Mathematical Sciences: Smoothed Nonparametric Hazard Regression

9501893 Grund Abstract The main objective of the project is to develop smoothing methods for nonparametric hazard regression with time-dependent regression coefficients, in the framework of an additive hazard regression model (Aalen model). The Aalen model incorporates the possibility that both value and contribution of covariates may change over time. Most important, no particular parametric shape of this time-dependence is assumed. In the current project, kernel smoothing will be used to estimate the regression coefficient curves. A major objective is to develop data-driven bandwidth selectors, and to investigate their properties. It is expected that the resulting methods will improve upon currently used empirical estimates. Moreover, kernel methods allow one to estimate the regression coefficient curves themselves, as opposed to cumulative coefficients. This is particularly important for graphical data analysis. The new smoothing methods will be implemented in XLISP-STAT, an object- oriented programming language; a user-friendly interface will be provided. Dynamic graphics will be used to support visual data exploration. As part of the project, the developed smoothing procedures will be used to analyze epidemiological data. On the side of education, the development of a new lecture course on ``Smoothing Methods in Curve Estimation'' for statistics majors at the M.S. or Ph.D. level is proposed. Research results of the current proposal will be included. Dynamic graphics software will be used to demonstrate smoothing techniques in class, thus giving students access to cutting edge technology An important problem in medicine is to predict the survival of patients, given their current condition and treatment. The condition of a patient is described by 'covariate values', such as blood cholesterol, blood pressure, number of antibodies, etc. A central problem in analyzing survival data is to assess the influence of covariates; for example, to quantify by how much an elevated level of blood cholesterol increases the risk of stroke. Often the influence of covariates is known to change with time. In this case standard methods tend to fail. The proposed project develops risk estimates based on the Aalen model. This model is extremely flexible. The influence of covariates is allowed to change over time, without assuming any particular shape of this time-dependence beforehand. In this project, modern smoothing techniques will be adapted to estimate the influence of covariates. Smoothing methods are extremely useful for descriptive data analysis, and widely used in statistics. In the context of survival data, however, the use of corresponding methods is a very recent development, with many open problems. Part of the project is the user-friendly computational implementation of the newly developed estimation procedures. Interactive graphics will be used extensively to support visual data exploration. With the provided software, smoothing methods in Aalen hazard regression will be available for practitioners for the first time. The new smoothing procedures will be used to analyze epidemiological data. On the side of education, the development of a new lecture course on ``Smoothing Methods in Curve Estimation'' for statistics majors at the M.S. or Ph.D. level is proposed. Research results of the current proposal will be included. Dynamic graphics software will be used to demonstrate smoothing techniques in class, thus giving students access to cutting edge technology.