Kesirli Polinomlar ile Yaşam Modelleri

Abstract

The use of regression models with fractional polynomial was proposed to model nonlinear effects of covariates. The inclusion of continuous covariates as continuous in the model and its inclusion in the model as a categorical covariate can change the results. Especially in health studies, continuous variables, for example age, are transformed into multi categorical variables. However, converting variables into categorical format causes a loss of information. There is also uncertainty about how to determine the levels of categorical variable. In this case, fractional polynomial models are a suitable alternative.

There are studies on the use of fractional polynomials in classical regression model and logistic regression model. In Cox regression model, fractional polynomials can be used to accurately model the relationship between the covariates and survival time. Applying the appropriate function selection method facilitates the control of whether a linear function or a non-linear fractional polynomial is appropriate.

In this thesis, the use of fractional polynomials in Cox regression model was investigated and applied on breast cancer and prostate cancer data sets. Cox regression model with continuous and categorical covariates and Cox regression model with fractional polynomial were applied to the data set. Cox regression models with fractional polinomials were applied for the breast cancer data set, however it was concluded that the age variable had a linear effect on the model and it was more appropriate to use classical Cox regression models. Proportional hazards assumption was not provided for classical Cox regression model in the prostate cancer dataset, so these results are not appropriate to use and interpret. When the Cox regression models with fractional polynomials were examined for this data set, it was found that the age variable had a nonlinear relationship with the dependent variable and it was observed that the proportional hazards assumption was provided. Accordingly, it was concluded that the Cox regression model with fractional polynomials is more suitable for the prostate cancer dataset.