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Non-linear transformations of age at diagnosis, tumor size, and number of positive lymph nodes in prediction of clinical outcome in breast cancer 11 Medical and Health Sciences 1112 Oncology and Carcinogenesis

Forsare, Carina LU ; Bak, Martin; Falck, Anna Karin LU ; Grabau, Dorthe LU ; Killander, Fredrika LU ; Malmström, Per LU ; Rydén, Lisa LU ; Stål, Olle; Sundqvist, Marie and Bendahl, Pär Ola LU , et al. (2018) In BMC Cancer 18(1).
Abstract

Background: Prognostic factors in breast cancer are often measured on a continuous scale, but categorized for clinical decision-making. The primary aim of this study was to evaluate if accounting for continuous non-linear effects of the three factors age at diagnosis, tumor size, and number of positive lymph nodes improves prognostication. These factors will most likely be included in the management of breast cancer patients also in the future, after an expected implementation of gene expression profiling for adjuvant treatment decision-making. Methods: Four thousand four hundred forty seven and 1132 women with primary breast cancer constituted the derivation and validation set, respectively. Potential non-linear effects on the log... (More)

Background: Prognostic factors in breast cancer are often measured on a continuous scale, but categorized for clinical decision-making. The primary aim of this study was to evaluate if accounting for continuous non-linear effects of the three factors age at diagnosis, tumor size, and number of positive lymph nodes improves prognostication. These factors will most likely be included in the management of breast cancer patients also in the future, after an expected implementation of gene expression profiling for adjuvant treatment decision-making. Methods: Four thousand four hundred forty seven and 1132 women with primary breast cancer constituted the derivation and validation set, respectively. Potential non-linear effects on the log hazard of distant recurrences of the three factors were evaluated during 10 years of follow-up. Cox-models of successively increasing complexity: dichotomized predictors, predictors categorized into three or four groups, and predictors transformed using fractional polynomials (FPs) or restricted cubic splines (RCS), were used. Predictive performance was evaluated by Harrell's C-index. Results: Using FP-transformations, non-linear effects were detected for tumor size and number of positive lymph nodes in univariable analyses. For age, non-linear transformations did, however, not improve the model fit significantly compared to the linear identity transformation. As expected, the C-index increased with increasing model complexity for multivariable models including the three factors. By allowing more than one cut-point per factor, the C-index increased from 0.628 to 0.674. The additional gain, as measured by the C-index, when using FP- or RCS-transformations was modest (0.695 and 0.696, respectively). The corresponding C-indices for these four models in the validation set, based on the same transformations and parameter estimates from the derivation set, were 0.675, 0.700, 0.706, and 0.701. Conclusions: Categorization of each factor into three to four groups was found to improve prognostication compared to dichotomization. The additional gain by allowing continuous non-linear effects modeled by FPs or RCS was modest. However, the continuous nature of these transformations has the advantage of making it possible to form risk groups of any size.

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Breast cancer, Categorical, Continuous, Fractional polynomials, Prognostic, Splines
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BMC Cancer
volume
18
issue
1
publisher
BioMed Central
external identifiers
  • scopus:85058107806
ISSN
1471-2407
DOI
10.1186/s12885-018-5123-x
language
English
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yes
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b42a78f4-7fce-447a-ae7f-2f97b4816c30
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2018-12-18 13:31:01
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2019-01-06 14:20:33
@article{b42a78f4-7fce-447a-ae7f-2f97b4816c30,
  abstract     = {<p>Background: Prognostic factors in breast cancer are often measured on a continuous scale, but categorized for clinical decision-making. The primary aim of this study was to evaluate if accounting for continuous non-linear effects of the three factors age at diagnosis, tumor size, and number of positive lymph nodes improves prognostication. These factors will most likely be included in the management of breast cancer patients also in the future, after an expected implementation of gene expression profiling for adjuvant treatment decision-making. Methods: Four thousand four hundred forty seven and 1132 women with primary breast cancer constituted the derivation and validation set, respectively. Potential non-linear effects on the log hazard of distant recurrences of the three factors were evaluated during 10 years of follow-up. Cox-models of successively increasing complexity: dichotomized predictors, predictors categorized into three or four groups, and predictors transformed using fractional polynomials (FPs) or restricted cubic splines (RCS), were used. Predictive performance was evaluated by Harrell's C-index. Results: Using FP-transformations, non-linear effects were detected for tumor size and number of positive lymph nodes in univariable analyses. For age, non-linear transformations did, however, not improve the model fit significantly compared to the linear identity transformation. As expected, the C-index increased with increasing model complexity for multivariable models including the three factors. By allowing more than one cut-point per factor, the C-index increased from 0.628 to 0.674. The additional gain, as measured by the C-index, when using FP- or RCS-transformations was modest (0.695 and 0.696, respectively). The corresponding C-indices for these four models in the validation set, based on the same transformations and parameter estimates from the derivation set, were 0.675, 0.700, 0.706, and 0.701. Conclusions: Categorization of each factor into three to four groups was found to improve prognostication compared to dichotomization. The additional gain by allowing continuous non-linear effects modeled by FPs or RCS was modest. However, the continuous nature of these transformations has the advantage of making it possible to form risk groups of any size.</p>},
  articleno    = {1226},
  author       = {Forsare, Carina and Bak, Martin and Falck, Anna Karin and Grabau, Dorthe and Killander, Fredrika and Malmström, Per and Rydén, Lisa and Stål, Olle and Sundqvist, Marie and Bendahl, Pär Ola and Fernö, Mårten},
  issn         = {1471-2407},
  keyword      = {Breast cancer,Categorical,Continuous,Fractional polynomials,Prognostic,Splines},
  language     = {eng},
  month        = {12},
  number       = {1},
  publisher    = {BioMed Central},
  series       = {BMC Cancer},
  title        = {Non-linear transformations of age at diagnosis, tumor size, and number of positive lymph nodes in prediction of clinical outcome in breast cancer 11 Medical and Health Sciences 1112 Oncology and Carcinogenesis},
  url          = {http://dx.doi.org/10.1186/s12885-018-5123-x},
  volume       = {18},
  year         = {2018},
}