| Author/Editor | Pohar-Perme, Maja | |
| Title | Prileganje regresijskih modelov za relativno preživetje | |
| Translated title | Goodness of fit of relative survival models | |
| Type | monografija | |
| Place | Ljubljana | |
| Publisher | Medicinska fakulteta | |
| Publication year | 2007 | |
| Volume | str. 139 | |
| Language | slo | |
| Abstract | Objectives The initial step in choosing a relative survival regression model is to make assumptions about the relationship between the observed and population hazard. This assumption has a crucial impact on the results and their interpretation, however, there is no way to check it. The goal of this thesis is twofold. First, to study the possibilities of a relative survival analysis without this assumption. Secondly; to introduce the goodness of fit methods for the chosen model; focusing particularly on the additive model, for which no methods have yet been proposed. Hypotheses The transformation approach; presented in the thesis; is a method that can provide us with additional information about the relative survival. It allows for modelling without making assumptions about the relationship between the observed and population hazard and has favourable theoretical properties. The partial residuals defined in the thesis, can give valuable information about the proportional excess hazards assumption in the additive model. The stochastic process constructed from the partial residuals can be shown to converge to the Brownian motion in the true coefficient beta°; the process in the estimated beta is a close enough approximation to Brownian bridge to enable powerful test statistics. Methods The properties of the transformation approach and the relationship between the Cox model in transformed time and the standard regression models are studied theoretically as well as illustrated on a practical example. The properties of the partial residuals and the convergence to the Brownian bridge are explored using the theory of counting processes. .The theory of the Brownian bridge then serves as a basis for defining sensible test statistics. All the simulations and practical examples are performed in R. (Abstract truncated at 2000 characters) | |
| Descriptors | MYOCARDIAL INFARCTION SURVIVAL ANALYSIS REGRESSION ANALYSIS PROPORTIONAL HAZARDS MODELS SEX FACTORS AGE FACTORS DIABETES MELLITUS |