Application of smoothing methods to evaluate treatment-prognostic factor interactions in breast cancer data

In breast cancer research, investigators often are interested in knowing any pattern of change in efficacy of a hormonal or chemo therapy over a continuum of a prognostic factor such as age or hormonal receptor level. Bonetti and Gelber (1) introduced a graphical method to evaluate treatment-covariate interactions by using the Cox model (2, 3). By combining their concepts and the well-known locally weighted regression smoothing procedure, Fisher, Jeong, Bryant et al. (4) evaluated pattern of average annual recurrence rates as a continuous function of age among breast cancer patients with histologically negative lymph nodes and positive estrogen receptors. In this article, we elaborate on the combined exploratory smoothing technique to evaluate an interaction between treatment effect and hormonal receptor level among breast cancer patients with positive estrogen receptors and positive progesterone receptors. The results reveal that the patients with higher estrogen receptor level tend to benefit more from tamoxifen and the incremental benefit from adding a chemotherapy to tamoxifen tend to be greater for the patients with lower estrogen receptor level. The progesterone level does not affect the size of benefit from tamoxifen, but the benefit from the addition of the chemotherapy is greater for patients with higher progesterone level.