Two-phase Sampling Design Research Articles

A modified efficient difference-type estimator for population mean under two-phase sampling design

A modified efficient difference-type estimator for population mean under two-phase sampling design

The characteristics and prevalence of phobias in pregnancy

ObjectiveThe primary objective was to estimate the population prevalence of specific phobias (including pregnancy related specific phobias) and associated mental disorders. The secondary objective was to investigate the effectiveness of routinely collected screening tools (depression and anxiety screens, Whooley and GAD-2 respectively) in identifying specific phobias. Specific phobias are the most common anxiety disorder to occur during pregnancy, but studies on prevalence and clinical correlates of specific phobias, including pregnancy related specific phobias are lacking. DesignCross-sectional survey using a two-phase sampling design stratified according to being positive or negative on the Whooley questions routinely asked by midwives. Approaching all whooley positive women and drawing a random sample of Whooley negative women. Sampling weights were used to account for the bias induced by the stratified sampling. Participants545 pregnant women attending their first antenatal appointment. Language interpreters were used where required. SettingInner-city maternity service, London, UK. MeasurementsThe Structured Clinical Interview for DSM-IV Axis I Mental Disorders were administered to assess mental disorders and 544 women responded to the anxiety module on specific phobias. ResultsThe maternity population prevalence estimate for specific phobias was 8.4% (95%CI: 5.8–12.1%) and for pregnancy related phobias was 1.5% (95%CI: 0.6–3.7%), most of which were needle phobias. The prevalence estimate of tokophobia was 0.032% (95%CI: 0.0044–0.23%). Over half (52.4%) the women with specific phobias had comorbid mental disorders. Routinely administered screening tools (Whooley and GAD-2) were not helpful in identifying phobias. Key conclusions and implications for practicePhobias in pregnancy are common but pregnancy related phobias are rare, particularly tokophobia. As routinely administered screening tools were not helpful in identifying phobias, other indicators could be considered, such as avoidance of blood tests and requests for caesarean sections.

Assessing pharmacokinetic marker correlates of outcome, with application to antibody prevention efficacy trials.

The Antibody Mediated Prevention efficacy trials are the first studies to evaluate whether passive administration of a broadly neutralizing monoclonal antibody can prevent human immunodeficiency virus (HIV) acquisition. The trials randomize 4600 HIV-negative volunteers to receive 10 infusions of the monoclonal antibody VRC01 or placebo. The primary objective compares the incidence of HIV infection between the study groups. The secondary objective assesses whether and how a marker defined as the serum concentration of VRC01 over time associates with the instantaneous rate of HIV infection, using a two-phase sampling design, a pharmacokinetic model for the time-concentration curve, and an estimator of HIV infection times. While a Cox model with a time-dependent covariate constitutes an important approach to this problem, the low interindividual versus intraindividual marker variability limits its power, motivating us to develop two alternative methods that condition on outcome status: (1) an indirect method that checks whether HIV-infected cases have unexpectedly long times from the most recent infusion to the estimated infection date and (2) a direct method that checks whether the marker itself is unexpectedly low at estimated infection dates. In simulations and a pseudo Antibody Mediated Prevention application, we find that method (2) (but not (1)) has greater power than the Cox model. We also find that the quality of the infection time estimator majorly impacts method performance, and thus, incorporating details of an optimized estimator is critical. The methods apply more generally for assessing a time-dependent longitudinal marker as a correlate of risk when the marker trajectory is modeled pharmacokinetically.

DEVELOPMENT OF CHAIN-TYPE EXPONENTIAL ESTIMATORS FOR POPULATION VARIANCE IN TWO-PHASE SAMPLING DESIGN IN PRESENCE OF RANDOM NON-RESPONSE

Abstract In this paper, an investigation has been carried out to deal with a unified approach of estimation procedures of population variance in two-phase sampling design under missing at random non-response mechanism circumstances. Using two auxiliary variables, we have developed different chain-type exponential estimators of finite population variance for two different set-ups and studied their properties under the different assumption of random non-response considered by Tracy and Osahan (1994). The comparisons of the proposed estimators have been made with some contemporary estimators of population variance under the similar realistic conditions. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey statisticians.

On the estimation of the incidence and prevalence in two-phase longitudinal sampling design.

Two-phase sampling design is a common practice in many medical studies. Generally, the first-phase classification is fallible but relatively cheap, while the accurate second phase state-of-the-art medical diagnosis is complex and rather expensive to perform. When constructed efficiently it offers great potential for higher true case detection as well as for higher precision at a limited cost. In this article, we consider epidemiological studies with two-phase sampling design. However, instead of a single two-phase study, we consider a scenario where a series of two-phase studies are done in a longitudinal fashion on a cohort of interest. Another major design issue is non-curable pattern of certain disease (e.g. Dementia, Alzheimer's etc.). Thus often the identified disease positive subjects are removed from the original population under observation, as they require clinical attention, which is quite different from the yet unidentified group. In this article, we motivated our methodology development from two real-life studies. We consider efficient and simultaneous estimation of prevalence as well incidence at multiple time points from a sampling design-based approach. We have explicitly shown the benefit of our developed methodology for an elderly population with significant burden of home-health care usage and at the high risk of major depressive disorder.

On the use of imputation methods for missing data in estimation of population mean under two-phase sampling design

Non-response is an unavoidable feature in sample surveys and it needs to be carefully handled to avoid the biased estimates of population characteristics/parameters. Imputation is one of the latest fascinating methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it makes the survey data complete before the beginning of generating the survey estimates. The present work proposes some new imputation methods to compensate the missing data in two-phase sampling when non-response observed in samples of both the phases. The proposed imputation methods result in chain type estimators of population mean of study variable and the resultant estimators have shown the efficacious performances in terms of producing the more precise estimates. Properties of the proposed estimators are examined with the help of empirical and simulation studies. Results are critically analyzed and suitable recommendations are put forward to the survey practitioners.

Generalized Exponential-Type Estimators for Population Mean Taking Two Auxiliary Variables for Unknown Means in Stratified Sampling with Sub-sampling the Non-Respondents

In this paper, we have considered stratified two-phase sampling design with sub-sampling the non-respondents in the presence of non-response for estimating population mean considering the information of two auxiliary variables. The proposed estimators are the exponential function of two auxiliary variables when means of the two auxiliary variables are not known in prior. Further the proposed estimators are provided with their generalized form. The bias and mean square error expressions of the proposed estimators have been derived in two different cases of non-response. The conditions for which proposed estimators are more efficient as compared to some other estimators, have also been discussed in each case of non-response. It is shown that the proposed estimators are more efficient as compared to Hansen and Hurwitz (J Am Stat Assoc 41:517–529, 1946) unbiased estimator and Tabasum and Khan (Assam Stat Rev 20(1):73–83, 2006) two-phase ratio and product estimators modified to the stratified sampling. An empirical study has also been carried out to demonstrate the performances of the estimators.

Large-area hybrid estimation of aboveground biomass in interior Alaska using airborne laser scanning data

Use of data from airborne laser scanning (ALS) is a well-established practice for enhancing the accuracy of forest inventories in combination with ground-based observations. For regular monitoring of large areas, wall-to-wall ALS data is economically prohibitive. However, when data are acquired in a strip-sampling mode, ALS can support the estimation of forest resources on large areas such as counties, states, and nations. This study investigated the combined use of ALS data acquired along parallel strips and co-located field observations of live and standing dead trees to estimate aboveground biomass (AGB) at regional and sub-regional levels. The study area comprised the Tanana Inventory Unit (TIU) (138,566km2), located in interior Alaska, and four sub-regions (106–7282km2) within the TIU. The field data consisted of 1676 ground observations from six independent field campaigns. Ninety-four plots came from the Forest Inventory and Analysis (FIA) program of the USDA Forest Service. The FIA plots, each consisting of four 1/60ha subplots, were acquired using a probabilistic sampling design. The remaining ground observations were collected during field inventories across TIU, and consisted of 335 independent field plots and 257 clusters containing up to four plots each. The estimation procedure followed a two-phase sampling design grounded within a hybrid inferential framework, which combines design-based estimation for the first phase and model-based inference in the second phase. Post-stratified estimation by land-cover class indicated that the hybrid estimation obtained 11–55% better precision compared to direct (design-based) estimation based solely on field observations. When the field sample sizes were reduced to 25%, the standard errors for the hybrid estimation increased by 3 to 5pp. Direct and hybrid estimates were compared for two sub-regions, and the hybrid estimated AGBs were 6.4% and 13.3% larger than the direct estimates. On both these study sub-regions, the 95% confidence interval of the hybrid estimated mean AGB included the direct estimate of the mean and vice versa.

Estimation of Stratified Mark-Specific Proportional Hazards Models under Two-Phase Sampling with Application to HIV Vaccine Efficacy Trials.

An objective of preventive HIV vaccine efficacy trials is to understand how vaccine-induced immune responses to specific protein sequences of HIV-1 associate with subsequent infection with specific sequences of HIV, where the immune response biomarkers are measured in vaccine recipients via a two-phase sampling design. Motivated by this objective, we investigate the stratified mark-specific proportional hazards model under two-phase biomarker sampling, where the mark is the genetic distance of an infecting HIV-1 sequence to an HIV-1 sequence represented inside the vaccine. Estimation and inference procedures based on inverse probability weighting of complete-cases and on augmented inverse probability weighting of complete-cases are developed. Asymptotic properties of the estimators are derived and their finite-sample performances are examined in simulation studies. The methods are shown to have satisfactory performance, and are applied to the RV144 vaccine trial to assess whether immune response correlates of HIV-1 infection are stronger for HIV-1 infecting sequences similar to the vaccine than for sequences distant from the vaccine. Augmented inverse probability weighting; auxiliary variables; case-cohort design; censored failure time; competing risks; HIV vaccine efficacy trial.

Estimation in the Semiparametric Accelerated Failure Time Model With Missing Covariates: Improving Efficiency Through Augmentation

ABSTRACTThis article considers linear regression with missing covariates and a right censored outcome. We first consider a general two-phase outcome sampling design, where full covariate information is only ascertained for subjects in phase two and sampling occurs under an independent Bernoulli sampling scheme with known subject-specific sampling probabilities that depend on phase one information (e.g., survival time, failure status and covariates). The semiparametric information bound is derived for estimating the regression parameter in this setting. We also introduce a more practical class of augmented estimators that is shown to improve asymptotic efficiency over simple but inefficient inverse probability of sampling weighted estimators. Estimation for known sampling weights and extensions to the case of estimated sampling weights are both considered. The allowance for estimated sampling weights permits covariates to be missing at random according to a monotone but unknown mechanism. The asymptotic properties of the augmented estimators are derived and simulation results demonstrate substantial efficiency improvements over simpler inverse probability of sampling weighted estimators in the indicated settings. With suitable modification, the proposed methodology can also be used to improve augmented estimators previously used for missing covariates in a Cox regression model. Supplementary materials for this article are available online.

Variance estimation of DEE and regression estimator when a first-phase cluster sample is restratified

ABSTRACTWe consider a variance estimation when a stratified single stage cluster sample is selected in the first phase and a stratified simple random element sample is selected in the second phase. We propose explicit formulas of (asymptotically), we propose explicit formulas of (asymptotically) unbiased variance estimators for the double expansion estimator and regression estimator. We perform a small simulation study to investigate the performance of the proposed variance estimators. In our simulation study, the proposed variance estimator showed better or comparable performance to the Jackknife variance estimator. We also extend the results to a two-phase sampling design in which a stratified pps with replacement cluster sample is selected in the first phase.

Mean Estimation under Imputation based on Two-Phase Sampling Design using an Auxiliary Variable

The present article offers more efficient imputation based estimators of the population mean under the framework of two-phase sampling in presence of an auxiliary variable. The theoretical conditions stating superiority of the proposed estimators, over some prevalent existing competitive estimators, in terms of relative efficiency is established by numerical illustrations based on three different data sets from the classical statistical literature.

Design and Cohort Characteristics of the Social Spectrum Study: A Multicenter Study of the Autism Spectrum Among Clinically Referred Children

This paper provides an overview of the design and cohort characteristics of the Social Spectrum Study: a clinical cohort study that used a two-phase sampling design to identify children at risk for ASD. After screening 1281 children aged 2.5–10 years who had been consecutively referred to one of six mental health services in the Netherlands, children who screened positive for ASD (n = 428) and a random selection of screen negatives (n = 240) were invited to participate in diagnostic assessments and questionnaires regarding the child, family and society. A 1-year follow-up was also conducted. Results from this study may contribute to knowledge of the identification and characterization of children with ASD, family processes, and the impact of ASD on the family and society.

A note on a difference-type estimator for population mean under two-phase sampling design.

In this manuscript, we have proposed a difference-type estimator for population mean under two-phase sampling scheme using two auxiliary variables. The properties and the mean square error of the proposed estimator are derived up to first order of approximation; we have also found some efficiency comparison conditions for the proposed estimator in comparison with the other existing estimators under which the proposed estimator performed better than the other relevant existing estimators. We show that the proposed estimator is more efficient than other available estimators under the two phase sampling scheme for this one example; however, further study is needed to establish the superiority of the proposed estimator for other populations.

Robust risk prediction with biomarkers under two-phase stratified cohort design.

Identification of novel biomarkers for risk prediction is important for disease prevention and optimal treatment selection. However, studies aiming to discover which biomarkers are useful for risk prediction often require the use of stored biological samples from large assembled cohorts, and thus the depletion of a finite and precious resource. To make efficient use of such stored samples, two-phase sampling designs are often adopted as resource-efficient sampling strategies, especially when the outcome of interest is rare. Existing methods for analyzing data from two-phase studies focus primarily on single marker analysis or fitting the Cox regression model to combine information from multiple markers. However, the Cox model may not fit the data well. Under model misspecification, the composite score derived from the Cox model may not perform well in predicting the outcome. Under a general two-phase stratified cohort sampling design, we present a novel approach to combining multiple markers to optimize prediction by fitting a flexible nonparametric transformation model. Using inverse probability weighting to account for the outcome-dependent sampling, we propose to estimate the model parameters by maximizing an objective function which can be interpreted as a weighted C-statistic for survival outcomes. Regardless of model adequacy, the proposed procedure yields a sensible composite risk score for prediction. A major obstacle for making inference under two phase studies is due to the correlation induced by the finite population sampling, which prevents standard inference procedures such as the bootstrap from being used for variance estimation. We propose a resampling procedure to derive valid confidence intervals for the model parameters and the C-statistic accuracy measure. We illustrate the new methods with simulation studies and an analysis of a two-phase study of high-density lipoprotein cholesterol (HDL-C) subtypes for predicting the risk of coronary heart disease.

Power/sample size calculations for assessing correlates of risk in clinical efficacy trials.

In a randomized controlled clinical trial that assesses treatment efficacy, a common objective is to assess the association of a measured biomarker response endpoint with the primary study endpoint in the active treatment group, using a case-cohort, case-control, or two-phase sampling design. Methods for power and sample size calculations for such biomarker association analyses typically do not account for the level of treatment efficacy, precluding interpretation of the biomarker association results in terms of biomarker effect modification of treatment efficacy, with detriment that the power calculations may tacitly and inadvertently assume that the treatment harms some study participants. We develop power and sample size methods accounting for this issue, and the methods also account for inter-individual variability of the biomarker that is not biologically relevant (e.g., due to technical measurement error). We focus on a binary study endpoint and on a biomarker subject to measurement error that is normally distributed or categorical with two or three levels. We illustrate the methods with preventive HIV vaccine efficacy trials and include an R package implementing the methods. Copyright © 2016 John Wiley & Sons, Ltd.

Joint modeling of longitudinal and survival data with the Cox model and two-phase sampling.

A common objective of cohort studies and clinical trials is to assess time-varying longitudinal continuous biomarkers as correlates of the instantaneous hazard of a study endpoint. We consider the setting where the biomarkers are measured in a designed sub-sample (i.e., case-cohort or two-phase sampling design), as is normative for prevention trials. We address this problem via joint models, with underlying biomarker trajectories characterized by a random effects model and their relationship with instantaneous risk characterized by a Cox model. For estimation and inference we extend the conditional score method of Tsiatis and Davidian (Biometrika 88(2):447-458, 2001) to accommodate the two-phase biomarker sampling design using augmented inverse probability weighting with nonparametric kernel regression. We present theoretical properties of the proposed estimators and finite-sample properties derived through simulations, and illustrate the methods with application to the AIDS Clinical Trials Group 175 antiretroviral therapy trial. We discuss how the methods are useful for evaluating a Prentice surrogate endpoint, mediation, and for generating hypotheses about biological mechanisms of treatment efficacy.

Effects of sample size and model form on the accuracy of model-based estimators of growing stock volume

In this study, we investigate the use of model-based inference in forest surveys in which auxiliary data are available as a probability sample. We evaluate the effects of model form and sample size on estimators of growing stock volume, based on different types of remotely sensed auxiliary data. The study was performed through Monte Carlo sampling simulation using a two-phase sampling design within a simulated study area resembling the conditions in mid-western Finland. We show that the choice of model has a minor to moderate effect on the precision of model-based estimators. Similarly, the choice of estimator of the variance–covariance matrix of model parameter estimates, which is at the core of uncertainty assessment in model-based inference, was also found to have a minor to moderate effect on the precision of model-based estimators. Regarding sample sizes, the model error contribution to the total variance remains the same regardless of the sample size of the first phase (i.e., the size of the sample of auxiliary data); to reduce the model-error contribution, there is a need to increase the sample size of the second phase (i.e., the size of the sample of field plots for developing regression models). As a baseline for comparisons, model-assisted estimators were applied and found to be about equally precise as the model-based estimators, in accordance with the theory for the case when models are estimated from the sample data.

Live above- and belowground biomass of a Mozambican evergreen forest: a comparison of estimates based on regression equations and biomass expansion factors

Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors (BEFs). Yet, national and regional biomass estimates are generally calculated based on BEFs, especially when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. The data were collected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were felled outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates; those estimates were then compared in terms of the following sources of error: plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3 % larger than the BEF-based ones. For the whole tree biomass stock, the percentage of the total error attributed to first phase (random plot selection and variability) was 90 and 88 % for regression- and BEF-based estimates, respectively, being the remaining attributed to biomass models (regression and BEF models, respectively). The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were −2.7 and 5.4 %, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models (than for regression models), except for stem and stem wood components. The regression equation based biomass stocks were found to be slightly larger, associated with relatively smaller errors and least biased than the BEF-based ones. For stem and stem wood, the percentages of their total errors (as total variance) attributed to BEF model were considerably smaller than those attributed to biomass regression equations.

A Note on Complex Two-Phase Sampling with Different Sampling Units of Each Phase

Two phase sampling design is useful to increase estimation efficiency using deep stratification, improved nonresponse adjustment and reduced coverage bias. The same sampling units are commonly used for the first and the second phases in complex two-phase sampling design. In this paper we consider a sampling scheme where the first phase sampling units are clusters and the second phase sampling units are list samples. Using selected clusters in first phase requires that we list up elements in the selected clusters from the first phase and then use the list as a secondary sampling frame for the second phase sampling design. Then we select second phase samples from the listed sampling frame. We suggest an estimator based on the complex two-phase sampling design with different sampling units of each phase. Also the estimated variances of the estimator obtained by using classic and replication variance methods are considered and compared using simulation studies. For real data analysis, 2010 Korea Farm Household Economy Survey (KFHES) and 2011 Korea Agriculture Survey (KAS) are used.