Hybrid likelihood methods

ABSTRACT Prop ID: DMS-0505201 PI: McKeague, Ian W. NSF Program: STATISTICS Institution: Columbia University Title: Hybrid likelihood methods Empirical likelihood is being extended in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than root-n rates of convergence, and settings in which there are a relatively large number of estimating equations compared to the sample size. This work is motivated in part by the need to more effectively compare survival distributions in clinical trials and cohort studies. Methods of finding confidence intervals for split points, as represented by jumps in parametric regression models within broader semiparametric models, are also being investigated. This involves developing cube-root asymptotics for hybrid likelihood methods. A new confidence set is constructed by inverting a hybrid likelihood ratio statistic. This part of the project is motivated by an application to the development of a phosphorus threshold standard for the Everglades. Finally, hybrid likelihood techniques are being developed for use in HIV vaccine efficacy trials in which it is important to take into account dependence of the relative risk of infection on the divergence of infecting HIV viruses. Hybrid likelihood provides a unified way of looking at techniques that adapt a nonparametric likelihood based approach in some way, for example through the use of plug-in estimates for nuisance parameters, or by the use of a likelihood derived from a working (but not "true") model. The use of hybrid likelihood has become increasingly common in recent years and is attractive in many applied areas because it combines the power of likelihood based methods with a pragmatic sense of the need to find tractable and easily implemented solutions to complex statistical problems. The investigator is extending the scope of hybrid likelihood methods in a variety of settings. Methodological work is conducted on three specific topics: empirical likelihood with applications in survival analysis, confidence intervals for split points with application to the estimation of pollution thresholds, and comparison of mark-specific relative risks with application to the detection of viral divergence in HIV vaccine efficacy trials.