Modelling the effects of standard prognostic factors in node-positive breast cancer

Abstract

Summary Prognostic models that predict the clinical course of a breast cancer patient are important in oncology. We propose an approach to constructing such models based on fractional polynomials in which useful transformations of the continuous factors are determined. The idea may be applied with all types of regression model, including Cox regression, the method of choice for survival-time data. We analyse a prospective study of node-positive breast cancer. Seven standard prognostic factors -age, menopausal status, tumour size, tumour grade, number of positive lymph nodes, progesterone and oestrogen receptor concentrations -were investigated in 686 patients, of whom 299 had an event for recurrence-free survival and 171 died. We determine a final model with transformations of prognostic factors and compare it with the more traditional approaches using categorized variables or assuming a straight line relationship. We conclude that analysis using fractional polynomials can extract important prognostic information which the traditional approaches may miss.

Is treatment with interferon-α effective in all patients with metastatic renal carcinoma? A new approach to the investigation of interactions

“…Continuous factors were modelled by using fractional polynomials (Royston and Altman, 1994;Sauerbrei et al, 1999). All survival analyses and tests of hypotheses were conducted within the Cox regression framework.…”

“…It extends the multivariable fractional polynomial (MFP) method used to investigate the simultaneous prognostic effect of several continuous factors. The main advantages of analysis of continuous factors with fractional polynomials are to extract more information from such factors, to improve the statistical power to detect influential variables and their interaction with treatment (Farewell et al, 2003), and to circumvent the problems of arbitrary categorisation Royston and Altman, 1994;Sauerbrei and Royston, 1999;Royston and Sauerbrei, 2003).…”

“…The MFPI algorithm is based on fractional polynomial analysis of continuous predictors (Royston and Altman, 1994;Sauerbrei et al, 1999) and is an extension of the MFP algorithm of Sauerbrei and Royston (1999). In the MFP algorithm, continuous predictors are subject to possible transformations including logarithm, square root, etc, or to two such transformations, giving a fractional polynomial model of degree 2 (FP2) (see Sauerbrei et al (1999) for an example in breast cancer explaining fractional polynomial analysis in detail).…”

“…In the MFP algorithm, continuous predictors are subject to possible transformations including logarithm, square root, etc, or to two such transformations, giving a fractional polynomial model of degree 2 (FP2) (see Sauerbrei et al (1999) for an example in breast cancer explaining fractional polynomial analysis in detail). Transformation(s) are applied only if the fit of the model is significantly improved, the default being a linear model.…”

Ratio Between Positive Lymph Nodes and Total Excised Axillary Lymph Nodes as an Independent Prognostic Factor for Overall Survival in Patients with Nonmetastatic Lymph Node-Positive Breast Cancer

“…Although the number of ALN involved with cancer has been demonstrated to be important for prognosis and is included in the 6th edition of the AJCC BC staging system, the role of the total number of ALN retrieved in an ALND specimen has received less emphasis. [20][21][22][23][24] This is despite data that clearly suggest that the likelihood of finding positive nodes in the axilla increases with the number of nodes dissected, and the likelihood of having residual disease in the axilla decreases with a more extensive dissection. 11,25 In an attempt to address the above, several studies have focused on the utility of the ALNR as an independent prognostic indicator of OS.…”