Weighted likelihood estimation under two-phase sampling

Saegusa, Takumi; Wellner, Jon A.

doi:10.1214/12-aos1073

Cited by 52 publications

(120 citation statements)

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“…A discrete stratification variable based on the phase one data is specified (which usually includes case status such that the sampling is outcome-dependent), and within each stratum subjects are selected into phase two. Some authors have restricted the term “two-phase sampling” to without replacement stratified sampling (Breslow et al, 2009a, 2009b, Saegusa and Wellner, 2013), whereas others have broadened the definition to include either Bernoulli sampling or without replacement sampling (Breslow and Lumley, 2013); here we adopt the broader definition. Most theoretical results for two-phase sampling methods have assumed Bernoulli sampling, which facilitates easier proofs of asymptotic properties because the sampling indicators are iid.…”

Section: Introductionmentioning

confidence: 99%

“…Most theoretical results for two-phase sampling methods have assumed Bernoulli sampling, which facilitates easier proofs of asymptotic properties because the sampling indicators are iid. Saegusa and Wellner (2013) is an exception that tackled the challenge of dependent sampling indicators in proving theoretical results under two-phase stratified without replacement sampling. In this paper we develop the results under Bernoulli two-phase sampling, which matches the sampling design of the real data application described below.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of two-phase sampling data with semiparametric additive hazards models

Sun

Qian

Shou³

et al. 2016

Lifetime Data Anal

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Under the case-cohort design introduced by Prentice (1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of two-phase sampling data with semiparametric additive hazards models

Sun

Qian

Shou³

et al. 2016

Lifetime Data Anal

View full text Add to dashboard Cite

show abstract

“…First, under our design, the subcohort is a simple random sample of the cohort selected by independent Bernoulli sampling. When the subcohort is selected by sampling without replacement, our method should work, though more complicated arguments would be needed to develop the asymptotic results (Saegusa & Wellner, 2013). Moreover, when some covariates are available for all cohort members, a stratified case-cohort design based on those covariates could be considered to improve the study efficiency and adapting our method to such design should be straightforward.…”

Section: Discussionmentioning

confidence: 99%

Case-cohort studies with interval-censored failure time data

Zhou¹,

Zhou²,

Cai³

2017

Biometrika

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Summary The case-cohort design has been widely used as a means of cost reduction in assembling or measuring expensive covariates in large cohort studies. The existing literature on the case-cohort design is mainly focused on right-censored data. In practice, however, the failure time is often subject to interval-censoring; it is known only to fall within some random time interval. In this paper, we consider the case-cohort study design for interval-censored failure time and develop a sieve semiparametric likelihood approach for analyzing data from this design under the proportional hazards model. We construct the likelihood function using inverse probability weighting and build the sieves with Bernstein polynomials. The consistency and asymptotic normality of the resulting regression parameter estimator are established and a weighted bootstrap procedure is considered for variance estimation. Simulations show that the proposed method works well for practical situations, and an application to real data is provided.

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“…Hence calibration to stratum frequencies enables one to reconcile the apparent difference between the two sampling schemes. Further calibration would in principle improve the efficiency of estimation under either scheme (Saegusa and Wellner 2013). …”

Section: Inverse Probability Weighted Z-estimationmentioning

confidence: 99%

Z-estimation and stratified samples: application to survival models

Breslow

Wellner

2015

Lifetime Data Anal

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The infinite dimensional Z-estimation theorem offers a systematic approach to joint estimation of both Euclidean and non-Euclidean parameters in probabiity models for data. It is easily adapted for stratified sampling designs. This is important in applications to censored survival data because the inverse probability weights that modify the standard estimating equations often depend on the entire follow-up history. Since the weights are not predictable, they complicate the usual theory based on martingales. This paper considers joint estimation of regression coefficients and baseline hazard functions in the Cox proportional and Lin-Ying additive hazards models. Weighted likelihood equations are used for the former and weighted estimating equations for the latter. Regression coefficients and baseline hazards may be combined to estimate individual survival probabilities. Efficiency is improved by calibrating or estimating the weights using information available for all subjects. Although inefficient in comparison with likelihood inference for incomplete data, which is often difficult to implement, the approach provides consistent estimates of desired population parameters even under model misspecification.

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Weighted likelihood estimation under two-phase sampling

Cited by 52 publications

References 33 publications

Analysis of two-phase sampling data with semiparametric additive hazards models

Analysis of two-phase sampling data with semiparametric additive hazards models

Case-cohort studies with interval-censored failure time data

Z-estimation and stratified samples: application to survival models

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