August 2019

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Tuesday, August 13, 2019 — 4:00 PM EDT

Spatial Cauchy processes with local tail dependence

We study a class of models for spatial data obtained using Cauchy convolution processes with random indicator kernel functions. We show that the resulting spatial processes have some appealing dependence properties including tail dependence at smaller distances and asymptotic independence at larger distances. We derive extreme-value limits of these processes and consider some interesting special cases. We show that estimation is feasible in high dimensions and the proposed class of models allows for a wide range of dependence structures.

Thursday, August 22, 2019 — 4:00 PM EDT

Development and Application of A Measure of Prediction Accuracy for Binary and Censored Time to Event Data

Clinical preventive care often uses risk scores to screen population for high risk patients for targeted intervention. Typically the prevalence is low, meaning extremely unbalanced classes. Positive predictive value and true positive fraction have been recognized as relevant metrics in this imbalanced setting. However, for commonly used continuous or ordinal risk scores, these measures require a subjective cut-off threshold value to dichotomize and predict class membership. In this talk, I describe a summary index of positive predictive value (AP) for binary and event time outcome data. Similar to the widely used AUC, AP is rank based and a semi-proper scoring rule. We also study the behavior of incremental values of AUC, AP and the strict proper scoring rule scaled Brier score (sBrier) when an additional risk factor Z is included. It is shown that the incremental values agreement between AP and sBrier increases as the class unbalance increases, while the agreement between AUC and sBrier decreases as class unbalance increases. Under certain configurations, the changes in AP and sBrier indicate worse prediction performance when Z is added to the risk profile, while the changes in AUC are almost always favor the addition of Z. Several real world examples are used throughout the talk to illustrate and contrast these metrics.

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