Two-phase Stratified Sampling Research Articles

A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling.

This paper proposes a new calibration estimator for population variance within a stratified two-phase sampling design. It takes into account random non-response and measurement errors, specifically applying this method to estimate the variance in Gas turbine exhaust pressure data. The study integrates additional information from two highly positively correlated auxiliary variables to develop a general class of estimators tailored for the stratified two-phase sampling scheme. The properties of these estimators, in terms of their biases and mean square errors, have been thoroughly examined and extensively analyzed through numerical and simulation studies. Furthermore, the calibrated weights of the strata are derived. The proposed estimators outperform the natural estimator of population variance. Finally, suitable recommendations have been made for survey statisticians intending to apply these findings to real-life problems.

Calibration-based approach in estimation of population mean under stratified two-phase sampling scheme

Calibration-based approach in estimation of population mean under stratified two-phase sampling scheme

Ratio estimation of two population means in two-phase stratified random sampling under a scrambled response situation

In this paper, we have described the development of an effective two-phase stratified random sampling estimation procedure in a scrambled response situation. Two different exponential, regression-type estimators were formed separately for different structures of two-phase stratified sampling schemes. We have studied the properties of the suggested strategy. The performance of the proposed strategy has been demonstrated through numerical evidence based on a data set of a natural population and a population generated through simulation studies. Taking into consideration the encouraging findings, suitable recommendations for survey statisticians are prepared for the application of the proposed strategy in real-life conditions.

Mean Estimation of a Sensitive Variable under Measurement Errors using Three-Stage RRT Model in Stratified Two-Phase Sampling

In the present study, the problem of mean estimation of a sensitive variable using three-stage RRT model under measurement errors is addressed. A generalized class of estimators is proposed using a mixture of auxiliary attribute and variable. Some members of the proposed generalized class of estimators are identified and studied. The bias and mean squared error (MSE) expressions for the proposed estimators are correctly derived up to first order Taylor's series of approximation. The proposed estimator's efficiency is investigated theoretically and numerically using real data. From the numerical study, the proposed estimators outperforms existing mean estimators. Furthermore, the efficiencies of the mean estimators’ decreases as the sensitivity level of the survey question increases.

Mean Estimation of a Sensitive Variable under Nonresponse Using Three-Stage RRT Model in Stratified Two-Phase Sampling

The present study addresses the problems of mean estimation and nonresponse under the three-stage RRT model. Auxiliary information on an attribute and variable is used to propose a generalized class of exponential ratio-type estimators. Expressions for the bias, mean squared error, and minimum mean squared error for the proposed estimator are derived up to the first degree of approximation. The efficiency of the proposed estimator is studied theoretically and numerically using two real datasets. From the numerical analysis, the proposed generalized class of exponential ratio-type estimators outperforms ordinary mean estimators, usual ratio estimators, and exponential ratio-type estimators. Furthermore, the efficiencies of the mean estimators are observed to decrease with an increase in the sensitivity level of the survey question. As the inverse sampling rate and nonresponse rate go up, so does the efficiency of the mean estimators, which makes them more accurate.

Generalized Estimator for Population Mean Using Auxiliary Attribute in Stratified Two-Phase Sampling

In sampling theory, the auxiliary information is widely used to increase precision of the estimators when the study variable is correlated with the auxiliary variable. In several practical situations, the auxiliary information is available in the form of the auxiliary attribute(s). In this paper, we proposed a generalized estimator for the estimation of finite population mean using the auxiliary attribute under stratified two-phase sampling. The mathematical expressions of approximate bias and mean square error (MSE) of the proposed estimator are obtained to the first-order. Many special cases of the proposed estimator are also obtained using the known parameters of the auxiliary attribute. The algebraic comparisons of the MSE of the proposed estimator have been made the MSE of the competing estimators. The performance of the proposed estimator is evaluated using real data-sets. The results illustrate the good performance of the proposed estimators and its sub-cases.

Combined Type Generalized Classes of Efficient Estimators of Mean in Joint Presence of Measurement Error and Non-response using Stratified Two-Phase Sampling

Combined Type Generalized Classes of Efficient Estimators of Mean in Joint Presence of Measurement Error and Non-response using Stratified Two-Phase Sampling

Two-phase stratified sampling and analysis for predicting binary outcomes.

The two-phase study design is a cost-efficient sampling strategy when certain data elements are expensive and, thus, can only be collected on a sub-sample of subjects. To date guidance on how best to allocate resources within the design has assumed that primary interest lies in estimating association parameters. When primary interest lies in the development and evaluation of a risk prediction tool, however, such guidance may, in fact, be detrimental. To resolve this, we propose a novel strategy for resource allocation based on oversampling cases and subjects who have more extreme risk estimates according to a preliminary model developed using fully observed predictors. Key to the proposed strategy is that it focuses on enhancing efficiency regarding estimation of measures of predictive accuracy, rather than on efficiency regarding association parameters which is the standard paradigm. Towards valid estimation and inference for accuracy measures using the resultant data, we extend an existing semiparametric maximum likelihood ethod for estimating odds ratio association parameters to accommodate the biased sampling scheme and data incompleteness. Motivated by our sampling design, we additionally propose a general post-stratification scheme for analyzing general two-phase data for estimating predictive accuracy measures. Through theoretical calculations and simulation studies, we show that the proposed sampling strategy and post-stratification scheme achieve the promised efficiency improvement. Finally, we apply the proposed methods to develop and evaluate a preliminary model for predicting the risk of hospital readmission after cardiac surgery using data from the Pennsylvania Health Care Cost Containment Council.

Calibration estimator of population mean under stratified two-phase sampling using two auxiliary variables

In the present paper, we have tried to discover a new calibration estimator of the population mean under stratified two-phase sampling design utilizing the information on two auxiliary variables. In order to develop the calibration estimator, we have obtained new optimum stratum weights so that the MSE/Variance of the estimator would be minimized. Moreover, we have compared the efficiency of the proposed calibration estimator with that of the calibration estimator considered under the stratified two-phase sampling scheme using single auxiliary variable. An empirical illustration along with a simulation analysis has also been presented to demonstrate the theoretical results.

On distribution function under two-phase stratified sampling using two auxiliary variables for mean estimation

We suggest a new class of difference-type estimators under two-phase stratified sampling when using information from two auxiliary variables including their distribution functions. The bias and MSE expressions are derived up to first degree of approximations. It is observed that the proposed class of difference-type estimators is more efficient as compared to the estimators: sample mean, ratio, exponential-ratio, traditional difference-types, Chand, Singh and Choudhury, and Anieting and Ezugwu regression type. The comparisons are made in Section 4 and results based on real data sets and simulation are given in Section 5. It is observed that the performances of the generalized class of estimators is remarkable.

Nonparametric inference for distribution functions with stratified samples

We consider nonparametric estimation of a distribution function when data are collected from two-phase stratified sampling without replacement. We study the inverse probability weighted empirical distribution function and propose a novel computational procedure to construct a confidence band. Two-phase sampling design induces heterogeneity across strata and dependence due to sampling without replacement. Two major statistical challenges from this design are: (1) the standard practice to approximate sampling without replacement by Bernoulli sampling leads to an incorrect coverage probability, and (2) a complicated limiting process of the proposed estimator does not allow one to analytically compute quantiles of the supremum of the limiting process nor to apply existing bootstrap methods to the proposed estimator. To address these issues, we rigorously establish the asymptotic properties of the proposed estimator and develop a simulation-based method to estimate the limiting process. The finite sample performance is evaluated through a simulation study. A Wilms tumor example is provided.

Sampling strategies to evaluate the prognostic value of a new biomarker on a time-to-event end-point

BackgroundThe availability of large epidemiological or clinical data storing biological samples allow to study the prognostic value of novel biomarkers, but efficient designs are needed to select a subsample on which to measure them, for parsimony and economical reasons. Two-phase stratified sampling is a flexible approach to perform such sub-sampling, but literature on stratification variables to be used in the sampling and power evaluation is lacking especially for survival data.MethodsWe compared the performance of different sampling designs to assess the prognostic value of a new biomarker on a time-to-event endpoint, applying a Cox model weighted by the inverse of the empirical inclusion probability.ResultsOur simulation results suggest that case-control stratified (or post stratified) by a surrogate variable of the marker can yield higher performances than simple random, probability proportional to size, and case-control sampling. In the presence of high censoring rate, results showed an advantage of nested case-control and counter-matching designs in term of design effect, although the use of a fixed ratio between cases and controls might be disadvantageous. On real data on childhood acute lymphoblastic leukemia, we found that optimal sampling using pilot data is greatly efficient.ConclusionsOur study suggests that, in our sample, case-control stratified by surrogate and nested case-control yield estimates and power comparable to estimates obtained in the full cohort while strongly decreasing the number of patients required. We recommend to plan the sample size and using sampling designs for exploration of novel biomarker in clinical cohort data.

Effects of Random Sampling Methods on Maximum Likelihood Estimates of a Simple Logistic Regression Model

The paper investigates the comparative effects of several random sampling methods on the maximum likelihood estimates of a simple logistic regression model. The study uses simulated data (logistic populations with pre-defined parameter values) that used Monte Carlo methods to simulate. Sampling techniques include Simple Random Sampling (SRS) and six variations of Stratified Sampling where two are single-stage Stratified Sampling and four are choice-based (two-phase) Stratified Sampling. Parameter estimates arising under each sampling technique were compared using performance measures Bias, Standard Error & Percentage of models that are feasibly estimated. The simulation-based analysis found that choice-based sampling with proportional allocation in both phases is the best-suited sampling technique for parameter estimation of a simple logistic regression model.

Exponential ratio and product type estimators of the mean in stratified two-phase sampling

In this study, we propose exponential ratio estimators in the stratified two-phase sampling utilizing an auxiliary attribute. The expressions for the mean squared error of these exponential-type estimators under two different cases are derived and theoretical comparisons are made with competing estimators. We show that the proposed estimators have a lower mean square error than the simple mean estimator, usual stratified two-phase sampling ratio, and product estimators, usual exponential ratio and product estimators for the stratified two-phase sampling under the obtained conditions in theory. In addition, these theoretical results are supported with the aid of a numerical example.

A general class of calibration estimators under stratified random sampling in presence of various kinds of non-sampling errors

This paper addresses the issue of estimating the population variance of a study character in the joint presence of random non-response and measurement errors and its application for estimating variations in biological data. Additional information on two highly positively correlated auxiliary variables has been incorporated to develop a general class of estimators under stratified two-phase sampling scheme. Its properties, in terms of bias and mean square error, have been examined. Optimum strata weights have been determined by employing suitable calibration techniques. Simulations using artificial data, as well as real data involving the variation in prostate specific antigen in different age groups when information about prostrate cancer volume and prostate weight is available, demonstrate the performance of the proposed class of estimators with respect to a contemporary estimator. Relevant R codes have been provided as Appendix.

New improved calibration estimator based on two auxiliary variables in stratified two-phase sampling

This paper considers the problem of estimating the population mean of the study variable when auxiliary information is not available and proposes new calibration approach alternative to the recent existing calibration estimators for estimating population mean of the study variable using two auxiliary variables in stratified two-phase sampling. The theory of new calibration estimation is given and optimum weights are derived under two-phase sampling approach. A simulation study is carried out to performance of the proposed calibration estimator with other existing calibration estimators. The results demonstrate that the proposed calibration estimator is more efficient than other existing calibration estimators of the population mean in stratified two-phase sampling.

Generalized Chain Exponential-Type Estimators under Stratified Two-Phase Sampling with Subsampling the Nonrespondents

In this paper some generalized exponential-type chain estimators have been proposed for the finite population mean in the presence of nonresponse under stratified two-phase sampling when mean of another auxiliary variable is readily available. The expressions for the bias and mean square error of proposed estimators have been derived. The comparisons for proposed estimators have been made in theory with Hansen-Hurwitz’s, J. Am. Stat. Assoc. 41 (1946), 517–529, and Tabasum and Khan’s, J. Indian Soc. Agric. Stat. 58 (2004), 300–306, 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.

Family of combined-type estimators for population mean using stratified two-phase sampling scheme under non-response

In this paper, we have proposed a family of combined-type estimators of the population mean in stratified random sampling using the information on an auxiliary variable under the situation in which non-response is observed on both study and auxiliary variables. In order to propose the family, we have adopted the idea of two-phase sampling scheme when the population mean of auxiliary variable is not known. The expressions for the bias and mean square error of the proposed family up to the first degree of approximation have been derived. A theoretical study on the cost of the survey has also been carried out. A numerical illustration has been presented to hold up the theoretical results.

Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

Validation of the Edinburgh Postnatal Depression Scale against both DSM-5 and ICD-10 diagnostic criteria for depression

BackgroundThe Edinburgh Postnatal Depression Scale (EPDS) is widely used in many countries to screen women for depression in the perinatal period. However, across studies the psychometric properties and cutoff scores of the EPDS have varied considerably; potentially due to different depression criteria and diagnostic systems being used. Therefore, we validated the Danish EPDS against a depression diagnosis according to both DSM-5 and ICD-10. Furthermore, we examined whether the Danish EPDS is multidimensional, as it has previously been suggested.MethodsWomen (N = 324) were recruited after routine screenings with the EPDS between 2 and 10 months postpartum (T1). At a subsequent home visit (T2), the EPDS and the Structured Clinical Interview for DSM-5 were administered. Diagnostic interviews were audio recorded to enable subsequent coding for ICD-10 diagnoses and inter-rater reliability analysis. A two-phase stratified sampling strategy with three sampling categories (EPDS-score at T1) was used. Using the distribution of 4931 T1 EPDS-scores from the same population from which we sampled the participants, we used sampling weighing to reweight the sample. The calculation of weights was based upon the mother’s sampling category at T1 (i.e. the probability of being sampled) and the weights were applied when assessing the receiver operation characteristics (ROCs) of the EPDS. Sensitivity, specificity, positive predictive value, negative predictive value and area under the ROC curve were computed from the reweighted data for all relevant cutoff values. CIs were computed by embedding the calculations in a weighted logistic regression. Exploratory factor analysis was done using oblique rotation. Parallel analysis was used to assess the number of factors.ResultsA score of 11 or more was found to be the optimal cutoff for depression according to both DSM-5 and ICD-10 criteria. Factor analysis suggested that the Danish EPDS consists of three factors, including an ‘anxiety factor’.ConclusionsThe Danish EPDS has reasonable sensitivity and specificity at a cutoff score of 11 or more. There are no notable differences with respect to using ICD-10 or DSM-5 criteria for depression in terms of optimal cutoff. The variation in cutoff scores is likely to be due to cultural variations in the expression of depressive symptoms.