Abstract P3-10-06: Modeling Prognostic Markers in Breast Cancer — Are We Using Them the Optimal Way?
Authors: Strand C , Falck A-K , Jirström K , Malmström P , Rydén L , Bendahl P-O , Fernö M. 
Published: April 2011

Abstract
Background: Prognostic and treatment predictive factors used for clinical decision making are often measured on a continuous scale, but categorized into 2-3 subgroups. More efficient use of the information obtained from the standard prognostic factors could improve risk stratification considerably. For survival data, a standard tool to evaluate the simultaneous effect of multiple prognostic markers is the Cox proportional hazards regression model. A more flexible approach is to model non-linear effects using fractional polynomials (FP). This modeling might optimize predictive information with important clinical implication.
Aim: To compare risk stratification based on categorized predictors, linear, and non-linear effects.
Patients and methods: Cox models combined with FP were used to predict time to recurrence in a cohort of n=3115 female breast cancer patients. Median age was 60 years, median tumor size 21 mm, and 46% were node-negative. Endpoint was defined as distant metastasis for 89% of the patients and as recurrence for the remaining 11%. Median follow-up was 6.1 years (777 events). Only three prognostic factors were used in the analyses - number of positive lymph nodes, age at diagnosis, and tumor size. Due to non-proportional hazards, we restricted the analyses to the first five years. Modeling was done using three different approaches; Model 1:
Categorization according to predefined cut points (&gt;20 mm, &lt;35 years and 0, 1-3 or ≥4 positive nodes). Model 2: Modeling of linear effects. Lymph node status was added to this model to allow a large increase in hazard from zero to one positive node and then a linear effect over number of positive nodes. Model 3: FP-modeling of non-linear effects. We restricted the class of possible functional forms for the relationship between number of positive nodes and hazard to monotonic functions. Results: In univariate analyses, non-linear effects were detected for all of the variables age, tumor size, and lymph nodes. Multivariable modeling with categorized variables (Model 1) resulted in highly significant effects. The model fit increased slightly when the continuous variables were used (Model 2). A more dramatic improvement, as measured by the Akaike Information Criterion (AIC), was seen when non-linear effects were modeled using FP (Model 3). A subgroup analysis was performed in the patient group with the lowest risk according to Model 1 (n=652). Based on risk predictions according to Model 3, this low-risk group was divided into quartiles, where the group with highest risk had 85% event-free 5-year survival, compared to 92-96% for the other three groups. Conclusions: Optimizing the use of standard prognostic and treatment predictive factors is of most importance. Using FP in combination with Cox regression, we detected non-linear relationships to risk for age, tumor size, and number of positive lymph nodes. Furthermore, a low-risk group found with traditional modeling could be subdivided into 4 groups with different event-free 5-year survival, ranging from 85% to 96%. Categorization of prognostic factors measured on a continuous scale leads to considerable information loss and should thus be avoided.
Citation Information: Cancer Res 2010;70(24 Suppl):Abstract nr P3-10-06.