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Fields Institute – Distinguished Lecture Series in Statistical Science – Prof. Norman Breslow

December 7, 2012

Distinguished Lecture Series in Statistical Science – Prof. Norman Breslow

December 7, 2012
Room 230, Fields Institute

Norman E. Breslow (Department of Biostatistics, University of Washington, Seattle)
Thomas Lumley (Department of Statistics, University of Auckland, NZ)
Jon A. Wellner (Department of Biostatistics; Department of Statistics, University of Washington, Seattle)
Talk Title: Inference on Hazard Ratios and Survival Probabilities from Two-phase Stratified Samples

Epidemiologists employ strati ed case-control studies nested within a de ned cohort so that collection of costly covariate information, such as bioassays of stored tissue samples, may be limited to the most informative participants. These designs involve two-phase stratified samples: a simple random sample (the main cohort) from an in nite super-population (model) at Phase I; and a nite population stratified (case-control) sample at Phase II. One approach to analysis involves inverse probability weighting (IPW) of general estimating equations.

In previous work we investigated IPW of in nite dimensional likelihood equations for both Euclidean and non-Euclidean parameters in semi-parametric models, of which the paradigm is the Cox model for survival data. The key idea was to separate the likelihood calculations, which are the same as those for simple random sampling, from weak convergence results for the IPW empirical process. For estimation of the Euclidean parameter (log hazard ratios), the problem was asymptotically equivalent to that of using the Phase II sample to estimate an unknown nite population total: the total of the unknown influence function contributions for subjects in the main cohort. Efficiency was improved, sometimes dramatically, through adjustment of the sampling weights by calibration to totals of auxiliary variables known for everyone or by estimation of the known weights using these same variables. After reviewing these results, this talk considers the extensions needed for joint estimation of hazard ratios and baseline hazard function in the Cox model, and hence for prediction of survival probabilities. The improvements in prediction possible with calibrated or estimated weights are illustrated via simulations conducted using Lumleys R survey package to analyze data from the National Wilms Tumor Study.


Breslow NE, Wellner JA. Scand J Stat 34:86-102, 2007; 35:186-192, 2008.
Breslow NE, Lumley T et al. Am J Epidemiol 35:1398-1405, 2009
Breslow NE, Lumley T et al. Stat Biosci 1:32-49, 2009
Breslow NE, Lumley T IMS Monograph Series { Wellner Festschrift, in press
Lumley T. Complex Surveys, New York: Wiley, 2010


December 7, 2012
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