Interactions Between Treatment and Continuous Covariates: A Step Toward Individualizing Therapy
Authors: Patrick Royston, Willi Sauerbrei
Journal: Journal of Clinical Oncology (2008)

Interactions between treatment and covariates, such as prognostic factors, in randomized oncology trials are important because they are essential ingredients of individualized cancer treatments rather than assuming that one size fits all. Such factors are often called predictive. When the covariate is continuous (such as age or hormone receptor level), such interactions are often unfortunately sought by crude statistical methods, typically involving dichotomizing the continuous covariate. Sometimes, treatment effects in subgroups are compared; the results may depend on the cut point chosen. A formal test of interaction is needed, but often omitted. Methods that keep all of the information in the covariate are more powerful than dichotomization. We therefore welcome the use of one such method, Subpopulation Treatment Effect Pattern Plot (STEPP), reported in this issue of the Journal of Clinical Oncology by Viale et al. At the same time, we would like to draw readers’ attention to an alternative approach, multivariable fractional polynomial interaction (MFPI), that we feel has much to offer. Viale et al investigate the predictive value of estrogen receptor (ER) and progesterone receptor (PgR) levels in node-negative breast cancer patients treated either with chemoendocrine or endocrine adjuvant therapy alone, in the randomized controlled trials VIII and IX of the International Breast Cancer Study Group (IBCSG). ER and PgR levels, measured by immunohistochemistry, were available for 2,248 patients. The authors used the Subpopulation Treatment Effect Pattern Plot (STEPP) to explore the association between hormone receptor levels and disease-free survival (DFS) at 5 years. The 5-year DFS rate in each subpopulation was plotted against receptor levels for each treatment arm. If a covariate has no effect, 5-year DFS rates should be similar for all subpopulations, with any differences resulting from chance alone. The plots used by Viale et al are one way of exploring prognostic effects of continuous variables nonparametrically, but a more relevant question is that of an interaction between treatment and a continuous prognostic factor. In such a situation, the difference in 5-year DFS rates between treatments would vary according to the value of the covariate. One example of an interaction is when the DFS rate for treatment A increases for larger ER values (ER has a prognostic effect in these patients), whereas for treatment B, no such change occurs (ER has no prognostic effect, and the corresponding STEPP plot is roughly a horizontal line). The magnitude of the treatment effect (A – B), expressed as the difference in 5-year DFS rates, increases with the value of the covariate. A test for interaction is available and can give better guidance as to whether the differences from the graph represent a statistically significant interaction. The authors present six comparisons in different situations, one of which indicates a significant interaction between ER and the effect of CMF (cyclophosphamide, methotrexate, fluorouracil) in trial IX. In this trial, postmenopausal patients received 5 years of tamoxifen treatment. Additional therapy with three cycles of CMF improved 5-year DFS in patients with low ER values, whereas in patients with high ER values, 5-year DFS rates were similar whether or not CMF was administered. How does STEPP work? STEPP is mainly intended to identify interactions between treatment and a continuous covariate of interest, avoiding dichotomization of the covariate. The observations are divided into many subpopulations based on the covariate. As illustrated in Figure 1, the treatment effect is estimated separately within each subpopulation. To increase the number of patients that contribute to each treatment-effect estimate, subpopulations overlap. This makes the individual estimates more precise. The subpopulations may be defined in two different ways, known as sliding window (SW) and tail-oriented (TO; Fig 1A and 1B, respectively). The horizontal axes in Figure 1 represent the subpopulations (here, 9) in which treatment effects are estimated. The vertical axes show the range of covariate values used to define the cohort of patients included in each subpopulation. Subpopulations in the SW variant have an overlapping portion and a part that differs between neighboring subpopulations. The numbers of subpopulations and of overlapping patients are important parameters of this variant, and must be chosen by the investigator. Viale et al evidently used the SW variant for their analyses, taking 90 and 80 patients in each subpopulation and 15 and 10 overlapping patients in their ER analyses of trials VIII and IX, respectively. The entire sample forms the central group in the TO variant. With increasing distance from the center, more and more patients with high covariate values (to the left side) or low covariate values (to the right side) are removed. The TO variant has a parameter called g, giving g 1 subpopulations from which patients with larger values are eliminated and the same number from which patients with smaller values are excluded. The total number of subpopulations is 1 2(g 1) 2g 1. In the graph g 5. JOURNAL OF CLINICAL ONCOLOGY E D I T O R I A L VOLUME 26 NUMBER 9 MARCH 2