The Swedish Two-County Trial has been described previously. Briefly, 55,985 women aged 40–74 were allocated to invitation to periodic mammographic screening (active study population, ASP) and 77,080 to no invitation (passive study population, PSP). Women in the ASP aged 40–49 at allocation were offered screening on average every 24 months. Women aged 50–74 were offered screening every 33 months. After 6–7 years, the PSP was invited to screening and the screening phase of the trial closed,^{15} but follow-up continued for deaths from breast cancers diagnosed during the screening phase. Subjects were randomized between 1977 and 1981 and spent an average of seven years in the screening phase of the trial. Thus, the screening in the trial took place between 1977 and 1988. In this paper, we have data on deaths till the end of 1998, a maximum of 21.5 years follow-up.

The UK National Breast Screening Programme was launched in 1988, although only approximately 2.5% of the target population was screened in that year. We therefore consider the screening epoch to be 1989 and thereafter. The programme was built up during the period 1989–1993. It offers three-yearly mammography screening. Originally, the age range intended was 50–64 years. In 2002–2004, this was expanded to 50–70 years, and a further expansion to the range 47–73 years is in progress. We have data by five-year age group and calendar year on breast cancer incidence between 1974 and 2003 and breast cancer mortality between 1974 and 2004, with the corresponding population denominators.

For the estimation of the absolute benefit of screening from the Two-County Trial, we used the same methodology as described previously,^{1} but applied it specifically to the age group 50–69 at randomization, to correspond approximately to the target group of the UK programme. Essentially we established the deficit in deaths from breast cancer in the study group compared with the control group and the numbers in the study group who were screened. Dividing the latter by the former gives an estimate of the number of women needed to screen to save one life. For the estimation of the benefit from the English Breast Cancer mortality data, we used Poisson regression to compare the difference in breast cancer mortality for ages 50–69 years between 1995 onwards and pre-1989 with that observed for other age groups. We calculated the absolute number of deaths prevented as the difference between those observed and those expected on the basis of the mortality changes in age groups <50 and 70 years or more. This is conservative because some of the deaths observed from 1995 onwards will be from tumours diagnosed before 1989, when there was no screening, and because some deaths in the period 1989–1994 will have been prevented by screening.^{2}

The estimation of overdiagnosis is more complicated. In the Swedish Two-County Trial, we first estimated the expected incidence in the absence of screening as follows: from the incidence in the control group, we used Poisson regression to estimate the trend in incidence in the first six years of the trial, before any screening of the control group in this age group took place in order that our estimate of the underlying incidence trend was not contaminated by screening. From the trend we estimated the expected average incidence in year 4 after randomization, the midpoint of the screening phase of the trial.

Subjects in the ASP were invited to one prevalence screen and, on average, two incidence screens. Let *P* be the observed prevalence at first screen in the ASP, *Q* the observed prevalence at the first screen of the PSP at closure of the screening phase, *P*_{T} the unknown prevalence of true cases at first screen in the ASP, *P*_{O} the unknown prevalence of overdiagnosed cases at first screen in the ASP, *S*_{T} the rate of true cases at incidence screen, *S*_{O} the unknown rate of overdiagnosed cases at incidence screen, *I* the average annual incidence in the ASP during the screening phase, *I*_{e} the expected average annual incidence from PSP, *t* the relative incidence of breast cancer after seven years (i.e. at the end of the trial), taking into account age and time trends. As entry to the trial was in the period 1977–1981, this seven-year period pertains mostly to the early 1980s, where *a*_{1} is the proportion attending first screen of ASP and *a*_{2} is the proportion attending incidence screens of ASP.

The following equations will therefore hold:

Here we are assuming that the same rate of overdiagnosed cases applies to the first screen of the ASP and PSP (approximately seven years older at the time of first screen), but that the true cases will reflect the trend with age and time. After excluding the prevalence screen, at which most length bias or overdiagnosis is likely to take place,

^{5,7,8} the age at diagnosis in the ASP was 1.2 years on average younger than that in the PSP, suggesting a 1.2 year correction for overdiagnosis in equation (

1). The exclusion of all of the prevalence screen cases in the estimation of lead time is likely to be conservative.

*P*,

*Q*,

*I*,

*a*_{1} and

*a*_{2} were all directly observed from the trial data.

*I*_{e} was observed in the PSP before the prevalence screen of this group and

*t* was estimated from changes in breast cancer incidence by age and time from Swedish national statistics.

^{16,17} In equation (

1) we approximated the average expected incidence by the fitted incidence in year 4, the midpoint of the seven-year screening phase. Equations (

1)–(

3) were then solved for the three unknown quantities

*P*_{O},

*P*_{T} and

*S*_{O}.

For the estimation of overdiagnosis from the English incidence data, we analysed age groups <45, 45–49, 50–64, 65–69 and 70+ separately. We first estimated the log–linear trends in incidence from 1974 to 1988, before the screening programme started, using Poisson regression. We then projected these to estimate the expected incidence in 1989–2003. To adjust for any non-linear trends in log incidence, we re-estimated the expected incidence relative to age group <45, in which very little screening took place (some women receive their first invitation before age 50 but very few before age 45). This entailed dividing the expected numbers by the relative excess for the under 45 age group.

Overdiagnosis was calculated as the observed cases in the age groups 45–49 and 50–64, minus any deficit in age groups 65–69 and 70+, which is the sum of the observed minus expected figures for the four age groups.