Nonlinear discriminant analysis and prognostic factor classification in node-negative primary breast cancer using...

We used non-linear kernel discriminant analysis (KDA) to predict the outcome of 134 axillary node-negative primary breast cancer patients not treated with adjuvant therapy in a non censored database.

Posterior probabilities of relapse at 5 years were estimated using probabilistic neural networks (PNN) and a cross-validation (leave-one-out) technique to avoid overfitting the data. A stepwise method was used to construct the models to define the best combination of risk factors among eleven prognostic factors: age, menopausal status, Scarff-Bloom-Richardson grade, clinical tumor size, pathological tumor size, estrogen and progesterone receptor status, urokinase-type plasminogen activator, p53 protein level, c-erbB-2 protein and epidermal growth factor receptor. The different variables were tested individually and in combination to determine their prognostic power using a ROC indicator, which measures the separation between the probability distributions of the output neuron activations under the null hypothesis (no recurrence at 5 years) and under the alternative hypothesis (recurrence at 5 years).

The best predictive one-dimensional model was obtained with uPA (ROC indicator = 0.75). A two-factor model including uPA and clinical tumor size (T) gave the best discrimination between recurrence and non recurrence at 5 years (ROC indicator = 0.84). Additional variables did not improve the accuracy of the prediction. The uPA-T model generated a map useful in predicting the posterior probability of cancer recurrence in a given patient. This representation allows the entire database to be easily visualized and each patient can be compared with the entire database.

This is a powerful approach to analyze the impact of prognostic factors and it could find clinical applications in breast cancer.