponding to the increased death risk. Between the starting ages of 50 and 60, the RRR from repeated screening is about 100 times the absolute risk reduction since the screen-free absolute death risk is approximately 1%.

Reduction in absolute death risk

Figure

The reciprocal of the RADR is the NNSR, which is 1050 (940–1160) at age 40, 570 (520–620) at age 50, and 430 (400–450) at age 60. This means that if screening starts at age 50, repeated screening of 570 mostly healthy women saves one life among the many women who develop cancer over 15 years. The survival percentage shown in Table

Frequency of survival for all women and women with cancer, deaths from breast cancer and lives saved from repeated screening mammography

**Frequency of survival for all women and women with cancer, deaths from breast cancer and lives saved from repeated screening mammography**. Starting at age 50, 51 out of 1000 women will develop breast cancer over 15 years (Figure 1). In terms of natural frequencies, the 1000 healthy average-risk women are the reference class. Figure 2 Group A shows 991 out of 1000 women will survive (not die from) breast cancer by age 65 without screening. Group B shows that 42 of the 51 breast cancer patients survive (positive framing) without screening. Therefore, nine women die (negative framing) without screening (Group C), and screening saves no lives (Group D). Assuming a 20% relative risk reduction (RRR) from repeated screening (row 3), mammography prevents two of nine deaths through earlier treatment, leaving seven cancer deaths. This means 44 of the 51 cancer patients and 993 of 1000 women will survive breast cancer.

Deaths from breast cancer and lives saved from repeated screening mammography

**Deaths from breast cancer and lives saved from repeated screening mammography**. Figure 3 is a magnification view of Groups C and D from Figure 2. Compared to Figure 1, the nine deaths without screening are the same as the screen-free absolute death risk, while the lives saved are the same as the corresponding reduction in absolute death risk. Four out of 1000 high-risk (double the average risk) women will have their lives saved assuming a 20% relative risk reduction (RRR).

Survival percentage: women not dying from breast cancer without and with repeated screening over 15 years.

**Age**

**No screening***

**10% RRR**
^{
†
}

**20% RRR**

**30% RRR**

**with screening**

**with screening**

**with screening**

**40**

99.52%

99.57%

99.62%

99.67%

**45**

99.32%

99.39%

99.45%

99.52%

**50**

99.12%

99.21%

99.29%

99.38%

**55**

98.95%

99.06%

99.16%

99.27%

**60**

98.82%

98.94%

99.06%

99.18%

**65**

98.73%

98.85%

98.98%

99.11%

* Survival percentage without screening is 100 times the complement of the screen-free absolute death risk from Figure 1.

^{† }Survival percentage with screening is the same as the reduction in absolute death risk in percentage form from Figure 1 added to column 2 of this table.

Average benefit

Table

Number of mammogram examinations needed to prevent one death.*

**Age**

**10% RRR**
^{
†
}

**15% RRR**

**20% RRR**

**Range 20%**
^{
‡
}

**25% RRR**

**30% RRR**

**40**

11050

7370

5530

2820–11630

4420

3680

**45**

7700

5130

3850

1980–8070

3080

2570

**50**

5950

3970

2970

1540–6160

2380

1980

**55**

5000

3330

2500

1320–5100

2000

1670

**60**

4460

2970

2230

1200–4450

1780

1490

**65**

4120

2750

2060

1130–4020

1650

1370

* Number of examinations is 5.25 times the number need to screen repeatedly (NNSR), which is the reciprocal of the reduction in absolute death risk (RADR) in Figure 1. The number needed to screen once (NNSO) is equivalent to the number of examinations if the benefit is the same for all mammograms. The average benefit of a subsequent screen is the inverse of the NNSO.

^{† }The 5.25 median screens from the trials are responsible for the relative risk reduction (RRR) for repeated screening. We assumed the baseline exam has twice the benefit of a subsequent exam

^{‡ }The range is calculated by using interval analysis.

Life-saving proportions

Finally, Table

Life-saving proportion: women with screen-detected cancers that have their lives saved by mammography.

**Age**

**Development risk/1000***

**CCDR/1000**
^{
†
}

**Death risk/1000**
^{
‡
}

**10%**

**RRR**
^{
§
}

**15%**

**RRR**

**20%**

**RRR**

**20%**

**NND**
^{
∥
}

**25%**

**RRR**

**30%**

**RRR**

**20%**

**RRR**

**No Rx**
^{
¶
}

**%**

**%**

**%**

**%**

**%**

**%**

**%**

**40**

31.9

25.5

4.8

1.9

2.8

3.7

27

4.7

5.6

4.7

**45**

41.9

33.5

6.8

2.0

3.0

4.1

25

5.1

6.1

5.1

**50**

51.0

40.8

8.8

2.2

3.2

4.3

23

5.4

6.5

5.3

**55**

59.2

47.3

10.5

2.2

3.3

4.4

23

5.5

6.7

5.2

**60**

64.4

51.5

11.8

2.3

3.4

4.6

22

5.7

6.9

5.1

**65**

66.3

53.0

12.7

2.4

3.6

4.8

21

6.0

7.2

5.0

* Cumulative 15-year development risk for breast cancer for average women, from Figure 1

^{† }Cumulative cancer detection rate (CCDR) over 15 years assumes a cumulative sensitivity of 80% from repeated screening.

^{‡ }Breast cancer screen-free absolute death risk is from Figure 1.

^{§ }The proportion is the screen-free absolute death risk multiplied by the relative risk reduction (RRR), and then divided by the CCDR.

^{∥ }Number of cancers needed to be detected (NND) is the reciprocal of the life-saving proportion.

^{¶ }Assumes maximum prescreening era (1978–1980) 15-year absolute death risk, with no adjustment for improved therapy.

Life-saving percentages

Using Figure

Will screening mammography save my life?

**Will screening mammography save my life?**. The answer depends on the reference class. The life-saving absolute benefit of mammography increases as the absolute death risk in the woman's prospective screening subset increases. For women starting at age 50 and assuming a 20% relative risk reduction (RRR), the chance that "mammography saves lives" appears as the bottom row for each of the five screening subsets. For instance, mammography saves 4.3% of screen-detectable cancer patients' lives (subset B). These life-saving percentages correspond to the RRR (A: Breast cancer deaths), life-saving proportions (B&C), reduction in absolute death risk (D: Repeated screening mammography – see Figure 1), and average benefit (E: Single mammogram). For a 20% RRR, the underlying absolute death risk (middle row) is five times the life-saving percentage. The number of events needed to save one life in each subset is the reciprocal of the life-saving percentage and increases from the smallest subset A (5) to the largest subset E (2970). Potential screening harm (top row, 100% minus bottom row) for women with cancer includes overdiagnosis, overtreatment, and delayed diagnosis. The potential harm for healthy women includes false-positive evaluations and biopsies, screening associated anxiety, and radiation-induced cancer.

Discussion

We have tried to explain the purpose of mammography by answering the question: how often will screening mammography "save" a woman's life? We have shown that since the RADR = RRR * absolute death risk, the answer for women undergoing repeated screening increases with the age-related absolute death risk. For the age range 50 to 60, the screen-free absolute death risk for average women is approximately 1%, so the RRR from repeated screening is about 100 times the RADR or absolute risk reduction.

The life-saving absolute benefit also depends on the prospective screening subset or reference class to which a woman will belong. For women who will develop cancer, the absolute death risk increases, so the life-saving absolute benefit of mammography increases. Women who will die of cancer have an absolute death risk of 100%, so the life-saving absolute benefit is the maximum or the RRR. For the base case age 50 and assuming a 20% RRR, women with a screen-detectable cancer have a 4.3% chance of truth for the claim that "screening mammography saved my life."

We can express the life-saving absolute benefit using percentage or frequency forms. The low extreme is the average benefit from a single mammogram of 1/11050 screens (0.009% at age 40/10% RRR). The high extreme is the life-saving proportion for women with a screen-detectable cancer of 1/1370 (7.3% at age 65/30% RRR). For the base case 20% RRR, the life-saving absolute benefit of a single mammogram is 1/2970 screens, or 0.034%. For multiple or repeated screening, the RADR is 1.8/1000, so the life-saving percentage is 0.18%. Viewing these results from a different perspective of the number of events needed to save one life in each screening subset, the following values are equivalent: five women dying of breast cancer, 23 women with screen-detectable cancers, 29 women with cancers present, 570 women screened repeatedly, and 2970 women screened once. In other words, by subtracting the one life saved in each prospective screening subset, there is no life-saving absolute benefit for 22 women with screen-detectable cancers, or for 2969 women screened once.

Prior analyses

Our findings are close to other estimates of absolute benefit from screening mammography, which will vary due to the RRR and the cumulative period used. For instance, the SEER 2002–2004 10-year cumulative risk of breast cancer death from age 40 to 50 is 0.194%, versus 0.373% or 3.73/1000 (Figure

Tabar et al found that the NNSR estimate from a single trial without any analysis of the effect of a woman's age was 465 (95% CI 324–819) over 20 years, given a 30% RRR, while the number of mammogram examinations was 1499 (95% CI 1046–2642)

Mammography benefit

First, we have quantified how the life-saving absolute benefit of mammography gradually increases with age, which is important for younger women considering the age at which to begin screening

Our analysis of "mammography saves lives" addresses a knowledge gap and may facilitate better information exchange before women initiate screening

Consequently, women should have improved insight and reduced anxiety with a balanced presentation of the absolute benefit of mammography in terms of the diagnosis risk as well as the death risk

Screening promotion

One reason for the public's confusion is that screening statistics can be difficult for even highly educated physicians to understand, and this innumeracy presents a roadblock to consumer insight about the true benefit of mammography

Figure

Besides the opportunity cost of time and money (buying the ticket), authorities acknowledge that screening mammography harms include a 30% increase in overdiagnosis and overtreatment, delayed diagnosis, and radiation-induced cancers

Instead of providing professional even-handed advice, breast radiologists usually enthusiastically promote expensive new screening technologies developed by the medical imaging industry despite the drawbacks

Consumer education

Voluntary informed participation requires that women and their physicians understand that earlier detection and treatment of breast cancer through screening mammography (and possibly through other imaging technology) certainly saves

Frequency of lives saved from screening mammography for 1000 women in three prospective screening subsets

**Frequency of lives saved from screening mammography for 1000 women in three prospective screening subsets**. Figure 5 is a magnification view for subsets B, C, and D from Figure 4 but with 1000 women in each reference class. The frequency of breast cancer deaths without screening and the frequency of lives saved from mammography are equivalent to the percentages in Figure 4. The top row is the difference, or the breast cancer deaths despite screening in each subset. Compared to Figure 3, the nine deaths without screening and the seven cancer deaths and two lives saved with screening starting at age 50 and 20% relative risk reduction are equivalent.

We have shown that between the starting ages of 50 and 60, the RADR or absolute risk reduction is only about 1% of the RRR. In order to address the problem of innumeracy, health organizations should advertise the absolute death risk and the absolute benefits along with the corresponding RRR

Analysts can best communicate statistical information by using natural frequencies (event counts using one reference class) or clarifying the reference class

A comparison with equivalent risks will help put the death risk from breast cancer in perspective. For example, the cumulative death risk from lung cancer is 0.93% or 9.3/1000 between the ages of 50 and 65

Limitations

From the RCT survival curves, analysts cannot tell if the mortality reduction associated with screening mammography is due to either a "cure" or "reduction in hazard". We have assumed that a "life saved" means screening helps cure one woman with breast cancer who would have otherwise died from the disease without screening. The end result from a cure is that a woman lives a normal life span beyond the point of expected death from breast cancer. However, all women with cancer may theoretically benefit from screening mammography through slowing the disease and therefore slightly prolonging their lives. These women would experience life extension but would still die from breast cancer. The source of the survival benefit from screening mammography may lie somewhere in between individual life saving and multiple smaller life extensions, so the distribution of women actually benefiting in some way from screening (although the total effect is the same) is not known

In economic theory, the marginal cost of a defensive measure taken to reduce the risk to health and life must be less than the marginal benefit from the reduced probability of disease and death, or the action should not be undertaken

Our study is limited because the screening effect on the absolute risk of death from any cause may be more meaningful than the screening effect on breast cancer mortality from the RCT

Conclusion

We have shown how the life-saving absolute benefit of screening mammography gradually increases with age as the screen-free absolute death risk increases, since RADR = RRR * absolute death risk. For 50- to 60-year-old women, the screen-free absolute death risk over 15 years is approximately 1%, so the RRR for repeated screening mammography is about 100 times the RADR or absolute risk reduction. The chance that "mammography saves lives" depends on the absolute death risk in the prospective screening subset or reference class to which a woman belongs. For a woman in the screening subset of mammography-detectable cancers, there is a less than 5% chance that a mammogram will save her life. By comparing screening mammography's life-saving absolute benefit with its expected harms and her opportunity cost, a well-informed woman along with her physician can make a reasonable decision to screen or not to screen for breast cancer.

Abbreviations

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

JDK conceived the study, developed the methodology, and drafted the manuscript. JEK performed the statistical analysis. Both JDK and JEK analyzed the results, and revised and approved the final manuscript.

Acknowledgements

This study did not receive any financial support. The authors thank the multiple reviewers who contributed to improving this manuscript.

Pre-publication history

The pre-publication history for this paper can be accessed here: