Introduction

Observational studies have been conducted since the 1980s to evaluate the effectiveness of breast cancer screening programs. These studies compare the risk of breast cancer death between women attending and not attending screening mammography. Case-control studies retrospectively assess the attendance at screening mammography of case women who died from breast cancer and of control women who were still alive when case women died from breast cancer. Cohort studies prospectively compare the risk of breast cancer deaths of women attending screening to the risk of women who do not attend screening. However, these studies are prone to self-selection bias (or “healthy user bias”). Women not attending screening are generally less educated and less health-aware, are more deprived, and have more comorbidities or disabilities, all of which are associated with increased risks of developing more aggressive cancers, as well as increased risk of breast cancer mortality and all-cause mortality. These increased risks are independent of the effect of screening.1–3 Because of this bias, observational studies tend to overestimate the benefits of screening.4

To address the issue of self-selection, a correction of relative risk estimates was proposed in 2002.5 The correction is based on the quantity Dr which is the ratio of breast cancer mortality rates in women invited but not attending screening to rates in a similar population of women not (yet) invited to screening. Authors willing to correct their relative risk estimates have to select a Dr quantity from another study, which included a group of women invited to screening but who did not participate and a group a women not (yet) invited to screening. Correction for self-selection has most often led to corrected relative risk estimates closer to the 25% reduction of breast cancer death associated with invitation to screening reported by Swedish randomized trials.6,7

The first Dr quantity estimate of 1.36 was derived from Swedish randomized trials.5 However, the estimate could not take heed of most recent results of the Swedish Malmo and Goteborg trials. In addition, the Dr correction method has never been tested against robust methods like the use of an instrumental variable associated with screening mammography but not causally associated with breast cancer death,8 or the use of an off-target outcome, ie, an outcome on which screening mammography has no influence.9 Screening mammography does not affect the causes of death other than breast cancer, and deaths from causes other than breast cancer are 20–50 times more common than deaths from breast cancer. A systematic review of 18 cohort studies on screening mammography attendance and the risk of breast cancer used non-breast cancer death has an off-target outcome. The review found that women attending screening mammography had a 45% reduction in the risk of breast cancer death as well as in their risk of death from any cause.10 Hence, the reduced risk of breast cancer death associated with screening attendance found in cohort studies could be due to self-selection. It also prompted the hypothesis that Dr quantities used to date, including Dr quantities derived from Swedish trials, cannot fully correct for the effect of self-selection on reductions in the risk of breast cancer reported by observational studies.

Although they have been conducted some twenty to forty years ago, the Swedish randomized trials remain the principal justification for breast screening activities. The objective of this study was to estimate the amount of self-selection present in Swedish randomized trials and in observational studies aimed to evaluate screening mammography effectiveness and to estimate Dr quantities that may correct for this bias.

Methods

The parameters, including self-selection and Dr quantities, derived from randomized trials and cohort studies were first described, after which the study unfolded in four successive steps: (1) the computation of a Dr quantity based on most recent results of Swedish trials, (2) the quantification of self-selection in cohort studies on screening mammography effectiveness, (3) the determination of a Dr quantity able to remove self-selection in these cohort studies, and (4) a systematic review of Dr quantities used in observational studies.

Self-Selection and Dr Quantities

A typical randomized trial for the evaluation of the reduction in the risk of cancer-related death associated with invitation to screening is displayed in Figure 1.

Figure 1 Randomised trials on screening mammography considered as two prospective cohorts with same follow-up (Keys: R stands for rates of No. of breast cancer deaths/ No. women in a group or subgroup; RR stands for relative risk).

The effectiveness of screening mammography is the relative risk RRITT equal to RI/RC, where ITT stands for intent-to-treat, RI is the breast cancer death rate in the intervention group, and RC is the breast cancer death rate in the control group.

The intervention group can be considered a cohort study of women invited to screening, with a subgroup A electing to attend screening and a subgroup N electing to not attend screening. The relative risk RR(A vs N) = RA/RN is the risk of breast cancer death in women attending screening compared with women not attending screening. RR(A vs N) could be the main outcome if the study was a cohort study that included only the intervention group.

By virtue of randomization, the control group includes a subgroup of pseudo attenders (A’) who would attend screening if they were invited to do so as well as a subgroup of pseudo non-attenders N’ who would not attend screening if they were invited to do so. Because of randomization, the rate of breast cancer death RN’ in the subgroup of pseudo non-attendees is the same as that in the subgroup of non-attendees, ie, RN’ = RN. In contrast, the rate of breast cancer in the subgroup of pseudo-attendees RA’ should be equal to or lower than the rate of breast cancer death in subgroup of attendees RA.

From Figure 1, one can compute an estimate of self-selection bias, which is the relative risk RA’/RN. This relative risk is an unbiased estimate of the risk of breast cancer death of women who would attend screening if invited to do so, to the risk of breast cancer death of women who would not attend screening if invited to do so. One can also compute the Dr quantity, which is the relative risk RN/RC.

RRITT is not biased by self-selection, whereas RR(A vs N) is biased. Using data from the intervention group only, RRITT can be estimated from RR(A vs N) after correction for self-selection using the Dr quantity and formulas of Duffy et al (2002). The Dr quantity and self-selection bias are algebraically related, and the estimated RRITT can be computed using the self-selection quantity, participation rate, and crude risk estimate but with equations somewhat different from those published by Duffy et al (2002)5 (not shown).

Step 1

The first step consisted of computing self-selection and Dr quantities using the most recent data from four Swedish randomized trials.11–14 After data extraction and adjustment for unequal sizes in the intervention and control groups, the rates of breast cancer death were calculated for each group and subgroup. In the publication of 1995, the Malmö trial did not report women attending or not attending screening.12 We assumed that the proportion of breast cancer deaths in attendees and non-attendees was the same as in Andersson et al 1988.15 The weighted average attendance rate for the four Swedish trials was 85%.

We corrected the number of breast cancer deaths in the control groups by multiplying the reported number of breast cancer deaths by 0.90, because 10% of breast cancer deaths in the two-county trial were due to cancers found during the first screening of control women.6 The Stockholm and Goteborg trials did not report the percentage of breast cancer deaths linked to breast cancer diagnosis during the first screening round in the control group. For the Malmö trial, the correction was 0.955 because the first screening of the control group was approximately 45% of the total number of control women included in the trial.16

Step 2

The second step involved quantifying self-selection in the cohort studies that evaluated screening effectiveness. In the aforementioned review, the random-effect summary relative risks RR(A vs N) attenders vs nonattenders were 0.55 (95% CI: 0.50–0.60) for breast cancer mortality in 13 cohort studies, and 0.54 (0.50–0.58) for all-cause mortality in 10 cohort studies.10 The summary relative risk of RRITT for all-cause deaths reported by Swedish trials was 0.98 (0.96–1.00).7 Because screening mammography has no effect on all-cause death, the RRITT of all-cause death is the benchmark of RR(A vs N) in the absence of self-selection. The formulae proposed in Refs.9,17 provided an estimate of the amount of self-selection, ie,

RRITT/ RR(A vs N), Where

RRITT is the relative risk of all-cause death of 0.98 associated with invitation to screening reported by Swedish randomized trials,7 and RR(A vs N) is the relative risk of all-cause death of 0.54 associated with screening attendance reported by cohort studies.10

Step 3

The third step was to determine which Dr quantity would be adequate for observational studies that evaluated the effectiveness of screening mammography. Using the linear relationship between self-selection and Dr quantities found in Swedish trials (step 1), and the self-selection from cohort studies (step 2), we computed the Dr quantity specific to observational studies.

Step 4

The fourth step was a systematic search of observational studies recorded in PubMed that were corrected for self-selection, following the method of Duffy et al.5 The literature search has been described elsewhere.10 In brief, case-control and cohort studies had to be published after 2001 and conducted in women invited to screening or where screening was widely available and recommended. Studies with cross-sectional or unclear designs were excluded.

Corrections for self-selection could follow the potential attendance approach (RR2 of Duffy et al, 2002), that is, the relative risk estimate for women willing to attend screening if invited. It could also follow the intent-to-treat approach (RR1 of Duffy et al, 2002), which is the relative risk estimate for all women invited to screening. Roder et al (2008)18 and Dunn et al (2021)19 reported a corrected odds ratio of 0.71 but not Dr quantities or attendance rates. We worked out the correction assuming that the potential participants method had been used, using attendance rates in the control groups and a Dr quantity of 1.11. Algood et al (2008) reported a corrected odds ratio of 0.65 but did not report the Dr quantity used or the attendance rate.20 We used an attendance rate of 75% as reported by Otten et al, 2008.21 Working out the correction, we estimated that Algood et al (2008) most likely used a Dr quantity of 1.36, as suggested by Duffy et al (2002).5

Statistical Analysis

Data handling was mentioned in step 4, and meta-analysis computations followed the methods described in ref.10

Results Step 1

Table 1 shows the numbers of randomized women and breast cancer deaths in Swedish randomized trials after subtraction of cancer deaths due to cancers diagnosed at the first invitation to screen for control women. The distributions of women and breast cancer deaths in the subgroups of attendees/non-attendees and pseudo-attendees/pseudo-non-attendees are detailed in Tables 2 and 3. The key parameters in Table 4 were derived from Tables 2 and 3. The summary effectiveness RRITT of 0.82 (0.72–0.93) was computed from the rates of breast cancer deaths in the intervention and control groups. The estimated summary relative risk RR(A vs N) of 0.36 (0.29–0.44) was computed using intervention groups as cohort studies. Hence, in the absence of control groups, intervention groups of Swedish trials taken as cohort studies would obtain results suggesting breast cancer mortality reductions of the order of 64% among women attending screening. The summary self-selection quantity of 2.10 indicates that in these four randomized trials, the risk of breast cancer death in the intervention groups was approximately two times higher in non-attendees than in attendees, and this increased risk was independent of the effects of screening.

Table 1 Swedish Randomized Trials on Screening Mammography: Results Corrected for Differences in Group Sizes and for Extra Breast Cancer Deaths in Control Groups

Table 2 Subgroups of Intervention Groups

Table 3 Subgroups of Control Groups

Table 4 Quantities Derived from the Four Swedish Randomized Trials On Screening Mammography

Table 5 Observational Studies on Attendance to Screening Mammography and the Risk of Breast Cancer Death

A Dr quantity of 1.78 denotes the risk of breast cancer death among invited women not attending screening compared to women in the control group. The linear correlation between self-selection (SS) and Dr quantities is

Cohort studies evaluating screening effectiveness typically assess the relative risk of cancer death among women attending screening compared to women not attending screening (RR(A vs N)). Using Dr quantities in Table 4, attendance rates specific to each trial or for all trials (Table 2), and Duffy et al (2002) equations, one can find back the screening mammography effectiveness. For instance, for all four trials,

a result identical to the summary relative risk RRITT of 0.82 reported in Nyström et al.7

Step 2

This step used summary relative risks from cohort studies on screening mammography effectiveness,10 which were 0.55 (0.50–0.60) for breast cancer death and 0.54 (0.50–0.58) for all-cause death.

Considering all-cause mortality as an off-target outcome for screening mammography, the self-selection bias was (0.98/0.54) = 1.78, which means that in cohort studies, the risk of breast cancer death was 1.78 higher in non-attendees than in attendees, and this increased risk was independent of the effects of screening.

Step 3

Using the linear relationship found in step 1 and the self-selection quantity from step 2, the average Dr quantity for cohort studies can be estimated as:

Step 4

Fourteen case-control and five cohort studies reported corrected relative risk estimates using the Duffy et al method (Table 5).18,19,22–38 The median attendance rate to screening mammography was 74% and the relative risk estimates of the 19 studies ranged from 0.35 to 0.65, with a summary risk estimate of 0.51 (95% CI: 0.47–0.55).

The corrected relative risk estimates ranged from 0.50 to 0.96, but approaches (intent-to-treat vs potential participation approach5) for correction varied across studies. Occasionally, the approach or Dr quantities used have not been reported. When known, Dr quantities ranged from 0.87 to 1.56, with a median of 1.16 (IQR: 1.11–1.28). In three instances, Dr quantities were less than 1.0, suggesting that women attending screening would have a greater risk of cancer death than those who do not attend screening. An inverse correlation was found between Dr quantities selected by the authors and relative risk estimates (correlation coefficient r = 0.52, slope of the linear trend: −0.82; 95% CI: −1.58 to −0.06; p = 0.035), indicating that there was an inclination to select Dr quantities closer to 1.0, if the relative risk estimates for breast cancer mortality tended to be closer to 1.0.

Discussion

Our study defined self-selection and Dr quantities in the context of randomized trials and cohort studies. Two types of cohorts were studied: intervention groups (ie women invited to screening) of Swedish randomized trials and cohort studies conducted in women who were invited to screening. The main results and consequences of our study are summarized in Figure 2.

Figure 2 Summary of study and main conclusions.

Our study suggests that in populations where 80% or more of women attend screening, as in Swedish trials, women not attending screening have an approximately 2.1-fold increased risk of death from breast cancer. This increased risk is independent of screening effects. When attendance rates diminish, non-attendees are a less extreme subgroup than attendees, which accords with a smaller self-selection quantity of about 1.78 found in cohort studies where the median attendance rate was 74%.

The summary Dr quantity estimated from Swedish randomized trials was 1.78. In the same trials, Duffy et al found a summary Dr quantity of 1.36. This difference was mainly due to two factors. First, Duffy et al did not use the most recent results of the Goteborg and Malmö trials. Second, Duffy et al did not exclude breast cancer deaths associated with breast cancers diagnosed at first screening of control groups.7,14,39 The high Dr quantity of 1.94 we estimated for the two-county trial indicates that compared to the control group, invited women who did not attend screening had a 2-fold increase in their risk of breast cancer death. In this trial, the hazard ratio of breast cancer-specific survival of non-attendees versus the control group was 1.97,40 which supports the likelihood of our estimates.

Duffy’s correction method is valid provided that the Dr quantity specific to each study is known. However, the 19 case-control and cohort studies that corrected for self-selection used Dr quantities usually less than 1.28, which was too small to achieve full correction of the bias. In real-world settings, knowledge of the Dr quantity appropriate for a specific observational study is rare. Because there is considerable uncertainty related to the extent of self-selection in any particular observational study,33Dr quantities have been highly variable between studies. Publications have provided few indications for reasons backing the selection of a particular Dr quantity. Moreover, the variation in the selected Dr quantities was correlated with the observed relative risk estimates, indicating that the authors may have chosen their correction factor post hoc.

An alternative to correcting for self-selection is to take the relative risk of all-cause death (0.54 (95% CI: 0.50–0.58)) as an unbiased benchmark result for observational studies (Figure 2).9,17,41 Uncorrected relative risk estimates (odds ratios or relative risks) equal to or greater than 0.54 would be the consequence of self-selection and equivalent to corrected relative risk estimates of 1.00 or greater. Similarly, if the 95% confidence interval upper bound of an uncorrected relative risk estimate is less than 0.54, it could be considered statistically significant (p < 0.05). Therefore, only five or 19 observational studies would have a statistically significant result, suggesting a lower risk of breast cancer death associated with screening attendance. In addition, considering all 19 observational studies, the summary relative risk estimate of 0.51 (0.47–0.55) suggests a non-significant 6% (95% CI: 0.93–1.05; ie, 0.51/0.54; 0.55/0.54; 0.47/0.54) decrease in the risk of breast cancer death associated with screening attendance.

Another alternative is to have recourse to an instrumental variable, ie, an exposure variable that is correlated with the exposure of interest but not causality associated with the outcome, for instance general practitioner preference or dental care habits.8

In 2015, a viewpoint issued by a group that met the International Agency on Cancer Research (IARC) recommended observational studies to evaluate the effectiveness of screening mammography.42 However, because of the intractability of biases affecting observational studies, an expert group on breast screening convened by the IARC in 2002 recommended against the use of observational studies to evaluate the effectiveness of mammography screening.43 The IARC 2002 recommended to monitor decreases in incidence rates of advanced cancers, which should be seen after screening introduction. A key advantage of this indicator is its independence from the influence of improved treatment on cancer mortality. Based on our study, the 2002 IARC recommendations should be reinstated.

Ethics Statement

The study was entirely based on the published literature and did not require ethical approval.

Funding

The International Prevention Research Institute funded works required by this study. This research received no specific grants from any funding agency in the public, commercial, or not-for-profit sector.

Disclosure

The author reports no conflicts of interest in this work.

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