br The linear regression models are applicable
The linear regression models are applicable over the range of observed recall rates, but not at lower or higher values. Note that the models predict impossible biopsy rate values of 6.74 per 1,000 and 5.41 per 1,000 for prevalent and incident screens when extrapolated back to 0% recall rates.
Figure 1 (a) Scatterplot of prevalent (first) screen needle biopsy rate for individual units versus recall rate with 95% confidence band. (b) Scatterplot of incident (subsequent) screen needle biopsy rate for individual units versus recall rate with 95% confidence band.
An alternative non-linear model (used later to examine the association between cancer detection rate and biopsy rates)
which goes through the origin (0,0) estimates that biopsy rate (p¼1,000) ¼ 0.92(1e0.94recall rate (%)). The model pro- vides meaningful biopsy rates over any recall rate and over the range of observed recall rates the estimated needle bi-opsy rate using this model is almost the same as for the linear model. This model can be used when we consider the association between cancer detection rates and biopsy rates as non-linear and where the cancer detection rate tends to plateau at increasing biopsy rates.
In summary, the association between biopsy and recall rates over the observed range of data can be modelled with a linear relationship, with increasing numbers of recalls leading to increasing numbers of biopsies. The rate of bi-opsies and therefore associated assessment workload per woman screened tends to be much greater at prevalent screens.
Invasive cancers detected per women having biopsy at different recall rates
Table 1 and Fig 2 show the number of biopsies per invasive cancer detected at different recall rates. As the recall rate increases there is only a small increase in invasive cancer detection rate, which leads to an increase in the number of women undergoing biopsy per invasive cancer
detected, and therefore, a diminishing return with increasing recall rate. As the recall rate is continually reduced, the number of women undergoing biopsy per cancer detected would be expected to decrease to nearly 1.0 as only features with a very high probability of being cancer (e.g., spiculate mass) would be recalled and biopsied. From linear regression models, it Cefepime can be predicted that at preva-lent screens, the number of women undergoing biopsy per invasive cancer detected increases from 4.6 per invasive cancer at a recall rate of 5% up to 8.1 per invasive cancer at 10%. At incident screens, a similar pattern of increasing numbers of biopsies per invasive cancer detected is seen.
Cancer detection rates and biopsy rates and non-linear models
Table 2 shows the results from the non-linear models for the predicted invasive cancer detection rate and the non/ micro-invasive cancer detection rate per woman at different levels of biopsy rate for prevalent and incident screens. The non-malignant/benign biopsy rate per 1,000 is simply the rate of women undergoing biopsy minus the cancer detection rate. These models examining the associ-ation between cancer detection and biopsy rates are non-linear and if extrapolated go through the origin (0, 0), where no biopsies are associated with no cancers detected. The fitted models (see Electronic Supplementary Material
Number of invasive cancers detected per women having biopsy at different recall rates for prevalent (first) and incident (subsequent) screens.
Recall group Recall rate (units) Mean recall Invasive cancers Women No. of biopsies to detect
Figure 2 Number of women biopsied per invasive cancer detected by recall rate at prevalent (first) and incident (subsequent) screens.
Appendix B) predict at a prevalent screen biopsy rate of 10 per 1,000 a cancer detection rate of 4.18 per 1,000, and a non-malignant/benign biopsy rate of 5.72 per 1,000 (57% of biopsies are non-malignant/benign). This rises to 86% of biopsies being non-malignant/benign at a biopsy rate of 60 per 1,000. The models also suggest that at a prevalent screen biopsy rate of more than 40 per 1,000 there is little increase in invasive cancer detection rate. The incremental gains at this point become very small. Increasing biopsy rates from 40 to 50 per 1,000 (an increase of 10 per 1,000) only increases the cancer detection rate by 0.25 per 1,000, which is 40 non-malignant/benign biopsies per additional cancer detected. In contrast, at lower biopsy rates, increasing biopsy rates from 10 per 1,000 to 20 per 1,000 detects 2.13 per 1,000 extra cancers, which is just under four biopsies per extra cancer.
Modelled non-malignant/benign biopsy rates for preva-lent screens and incident screens are shown in Fig 3a and 3b, respectively. Fig 3a shows how the non-malignant/ benign biopsy rate at prevalent screens increases rapidly from about five per 1,000, in contrast to incident screens