Brown University Center for Statistical Sciences Seminar
Department of Biostatistics, University of Washington School of Public Health | |
Abstract: ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time-dependent, $D(t)$, and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status where $D(t)=1$ if a patient has died prior to time $t$ and is $0$ otherwise.
In Heagerty, Lumley and Pepe (2000) we have proposed summarizing the discrimination potential of a marker X, measured at baseline (t=0), by calculating ROC curves for cumulative disease or death by time t. In other study designs both the disease outcome, D(t), and the marker, X(t), are measured longitudinally. For this situation there are alternative approaches to defining and estimating sensitivity and specificity. One approach directly estimates the distribution of the marker process conditional on the survival time using semi-parametric regression quantiles as described in Heagerty and Pepe (1999). A second approach uses "partly conditional" survival methods and more naturally handles censored onset times. The alternative definitions and estimation approaches will be illustrated using longitudinal pulmonary function measurements among cystic fibrosis subjects, and using the Multicenter Aids Cohort (MACS) data.
Scientific Computing Seminar
Abstract: The present work proposes a methodology to simulate samples of two-phase random media based on their first and second order moments. The methodology models the two-phase medium as a binary random field that can assume only two values (e.g. the elastic properties of the two phases). The proposed approach makes use of the zero-crossings of a Gaussian random field to determine the binary random field. A general algorithm is presented that calculates the optimum autocorrelation of the underlying Gaussian field, given the autocorrelation of the binary field. Examples in one and two dimensions are provided. It is also shown that the capabilities of the method can be significantly expanded by introducing a parameter in the mapping of the Gaussian field to the binary field.
PDE Seminar
Special Department of Mathematics Colloquium
Department of Mathematics Colloquium
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