Non-Linear Survival Models and Their Applications Within Breast Cancer Prognosis (Niet-lineaire overlevingsmodellen en hun toepassingen in borstkankerprognose)

Everybody is confronted with the diagnosis of cancer during their life. If not personally, it might be a family member or a friend. The diagnosis of cancer creates a feeling of fear. Fear for the unknown, fear for the therapy, fear to die. Thanks to the knowledge of clinical doctors the patients can be informed on their disease and can be treated adequately. In order to decide on treatment options, estimation of risk of survival is crucial. Although chemotherapy might reduce the risk on metastatic tumors, the therapy in itself might be harmful. Deciding which patients might benefit from a specific type of therapy in a way that the benefit is higher than the negative effects of the therapy, is of major importance in clinical practice. These questions are answered by means of survival analysis. By studying patient variables and their relation with survival time (time to relapse, time to death, time to healing) an estimate of the patient specific risk can be calculated. In addition, this type of models allows to estimate the effect of different types of treatment. The information which is provided to clinicians in this way can help them making a more adequate treatment choice. Survival data are most often analyzed by parametric and semi-parametric models. Although these models perform well in general, some drawbacks remain. The most popular model for survival analysis is the proportional hazards model (ph). The name of this model reveals that hazards for observations with different variable values are assumed to be proportional. However, this assumption is not always realistic. Secondly, the model assumes a linear parametric form of the variables. To overcome these drawbacks, this research presents a new mathematical model for the analysis of survival data. The largest threshold in developing survival models is the occurrence of censoring in the data. Censoring indicates that not all survival times are observed exactly. Some patients might not experience the event under study during the study time, others might be lost to follow-up. To deal with this issue, the survival problem is reformulated as a ranking problem, where only pairs of observations for which the event order is known, are taken into account. This principle is combined with the methodology of support vector machines. However, the maximal margin principle is replaced by minimizing the Lipschitz constant. This model is further explored by considering different adaptations, such as L2 instead of L1 norms and regression constraints instead of ranking constraints. This research revealed that the use of equality constraints is less appropriate in analyzing survival data since the information provided by censored data can not completely be included. In addition, it is shown that the inclusion of regression constraints improves the performance significantly. A second achievement of this research is that the proposed method appears to be very promising when handling high dimensional data. The last decade, more and more research was done with regard to genomics, proteomics and other omics , resulting in high dimensional data. The problem with conventional techniques is that the estimates of the effects of each variable becomes less reliable when more and more variables are included. The presented method overcomes this problem by solving the optimization problem in the dual space. Although our experiments illustrate that the proposed model results in well performing models, the chance that this model will be used in clinical practice is very small. The problem with the clinical use of non-parametric models is that they are black-box models. As a result, clinicians can not be provided with information on how the model estimates a certain risk, making it hard for clinicians to trust the model. In addition, this type of models can not be used to search for new predictive and prognostic markers since one does not know which variables contribute to the result. These major drawbacks are solved in the interval coded scoring index (ics). Although this new model starts from the model explained above, the results are highly interpretable and easily applicable in clinical practice. The basic idea of the ics is that variables can be divided into a relatively small number of intervals, in which the effect on the risk of the event remains the same. In addition, it is assumed that the effects of all variables can be summed up to become the final risk. Classification and prognostic models developed by means of this new methodology can be presented as a questionnaire or by means of colorbars, which makes application possible within software applications as well as on paper.nrpages: 210status: publishe