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1.  Mixed effect regression analysis for a cluster-based two-stage outcome-auxiliary-dependent sampling design with a continuous outcome 
Biostatistics (Oxford, England)  2012;13(4):650-664.
Two-stage design is a well-known cost-effective way for conducting biomedical studies when the exposure variable is expensive or difficult to measure. Recent research development further allowed one or both stages of the two-stage design to be outcome dependent on a continuous outcome variable. This outcome-dependent sampling feature enables further efficiency gain in parameter estimation and overall cost reduction of the study (e.g. Wang, X. and Zhou, H., 2010. Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling. Biometrics 66, 502–511; Zhou, H., Song, R., Wu, Y. and Qin, J., 2011. Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome. Biometrics 67, 194–202). In this paper, we develop a semiparametric mixed effect regression model for data from a two-stage design where the second-stage data are sampled with an outcome-auxiliary-dependent sample (OADS) scheme. Our method allows the cluster- or center-effects of the study subjects to be accounted for. We propose an estimated likelihood function to estimate the regression parameters. Simulation study indicates that greater study efficiency gains can be achieved under the proposed two-stage OADS design with center-effects when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a dataset from the Collaborative Perinatal Project.
doi:10.1093/biostatistics/kxs013
PMCID: PMC3440236  PMID: 22723503
Center effect; Mixed model; Outcome-auxiliary-dependent sampling; Validation sample
2.  Partial linear inference for a 2-stage outcome-dependent sampling design with a continuous outcome 
Biostatistics (Oxford, England)  2010;12(3):506-520.
The outcome-dependent sampling (ODS) design, which allows observation of exposure variable to depend on the outcome, has been shown to be cost efficient. In this article, we propose a new statistical inference method, an estimated penalized likelihood method, for a partial linear model in the setting of a 2-stage ODS with a continuous outcome. We develop the asymptotic properties and conduct simulation studies to demonstrate the performance of the proposed estimator. A real environmental study data set is used to illustrate the proposed method.
doi:10.1093/biostatistics/kxq070
PMCID: PMC3114650  PMID: 21156990
Biased sampling; Partial linear model; P-spline; Validation sample; 2-stage
3.  Semiparametric inference for a 2-stage outcome-auxiliary-dependent sampling design with continuous outcome 
Biostatistics (Oxford, England)  2011;12(3):521-534.
Two-stage design has long been recognized to be a cost-effective way for conducting biomedical studies. In many trials, auxiliary covariate information may also be available, and it is of interest to exploit these auxiliary data to improve the efficiency of inferences. In this paper, we propose a 2-stage design with continuous outcome where the second-stage data is sampled with an “outcome-auxiliary-dependent sampling” (OADS) scheme. We propose an estimator which is the maximizer for an estimated likelihood function. We show that the proposed estimator is consistent and asymptotically normally distributed. The simulation study indicates that greater study efficiency gains can be achieved under the proposed 2-stage OADS design by utilizing the auxiliary covariate information when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a data set from an environmental epidemiologic study.
doi:10.1093/biostatistics/kxq080
PMCID: PMC3114654  PMID: 21252082
Auxiliary covariate; Kernel smoothing; Outcome-auxiliary-dependent sampling; 2-stage sampling design

Results 1-3 (3)