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Methods for the analysis of sampled cohort data in the Cox proportional hazards model. (English) Zbl 0843.62094
Summary: Methods are provided for regression parameter and cumulative baseline hazard estimation in the Cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law. The key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes, leading to estimation methods parallel to those for full cohort data.
These techniques are illustrated for a number of sampling designs, inlcuding three novel designs: counter-matching with additional randomly sampled controls; quota sampling of controls; and nested case-control sampling with number of controls dependent on the failure’s exposure status. General asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs.

62M99 Inference from stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62P10 Applications of statistics to biology and medical sciences; meta analysis
62D05 Sampling theory, sample surveys
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