Efficient Semiparametric Inference Under Two-Phase Sampling, With Applications to Genetic Association Studies

Semiparametric Inference for Data with a Continuous Outcome from a Two-Phase Probability Dependent Sampling Scheme.

Multi-phased designs and biased sampling designs are two of the well recognized approaches to enhance study efficiency. In this paper, we propose a new and cost-effective sampling design, the two-phase probability dependent sampling design (PDS), for studies with a continuous outcome. This design will enable investigators to make efficient use of resources by targeting more informative subjects...

On the Semiparametric Efficiency of the Scott-Wild Estimator under Choice-Based and Two-Phase Sampling

Suppose that for each of a number of subjects, we measure a response y and a vector of covariates x, in order to estimate the parameters β of a regression model which describes the conditional distribution of y given x. If we have sampled directly from the conditional distribution, or even the joint distribution, we can estimate β without knowledge of the distribution of the covariates. In the ...

Consistency of Semiparametric Maximum Likelihood Estimators for Two-Phase Sampling

Semiparametric maximum likelihood estimators have recently been proposed for a class of two-phase, outcome-dependent sampling models. All of them were "restricted" maximum likelihood estimators, in the sense that the maximization is carried out only over distributions concentrated on the observed values of the covariate vectors. In this paper, the authors give conditions for consistency of thes...

Optimal Calibration Estimators under Two-phase Sampling

Weighted Likelihood Estimation under Two-phase Sampling.

We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko-Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probabi...