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theses

Survival outcome has been one of the major endpoints for clinical trials; it gives information on the probability of a time-to-event of interest. There has been increasing interest in survival analysis tools over the recent years, especially for high dimensional survival data. Common statistical approaches include nonparametric, semi-parametric and complete parametric analysis, several of which are widely used and readily available from major commercial software applications. However most of these approaches have limitations. Typical nonparametric approaches, such as the log-rank (or Cox-Mantel) test, are not concerned about model assumptions, but can only deal with a limited number of categorical predictors. Typical semi-parametric approaches, such as Cox proportional hazard model, depend very much on the model assumptions, such as linearity, interactions and proportionality; also these approaches can only deal with survival data when the number of predictors is less than the total number of events. Complete parametric models, such as accelerate failure time models, are similar to semi-parametric models except that they make further assumptions about the baseline hazard function. In this research paper, we studied several techniques for evaluating survival data, the typical Cox PH models including the generalized Cox linear model and the multivariate Cox regression models with nonlinear transformations, the nonparametric random survival forest approaches, penalized Cox regression models including lasso, ridge and elastic-net Cox regression models, derived-input Cox regression models including principal component Cox regression and partial least squares Cox regression models. These models were implemented and evaluated with one simulation study and one real world case study. The typical Cox models including the generalized Cox linear model and the multivariate Cox regression models with nonlinear transformations should always provide unbiased estimates, and the models are flexible for handling recurrent-event survival response; but they are incapable of making inferences for cases when there are more predictors than the actual number of events; and since they are semi-parametric approaches, model assumptions such as linearity, interaction and proportionality, should be carefully examined before the models were implemented. In this paper, a systematic procedure was proposed for examining the model assumptions, which should help to ensure the correct model was employed for the survival data. In terms of prediction performance, they are among the best approaches. In the paper, we also introduced nonparametric random survival forest approaches, log-rank based and conditional inference based random survival forest models, which have many advantages over the typical nonparametric, semi-parametric or parametric approaches. There are no concerns about model assumptions, and these methods can deal with many more predictors than typical survival models. In terms of prediction performance, these models are moderate and slightly worse than the typical Cox models. The penalized Cox regression models, on the other hand, should always give biased estimates; but they work quite well for cases when the number of factors is no less than the number of events. Of all penalized Cox models, the elastic-net Cox model works extremely well for correlated high dimensional data; the prediction performance is extremely good. However, they do not work for multiple event type of survival data. The principal component Cox regression model is a very useful tool for variable reduction with similar prediction performance as the typical Cox models. The model also has similar features as the typical Cox models; it can deal with recurrent event or interval censored survival data. But it also has many disadvantages, in cases when the number of components is no less than the total number of observations, the model may not be estimable; more importantly, analysis results from this model may be difficult to interpret. The partial least squares Cox regression model was developed; it shares some resemblance with principal component Cox regression model, the only difference is the construction of the components, instead of the building orthogonal components independent from the survival outcome, the model builds the PLS components to attain the strongest correlation with the survival outcome, otherwise it has similar features as the principal component Cox regression model. Additionally, the prediction performance of this model is unexpectedly very disappointing.

ETD_6022

doi:10.7282/T3222WHN

Ph.D.

Includes bibliographical references

by Duo Zhou

ETD doctoral

The author owns the copyright to this work.