Quantitative Target Sizes for Breast Tumor Detection Prior to Metastasis: A Prerequisite to Rational Design of 4D Scanners for Breast Screening

It is important to determine a breast cancer tumor target size for new screening equipment and molecular detection. Records of women aged 40–69 years diagnosed in 1988–1997 with a nonmetastasized, node-negative, or node-positive T1-stage breast cancer were abstracted from the Surveillance, Epidemiology, and End Results (SEER) public-use database. The linear, Gompertzian, lognormal, and power-exponential models of the effect of tumor size on breast cancer specific mortality were compared using corresponding transforms of size in multivariate Cox proportional hazard models. Criteria for comparison were the linearization of the size transforms and the Nagelkerke R² _N index for the Cox models. Our results show that the assumption of a linear effect of tumor size was rejected by the linearity test (P=0.05). The Gompertzian, lognormal, and power-exponential transforms satisfied the test with P-values of 0.08, 0.29, and 0.14, respectively. The corresponding R² _N were 0.08410, 0.08420, and 0.08414, respectively, showing a marginally best fit with the lognormal model, which was selected as a model for small tumors. The lognormal function with unadjusted crude death rates gave a lognormal-location parameter of 25 and shape parameter of 1.7, while the corresponding values in multivariate models were 18 and 2, respectively. The derivation of the lognormal model indicates tumor growth acceleration starting at 3 mm (unadjusted crude data) or 2 mm (multivariate model). The breast cancer tumor target size for screening equipment, whether by imaging or molecular detection, is therefore 2 mm.