Unequal Probability Sampling Research Articles

New Generalized Regression Estimators Using a Ratio Method and Its Variance Estimation for Unequal Probability Sampling without Replacement in the Presence of Nonresponse

One of the most important problems for planning in economics is that reliable data can be difficult to obtain either because it has not been recorded or because of nonresponse in surveys. This paper is aimed at proposing new generalized regression estimators using the ratio method of estimation for estimating population mean and population total and also variance estimators of the proposed generalized regression estimators in the presence of uniform nonresponse of a study variable. We show in theory that the proposed estimators are almost unbiased under unequal probability sampling without replacement when nonresponse occurs in the study. In the simulation studies, the performances of the proposed estimators were better when compared to the existing ones in terms of minimum relative bias and relative root mean square error. In an application to Thai maize in Thailand with 2019 data, we can see that the proposed estimators gave smaller variance estimates when compared to the existing estimators

Prevalence and factors associated with self-reported HIV testing among adolescent girls and young women in Rwanda: evidence from 2019/20 Rwanda Demographic and Health Survey

BackgroundHIV/AIDS remains a major public health problem globally. The majority of people living with HIV are from Sub-Saharan Africa, particularly adolescent girls and young women (AGYW) aged 15-24 years. HIV testing is crucial as it is the gateway to HIV prevention, treatment, and care; therefore this study determined the prevalence and factors associated with self-reported HIV testing among AGYW in Rwanda.MethodsWe conducted secondary data analysis on the AGYW using data extracted from the nationally representative population-based 2019/2020 cross-sectional Rwanda Demographic and Health Survey (DHS). We described the characteristics of study participants and determined the prevalence of HIV testing and associated factors using the multivariable logistic regression model. We adjusted all our analyses for unequal sampling probabilities using survey weights.ResultsThere were a total of 5,732 AGYW, with the majority (57%) aged 15-19 years, 83% were not living with a man, 80% were from rural areas, 29% were from the East region, and 20% had a history of pregnancy. Self-reported HIV testing prevalence was 55.4% (95%CI: 53.7 to 57.0%). The odds of ever having an HIV test were significantly higher for those aged 20-24 years (aOR 2.87, 95%CI: 2.44 to 3.37); with higher education (aOR 2.41, 95%CI:1.48 to 3.93); who were rich (aOR 2.06, 95%CI:1.57 to 2.70); with access to at least one media (aOR 1.64, 95%CI: 1.14 to 2.37); who had ever been pregnant (aOR 16.12, 95%CI: 9.60 to 27.07); who ever had sex (aOR 2.40, 95%CI: 1.96 to 2.95); and those who had comprehensive HIV knowledge (aOR 1.34, 95%CI: 1.17 to 1.54).ConclusionsWe report an unmet need for HIV testing among AGYW in Rwanda. We recommend a combination of strategies to optimize access to HIV testing services, especially among the 15-19 years adolescent girls, including facility-based testing, school and community outreach, awareness campaigns on HIV testing, and home-based testing through HIV self-testing.

Combining Design- and Model-based Analyses for Cross-national Survey Data

Survey weighting matters when different sampling probabilities between countries, as well as within a country, are related to the response variable conditional on its predictors. This study aims at improving estimation of regression coefficients from a cross-national data set by assessing the relative effectiveness of different techniques for survey weighting to gain in precision. Data came from the Asian subset of the World Values Survey. Using pooled data across five Asian countries, the logistic regression analysis is fitted to examine the relationship between information seeking behaviors as predictor variables and political participation as a response variable in the context of East and Southeast Asia. The results show that, sampling weights have an advantage of reducing standard errors when estimating a structural relationship among the variables, so much so that the population is stratified into different countries where the regression model is likely to vary in explaining the within-country data. Therefore, the unequal sampling probability of the cross-national survey needs to be adjusted for by accounting for different probabilities of selection between countries. Incorporating the between-country survey weighting into a model-based analysis is a remedy for the problem in the estimated regression parameters.

Ultraprocessed Food Consumption, Diet Patterns, and Perception of Diet Quality and Body Weight in the US

ObjectivesUltraprocessed foods (UPF) have recently been examined as a risk factor for diet-related disease in adults. Studies have demonstrated changes in trends in consumption patterns of UPF over the past several decades, but few studies have evaluated the association between UPF and perception of diet along with measured dietary intake. The objective of this study was to examine the association between UPF consumption, dietary intake patterns, and self-perceived diet quality in a nationally representative sample of US children and adults. MethodsData from the 2017–2018 NHANES was used for this study. Dietary intake information was collected using 24-hour recall; recalled foods were classified using the NOVA classification system and NOVA Category 4 (ultraprocessed) were identified. All data were analyzed using SAS 9.4 survey procedures to account for the unequal sampling probability and complex survey design of the. ResultsConsumption of ultraprocessed foods is associated with poor diet in US children and adults. In adults, higher consumption of ultraprocessed foods was is associated with higher dietary energy density (p = 0.0001), lower vegetable consumption (p = 0.002), greater intake of added sugars (p < 0.0001), and lower intake of plant-based protein foods (p < 0.0001). In children, consumption of ultraprocessed foods was associated with higher dietary energy density (p < 0.0001), lower consumption of vegetables (p < 0.0001) even when including fewer servings of white potatoes (p = 0.04). Interestingly, perception of diet quality was also strongly associated with ultraprocessed food consumption. Individuals who self-reported a ‘poor’ diet consumed 84% of daily calories from ultraprocessed foods, compared to individuals who self-reported an ‘excellent’ diet reporting 52% of daily calories from ultraprocessed foods, p < 0.0001. Adults who perceived themselves to be overweight also reported higher consumption of processed foods than adults who perceived themselves to be about the right weight (60% vs. 56%, p = 0.004). There was no association with processed food consumption and parent perception of child weight. ConclusionsUltraprocessed food consumption is associated with lower diet quality in US children and adults. Additionally, UPF consumption is associated with perception of diet quality and body weight. Funding SourcesNone.

Ultraprocessed Food Intake Is Associated With Poor Cardiovascular Fitness in US Children and Adolescents

ObjectivesUltraprocessed food intake is an established risk factor for cardiovascular disease in adults, however few studies have examined the association between intake of ultraproecssed foods during childhood and risk for cardiovascular disease. The objective of this study was to determine the association between eating patterns, specifically consumption of ultraprocessed foods, and markers of physical fitness in a nationally representative sample of children and youth. MethodsUsing data from NHANES National Youth Fitness Survey, the association between ultraprocessed food consumption and cardiovascular fitness level was evaluated. During the NNYFS, cardiovascular fitness was assessed in adolescents aged 12–15 y and locomotor development was assessed in children age 3–5. Dietary intake information was collected using 24-hour recall; recalled foods were classified using the NOVA classification system and NOVA Category 4 (ultraprocessed) were identified. Cardiovascular fitness level was categorized based on gender-age specific cut-points of estimated VO2max. All data were analyzed using SAS 9.4 survey procedures to account for the unequal sampling probability and complex survey design of the. ResultsIn older children, we observed a significant positive association between consumption of ultraprocessed foods and cardiovascular fitness level after controlling for age, sex, race, and household income. Children with cardiovascular fitness levels categorized as “high risk” consumed approximately 200kcal more/day of ultraprocessed foods than children in the “healthy fitness zone”, p = 0.002. In younger children, greater intake of ultraprocessed foods was associated with lower locomotor development score; children with the lowest locomotor development scores consumed 273kcal/more day of ultraprocessed foods than children with the highest locomotor development scores, p = 0.0006. ConclusionsThese findings expand on previous work from our group evaluating the association between childhood eating behaviors and fitness indicators. Interventions that aim to educate families about cost-effective methods of reducing ultraprocessed food intake may assist in decreasing risk for cardiovascular health problems in adulthood. Funding SourcesNone.

Bootstrap Assessment of Crop Area Estimates Using Satellite Pixels Counting

Crop area estimates based on counting pixels over classified satellite images are a promising application of remote sensing to agriculture. However, such area estimates are biased, and their variance is a function of the error rates of the classification rule. To redress the bias, estimators (direct and inverse) relying on the so-called confusion matrix have been proposed, but analytic estimators for variances can be tricky to derive. This article proposes a bootstrap method for assessing statistical properties of such estimators based on information from a sample confusion matrix. The proposed method can be applied to any other type of estimator that is built upon confusion matrix information. The resampling procedure is illustrated in a small study to assess the biases and variances of estimates using purely pixel counting and estimates provided by both direct and inverse estimators. The method has the advantage of being simple to implement even when the sample confusion matrix is generated under unequal probability sample design. The results show the limitations of estimates based solely on pixel counting as well as respective advantages and drawbacks of the direct and inverse estimators with respect to their feasibility, unbiasedness, and variance.

Evaluation of multiple imputation approaches for handling missing covariate information in a case-cohort study with a binary outcome

BackgroundIn case-cohort studies a random subcohort is selected from the inception cohort and acts as the sample of controls for several outcome investigations. Analysis is conducted using only the cases and the subcohort, with inverse probability weighting (IPW) used to account for the unequal sampling probabilities resulting from the study design. Like all epidemiological studies, case-cohort studies are susceptible to missing data. Multiple imputation (MI) has become increasingly popular for addressing missing data in epidemiological studies. It is currently unclear how best to incorporate the weights from a case-cohort analysis in MI procedures used to address missing covariate data.MethodA simulation study was conducted with missingness in two covariates, motivated by a case study within the Barwon Infant Study. MI methods considered were: using the outcome, a proxy for weights in the simple case-cohort design considered, as a predictor in the imputation model, with and without exposure and covariate interactions; imputing separately within each weight category; and using a weighted imputation model. These methods were compared to a complete case analysis (CCA) within the context of a standard IPW analysis model estimating either the risk or odds ratio. The strength of associations, missing data mechanism, proportion of observations with incomplete covariate data, and subcohort selection probability varied across the simulation scenarios. Methods were also applied to the case study.ResultsThere was similar performance in terms of relative bias and precision with all MI methods across the scenarios considered, with expected improvements compared with the CCA. Slight underestimation of the standard error was seen throughout but the nominal level of coverage (95%) was generally achieved. All MI methods showed a similar increase in precision as the subcohort selection probability increased, irrespective of the scenario. A similar pattern of results was seen in the case study.ConclusionsHow weights were incorporated into the imputation model had minimal effect on the performance of MI; this may be due to case-cohort studies only having two weight categories. In this context, inclusion of the outcome in the imputation model was sufficient to account for the unequal sampling probabilities in the analysis model.

Adapting Nearest Neighbor for Multiple Imputation: Advantages, Challenges, and Drawbacks

Abstract The U.S. Census Bureau has historically used nearest neighbor (NN) or random hot deck (RHD) imputation to handle missing data for many types of survey data. Using these methods removes the need to parametrically model values in imputation models. With strong auxiliary information, NN imputation is preferred because it produces more precise estimates than RHD. In addition, NN imputation is robust against a misspecified response mechanism if missingness depends on the auxiliary variable, in contrast to RHD which ignores the auxiliary information. A compromise between these two methods is k-NN imputation, which identifies a set of the k closest neighbors (“donor pool”) and randomly selects a single donor from this set. Recently these methods have been used for multiple imputation (MI), enabling variance estimation via the so-called Rubin’s Combining Rules. The Approximate Bayesian Bootstrap (ABB) is a simple-to-implement algorithm that makes the RHD “proper” for MI. In concept, ABB should work to propagate uncertainty for NN MI; bootstrapping respondents mean each nonrespondent’s one “nearest” donor will not be available for every imputation. However, we demonstrate through simulation that NN MI using ABB leads to variance underestimation. This underestimation is somewhat but not entirely attenuated with k-NN imputation. An alternative approach to variance estimation after MI, bootstrapped MI, eliminates the underestimation with NN imputation, but we show that it suffers from overestimation of variance with nonnegligible sampling fractions under both equal and unequal probability sampling designs. We propose a modification to bootstrapped MI to account for nonnegligible sampling fractions. We compare the performance of RHD and the various NN MI methods under a variety of sampling designs, sampling fractions, distribution shapes, and missingness mechanisms.

SynthACS: Spatial Microsimulation Modeling with Synthetic American Community Survey Data

synthACS is an R package that provides flexible tools for building synthetic microdatasets based on American Community Survey (ACS) base tables, allows data-extensibility and enables to conduct spatial microsimulation modeling (SMSM) via simulated annealing. To our knowledge, it is the first R package to provide broadly applicable tools for SMSM with ACS data as well as the first SMSM implementation that uses unequal probability sampling in the simulated annealing algorithm. In this paper, we contextualize these developments within the SMSM literature, provide a hands-on user-guide to package synthACS, present a case study of SMSM related to population dynamics, and note areas for future research.

855Multiple Imputation in the Context of Case-Cohort Studies: Simulation and Case Study

Abstract Background Multiple imputation (MI) is commonly used to address missing data in epidemiological studies, but valid use requires compatibility between the imputation and analysis models. Case-cohort studies use unequal sampling probabilities for cases and controls which are often accounted for during analyses through inverse probability weighting (IPW). It is unclear how to apply MI for missing covariates while achieving compatibility in this setting. Methods A simulation study was conducted with missingness in two covariates, motivated by a case-cohort investigation within the Barwon Infant Study. MI methods considered involved including interactions between the outcome (as a proxy for weights) and analysis variables, stratification by weights, and ignoring weights, within the context of an IPW analysis. Factors such as the target estimand, proportion of incomplete observations, missing data mechanism and subcohort selection probabilities were varied to assess performance of MI methods. Results There was similar performance in terms of bias and efficiency across the MI methods, with expected improvements compared to IPW applied to the complete cases. Precision tended to decrease as the subcohort selection probability decreased. Similar results were observed irrespective of the proportion of incomplete cases. Conclusions Our results suggest that it makes little difference how weights are incorporated in the MI model in the analysis of case-cohort studies, potentially due to only two weight classes in this setting. Key messages If and how the weights are incorporated in the imputation model may have little impact in the analysis of case-cohort studies with incomplete covariates

Kenneth (Ken) Ronald Walter Brewer (1931–2021)

Kenneth (Ken) Ronald Walter Brewer (1931–2021)

On the correct implementation of the Hanurav-Vijayan selection procedure for unequal probability sampling without replacement

The Hanurav-Vijayan procedure belongs to the class of exact, draw-by-draw algorithms for unequal probability sampling without replacement. This procedure has been implemented in market-leading commercial statistical packages such as SAS/STAT and SPSS, which have popularized its use. Unfortunately, the description of the Hanurav-Vijayan procedure in the documentation of these softwares is partially flawed, propagating errors issued from the statistical literature. Besides, despite it is often used, this procedure has almost fallen in oblivion in the literature devoted to sampling probability designs, and no comparisons were made with other competing methods. It is the purpose of the present paper to rehabilitate the Hanurav-Vijayan procedure by correctly describing its implementation details and providing some basic elements of comparison with the well-known Rao-Sampford procedure.

Prevalence of self-reported HIV testing and associated factors among adolescent girls and young women in South Africa: Results from a 2017 nationally representative population-based HIV survey

ObjectivesThis article estimated the prevalence of self-reported HIV testing and identified associated factors among sexually active adolescent girls and young women (AGYW), aged 15–24 years, in South Africa. Study designThis is a secondary data analysis of a nationally representative population-based cross-sectional multi-stage cluster survey of households in South Africa conducted in 2017. MethodsDescriptive statistics were used to describe AGYW characteristics and the multivariable logistic regression model was used to determine factors associated with HIV testing. All analyses were adjusted for unequal sampling probabilities using survey weights. ResultsFrom the 1360 AGYW analysed (70.3% aged 20–24 years, 89.0% Black African, 95.5% unmarried, 88.7% unemployed), 1154 (estimate 85.8% (95% Confidence Interval (CI): 83.0 to 88.1)) had ever tested for HIV. In adjusted analysis, AGYW who had been pregnant in the past 24 months (adjusted Odds Ratio [aOR] 3.67, 95%CI: 1.68 to 8.02), were older (20–24 years: aOR 3.13, 95%CI: 1.86 to 5.28), or did not use condoms consistently compared to using them every time (almost every time: aOR 3.31, 95%CI: 1.07 to 10.22; sometimes: aOR 2.54, 95%CI: 1.29 to 4.98) had significantly higher odds of ever testing for HIV. ConclusionsThis research identified an unmet need for HIV testing among AGYW and increasing awareness of HIV counselling and testing among AGYW in South Africa is recommended.

A prediction approach in adaptive sampling

Adaptive cluster sampling (ACS) due to Thompson (J Am Stat Assoc 85(412):1050–1059, 1990) is a tool to survey rare and hidden elements in a population as an improvement over traditional survey procedures. In ACS, if an observed sampled unit satisfies the given criterion of rarity, its neighboring units are added to the sample and this is continued until one is detected with no rarity. Chaudhuri (Calcutta Stat Assoc Bull 50(3–4):238–253, 2000) extended the above to unequal probability sampling as Adaptive sampling. In practice, often network sizes turn out too big demanding high cost and time. So, Chaudhuri et al. (J Stat Plan Inference 121: 175–189, 2004) gave a subsampling technique to restrict the sample size in Adaptive Sampling. Towards this end, Chaudhuri et al. (J Stat Plan Inference 134: 254–267, 2005) developed a sample size restriction technique. But in Adaptive sampling, capturing neighboring rare units turn out difficult because of various hazards. We propose to try Royall’s (Biometrika 57: 377–389, 1970) prediction approach here to model features of uncaptured network units. We employ Brewer’s (J Am Stat Assoc 74 (368): 911–915, 1979) model-assisted approach to derive a predictor with asymptotic design unbiasedness based on unequal probability samples and examine its efficacy by simulations.

A new generalized regression estimator and variance estimation for unequal probability sampling without replacement for missing data

The aim of this paper is to develop a new generalized regression estimator along with a method for estimating the variance of a population total using unequal probability sampling without replacement in the presence of nonresponse. We consider under less restricted situations where response probabilities are non-uniform and a sampling fraction can be both negligible and not negligible where both circumstances are more realistic in practice under the reverse framework. Theoretical proof shows that the new estimator is an almost unbiased estimator measured under the missing at random mechanism. Simulation studies and real data are used to exhibit some properties of the proposed estimators.

A Note on Chromy’s Sampling Procedure

Abstract Chromy (1979) proposed an unequal probability sampling algorithm, which is the default sequential method used in the SURVEYSELECT procedure of the SAS software. In this article, we demonstrate that Chromy sampling is equivalent to pivotal sampling. This makes it possible to estimate the variance unbiasedly for the randomized version of the method programmed in the SURVEYSELECT procedure.

Multiple imputation methods for handling missing values in longitudinal studies with sampling weights: Comparison of methods implemented in Stata.

Many analyses of longitudinal cohorts require incorporating sampling weights to account for unequal sampling probabilities of participants, as well as the use of multiple imputation (MI) for dealing with missing data. However, there is no guidance on how MI and sampling weights should be implemented together. We simulated a target population based on the Australian Bureau of Statistics Estimated Resident Population and drew 1000 random samples dependent on three design variables to mimic the Longitudinal Study of Australian Children. The target analysis was the weighted prevalence of overweight/obesity over childhood. We evaluated the performance of several MI approaches available in Stata, based on multivariate normal imputation (MVNI), fully conditional specification (FCS) and twofold FCS: a weighted imputation model, imputing missing data separately for each quintile sampling weight grouping, including the design stratum indicator in the imputation model, and using sampling weights as a covariate in the imputation model. Approaches based on available cases and inverse probability weighting (IPW), with time-varying weights, were also compared. We observed severe issues of convergence with FCS and twofold FCS. All MVNI-based approaches performed similarly, producing minimal bias and nominal coverage, except for when imputation was conducted separately for each quintile sampling weight group. IPW performed equally as well as MVNI-based approaches in terms of bias, however, was less precise. In similar longitudinal studies, we recommend using MVNI with the design stratum as a covariate in the imputation model. If this is unknown, including the sampling weight as a covariate is an appropriate alternative.

An estimation of a sensitive attribute using adjusted Kuk’s randomization device with stratified unequal probability sampling

In this article, we develop the estimation of the sensitive attribute proportion of the population which is composed of several clusters by applying unequal probability sampling to the Su et al.’s model which is an adjusted Kuk’s model. We estimate the sensitive parameter, its variance and variance estimator for each unequal probability sampling and two-stage equal probability sampling. We extend our model to the case of stratified unequal probability sampling and stratified two-stage equal probability one. Finally, we compare the efficiency of the two sensitive estimators, one is obtained by unequal probability sampling and the other is obtained by stratified unequal probability sampling.

Uncertainty Estimation for Pseudo‐Bayesian Inference Under Complex Sampling

SummarySocial and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilised by federal statistical agencies are typically constructed to maximise the efficiency of the target domain level estimator (e.g. indexed by geographic area) within cost constraints for survey administration. Such designs may induce dependence between the sampled units; for example, with employment of a sampling step that selects geographically indexed clusters of units. A sampling‐weighted pseudo‐posterior distribution may be used to estimate the population model on the observed sample. The dependence induced between coclustered units inflates the scale of the resulting pseudo‐posterior covariance matrix that has been shown to induce under coverage of the credibility sets. By bridging results across Bayesian model misspecification and survey sampling, we demonstrate that the scale and shape of the asymptotic distributions are different between each of the pseudo‐maximum likelihood estimate (MLE), the pseudo‐posterior and the MLE under simple random sampling. Through insights from survey‐sampling variance estimation and recent advances in computational methods, we devise a correction applied as a simple and fast postprocessing step to Markov chain Monte Carlo draws of the pseudo‐posterior distribution. This adjustment projects the pseudo‐posterior covariance matrix such that the nominal coverage is approximately achieved. We make an application to the National Survey on Drug Use and Health as a motivating example and we demonstrate the efficacy of our scale and shape projection procedure on synthetic data on several common archetypes of survey designs.

Dietary Energy Density, Not Caloric Intake, Is Associated with Sedentary Behavior in Older US Adults

Abstract Objectives National surveillance data has demonstrated that fewer than 1 in 5 older adults meet physical activity (PA) guidelines, despite research showing that PA is associated with decreased functional limitations in older adults. Most strategies for healthy eating focus on caloric intake as opposed to overall diet quality. Energy density (ED; kcal/g) is an established indicator of diet quality as well as an established risk factor for chronic disease. Studies in children and adolescents have also demonstrated that dietary ED is associated with physical functioning, however there has been minimal research in older adults. The objective of the present study was to evaluate the association between dietary energy density and physical activity in a nationally representative sample of older adults. Methods Using data from a sample of 4484 adults &amp;gt; 60y who participated in the 2014–2016 NHANES, the association between dietary ED and physical functioning was assessed. During the NHANES, participants were asked to report whether or not they engaged in moderate PA (mPA) and report hours of sedentary behaviors. All data were analyzed using SAS 9.4 survey procedures to account for the unequal sampling probability and complex survey design of the NHANES. Results Energy-dense diets were associated with sedentary behavior and lower physical abilities in older adults. Individuals who reported engaging in mPA had a significantly lower dietary ED than those who did not engage in any mPA; this was observed in men (1.71 vs. 1.87, P = 0.03) and women (1.61 vs. 1.72, P = 0.02) after controlling for age, education, race/ethnicity, and beverage ED. Further, each unit increase in dietary energy density was associated with a 39% decrease in probability of engaging in mPA (P &amp;lt; 0.001). In contrast, there was no association between caloric intake and sedentary behavior in this population Low-ED diets were also lower in saturated fat; higher in vegetable, fiber and micronutrient content, offering additional health benefits. Conclusions These results indicate the energy density of the diet is associated with diet quality and active lifestyle behaviors. Strategies that promote low-ED diets may be effective tools in the promotion of healthy aging in the US population. Funding Sources None.