Unequal Selection Probabilities Research Articles

Model selection for incomplete and design-based samples

The Akaike information criterion, AIC, is one of the most frequently used methods to select one or a few good, optimal regression models from a set of candidate models. In case the sample is incomplete, the naive use of this criterion on the so-called complete cases can lead to the selection of poor or inappropriate models. A similar problem occurs when a sample based on a design with unequal selection probabilities, is treated as a simple random sample. In this paper, we consider a modification of AIC, based on reweighing the sample in analogy with the weighted Horvitz-Thompson estimates. It is shown that this weighted AIC-criterion provides better model choices for both incomplete and design-based samples. The use of the weighted AIC-criterion is illustrated on data from the Belgian Health Interview Survey, which motivated this research. Simulations show its performance in a variety of settings.

Association between psychiatric disorders and smoking stages among Latino adolescents

Objective We examined the prevalence of smoking behaviors and their association with psychiatric disorders within a representative sample of youth from Puerto Rico. Method A complex sampling design was used and analyses were conducted to account for the unequal selection probability, stratification and clustering. All analyses were weighted back to the population from which they were drawn. Psychiatric and substance use disorders were assessed using the parent and youth versions of the Diagnostic Interview Schedule for Children, Version 4.0 (DISC-IV). Results After controlling for other comorbidity, major depression and oppositional defiant disorder were significantly associated with nicotine dependence, rather than with lower levels of use. In contrast, conduct disorder was generally associated with lower levels of use rather than with nicotine dependence. As expected, the alcohol and drug use disorders demonstrated some of the strongest associations with individual smoking stages. Conclusions By examining psychiatric correlates of smoking stages within an island-wide sample of adolescents, the present study highlights those disorders that may play a role in the development and/or persistence of smoking behavior in Puerto Rico and further clarifies the appropriate targets for smoking intervention conducted in community settings.

Chronic sinusitis and arterial hypertension in a national population health survey

Background To determine if sinusitis is associated with arterial hypertension in the Canadian population. Methods Complex survey design incorporating stratification, multiple stages of selection, and unequal probabilities of selection of respondents. Cross-sectional data from 52,992 subjects (25,324 males and 27,668 females) 20–64 years of age who participated in the second cycle of the National Population Health Survey (NPHS), conducted in 1996–1997. All these individuals were asked if they had certain chronic health conditions, that had lasted or were expected to last 6 months or more, including sinusitis and high blood pressure. Results Overall, males with sinusitis were just over 2% more likely to have hypertension (9.3% vs. 7.1%) whereas the difference was 4% for women (11.8% vs. 7.6%). Adjusted for age, region, habitation, immigrant status, household size, number of bedrooms, income adequacy, education level, smoking status, alcohol consumption, regular exercise and body mass index, the adjusted odds ratio for females was 1.42 (95% CI 1.04, 1.95). Conclusions Reported sinusitis is associated with hypertension but only in women. Mechanisms linking upper respiratory disorders to hypertension merit investigation.

Geographically Stratified Importance Sampling for the Calibration of Aggregated Destination Choice Models for Trip Distribution

A key feature in estimating and applying destination choice models with aggregate alternatives is to sample a set of nonchosen traffic analysis zones (TAZs), plus the one a trip maker chose, to construct a destination choice set. Computational complexity is reduced because the choice set would be too large if all study area TAZs were included in the calibration. Commonly, two types of sampling strategies are applied to draw subsets of alternatives from the universal choice set. The first, and simplest, approach is to select randomly a subset of nonchosen alternatives with uniform selection probabilities and then add the chosen alternative if it is not otherwise included. The approach, however, is not an efficient sampling scheme because most alternatives for a given trip maker may have small choice probabilities. The second approach, stratified importance sampling, draws samples with unequal selection probabilities determined on the basis of preliminary estimates of choice probabilities for every alternative in the universal choice set. The stratified sampling method assigns different selection probabilities to alternatives in different strata. Simple random sampling is applied to draw alternatives in each stratum. However, it is unclear how to divide the study area so that destination TAZs may be sampled effectively. The process of and findings from implementing a stratified sampling strategy in selecting alternative TAZs for calibrating aggregate destination choice models in a geographic information system (GIS) environment are described. In this stratified sampling analysis, stratum regions varied by spatial location and employment size in the adjacent area were defined for each study area TAZ. The sampling strategy is more effective than simple random sampling in regard to maximum log likelihood and goodness-of-fit values.

Geographically Stratified Importance Sampling for the Calibration of Aggregated Destination Choice Models for Trip Distribution

A key feature in estimating and applying destination choice models with aggregate alternatives is to sample a set of nonchosen traffic analysis zones (TAZs), plus the one a trip maker chose, to construct a destination choice set. Computational complexity is reduced because the choice set would be too large if all study area TAZs were included in the calibration. Commonly, two types of sampling strategies are applied to draw subsets of alternatives from the universal choice set. The first, and simplest, approach is to select randomly a subset of nonchosen alternatives with uniform selection probabilities and then add the chosen alternative if it is not otherwise included. The approach, however, is not an efficient sampling scheme because most alternatives for a given trip maker may have small choice probabilities. The second approach, stratified importance sampling, draws samples with unequal selection probabilities determined on the basis of preliminary estimates of choice probabilities for every alternative in the universal choice set. The stratified sampling method assigns different selection probabilities to alternatives in different strata. Simple random sampling is applied to draw alternatives in each stratum. However, it is unclear how to divide the study area so that destination TAZs may be sampled effectively. The process of and findings from implementing a stratified sampling strategy in selecting alternative TAZs for calibrating aggregate destination choice models in a geographic information system (GIS) environment are described. In this stratified sampling analysis, stratum regions varied by spatial location and employment size in the adjacent area were defined for each study area TAZ. The sampling strategy is more effective than simple random sampling in regard to maximum log likelihood and goodness-of-fit values.

Christofides? randomized response technique in complex sample surveys

Christofides (2003) has given an improved modification of Warner’s (1965) pioneering randomized response (RR) technique in estimating an unknown proportion of people bearing a sensitive characteristic in a given community. As both these RR devices are shown to yield unbiased estimators based only on simple random sampling (SRS) with replacement (WR) but in practice samples are mostly taken with unequal selection probabilities without replacement (WOR), here we present methods of estimation when Christofides’ RR data are available from unequal probability samples. Warner’s (1965) RR device was earlier shown by Chaudhuri (2001) to be applicable in complex surveys. For completeness we present estimators for the variance of our estimator and also describe what to do if some people opt to divulge truths.

The relationship between adult or adolescent sexual abuse and sexual dysfunction: preliminary results from the Boston Area Community Health Survey (BACH)

To examine the relationship between adult or adolescent sexual abuse (ASA) and erectile dysfunction (ED). The analyses were conducted using preliminary data from the Boston Area Community Health Survey (BACH), a population-based random sample survey of Hispanic, non-Hispanic African American, and non-Hispanic Caucasian men aged 30 to 79 years of age residing in Boston, MA. We conducted multiple logistic regression analyses in our sample of 741 men with complete data on ED and ASA. We used complex sampling strategies with stratification and multiple stages; therefore, the data were weighted to account for the unequal probability of subject selection. Weighted and unweighted data were analyzed in this study. ED and ASA were each operationalized using a self-administered questionnaire. The presence of ED was determined based on the subjects response to a question related to impotence, where a response of “Not impotent” was scored as no ED and “minimally”, “moderately,” and “completely impotent” responses were scored as ED present. The presence of ASA was determined based on the subjects responses to questions related to sexual abuse occurring at age 14 or older. Our sample included 262 men with ED and 479 without ED. In addition, 99 men experienced ASA with 642 men having no such experience. In the unweighted analyses, the multiple logistic regression model, controlling for race and age, ASA (odds ratio OR = 1.65, 95% confidence interval CI = 1.10, 2.60) was positively associated with ED. We hypothesized that depression was a mediator here; however, adding depression to the model had only a minor influence on the odds ratio for ASA (OR = 1.59, 95% CI = 1.01, 2.50). The weighted analyses yielded similar results. The multiple logistic regression model, controlling for race and age, yielded ASA OR = 1.75 (95% CI = 0.83, 3.69). The weighted data including depression in the model yielded ASA OR = 1.55 (95% CI = 0.78, 3.08). Men who have experienced sexual abuse as adolescents or adults appear to experience more erectile dysfunction than other men.

The Epidemiology of Chronic Rhinosinusitis in Canadians

To study the prevalence of chronic rhinosinusitis and its risk factors among Canadians. Complex survey design incorporating stratification, multiple stages of selection, and unequal probabilities of selection of respondents. We used the cross-sectional data from 73,364 subjects (34,241 male and 39,123 female subjects) 12 years of age or older who participated in the second cycle of the National Population Health Survey, which was conducted from 1996 to 1997. All these individuals were asked whether they had certain chronic health conditions that had lasted or were expected to last 6 months or longer, including rhinosinusitis. The prevalence of rhinosinusitis was higher in female (5.7%) than in male (3.4%) subjects. The sex difference was consistent across age groups. The prevalence increased with age and leveled off after the age of 60 years. In female but not in male subjects, the prevalence was slightly higher among those living the eastern region or among native Canadians as compared with those living in the central or western regions or immigrants. Cigarette smoking and low income were associated with a higher prevalence of rhinosinusitis in both sexes. The smoking effect was modified by allergy history in male subjects. Rhinosinusitis was more common among subjects with allergy history, asthma, or chronic obstructive pulmonary disease. The prevalence of rhinosinusitis was similar in subjects with or without reporting regular alcohol drinking and exercise. Previous data indicating an increased susceptibility of women to asthma and chronic obstructive pulmonary disease, together with the similar finding for rhinosinusitis, suggest that women have a general increase in susceptibility to respiratory tract disease.

9% of a US community sample had a DSM-IV personality disorder

Samuels J, Eaton W, Bienvenu J et al. Prevalence and correlates of personality disorders in a community sample. British Journal of Psychiatry2002 June ; 180 : 536 –42 . [OpenUrl][1][Abstract/FREE...

A Pseudo Maximum Likelihood Approach to Multilevel Modelling of Survey Data

An application of the pseudo maximum likelihood method to estimation of a multilevel linear model fitted to the dependent observations coming from a finite population is demonstrated. The proposed approach provides a closed form solution for estimating of the model parameters. It is computationally simpler than the iterative procedures suggested in the literature (e.g., the iterative probability weighted least squares method of Pfeffermann et al. (Pfeffermann, D., Skinner, C.J., Holmes, D.J., Goldstein, H., Rasbash, J. (1998). Weighting for unequal selection probabilities in multilevel models. Journal of Royal Statistical Society B 60:23–40)). Issues related to model and sample design hierarchies and their impact on estimation are discussed. A problem of weighting at different levels is addressed. A small simulation study showed that the proposed procedure is efficient even for small within group sample sizes.

Estimating Incidence Rates from Population-Based Case-Control Studies in the Presence of Nonrespondents

In population-based case-control studies, it is of great public-health importance to estimate the disease incidence rates associated with different levels of risk factors. This estimation is complicated by the fact that in such studies the selection probabilities for the cases and controls are unequal. A further complication arises when the subjects who are selected into the study do not participate (i.e. become nonrespondents) and nonrespondents differ systematically from respondents. In this paper, we show how to account for unequal selection probabilities as well as differential nonresponses in the incidence estimation. We use two logistic models, one relating the disease incidence rate to the risk factors, and one modelling the predictors that affect the nonresponse probability. After estimating the regression parameters in the nonresponse model, we estimate the regression parameters in the disease incidence model by a weighted estimating function that weights a respondent's contribution to the likelihood score function by the inverse of the product of his/her selection probability and his/her model-predicted response probability. The resulting estimators of the regression parameters and the corresponding estimators of the incidence rates are shown to be consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use and that failure to adjust for nonresponses could result in severe biases. An illustration with data from a cardiovascular study that motivated this work is presented.

Analysis of domain means in complex surveys

Under simple random sampling, standard methods of analysis of data apply, but data are often collected from complex surveys involving clustering, stratification and unequal probabilities of selection. As a result, application of standard methods to these data without some adjustment for survey design can lead to erroneous inferences. Here the analysis of domain means under complex sampling designs is examined. Rao–Scott-type corrections that take account of the design effects are obtained. The case of one- and two-way analyses of variance of domain means is first studied and then extended to include generalized linear models. The special case of a Poisson model is studied in detail. Finally, data analysis is carried out on domain estimates from two complex surveys to illustrate the proposed methods.

A PROBLEM IN ASCERTAINMENT

In studies of disease inheritance, it is more convenient to collect family data by first locating an affected individual and then enquiring about the status of his or her relatives. Although the different categories of children classified by disease, sex, and other covariates may have a particular multinomial distribution among families of a given size, the numbers as ascertained do not have the same distribution because of unequal probabilities of selection of families. The introduction of weighted distributions to correct for ascertainment bias in the estimation of parameters in the classical segregation model can be traced to Fisher in 1934. This theory was presented in a general formulation by C. R. Rao at the First International Symposium on Classical and Contagious Distributions in 1963. Further expansion on the topic was given by C. R. Rao in the ISI Centenary Volume published in 1985. The effects of different two-phase sampling designs on the estimation of parameters in the classical segregation model are examined. An approximation to the classical segregation likelihood model is found to produce results close to those of the exact likelihood function in Monte Carlo simulations for a balanced two-phase design. This has implications for more complex models in which the computation of the exact likelihood is prohibitive, such as for the enhancement of a typical survey sampling plan designed initially for linkage analysis but then used retroactively for a combined segregation and linkage analysis.

Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population

Abstract In estimating the proportion θA of people in a given community bearing a sensitive characteristic A, in order to protect the respondent's privacy, various techniques of generating randomized response (RR) rather than direct response are available in the literature. But the theory concerning them is developed only for samples selected by ‘simple random sampling’ (SRS) ‘with replacement’ or at most by SRS without replacement method. Illustrating two such RR devices we show how an estimator along with an estimated measure of its error may be developed if the sample of persons may be drawn adopting a complex survey design involving unequal selection probabilities with or without replacement.

ANALYSIS OF LARGE-SCALE SECONDARY DATA IN HIGHER EDUCATION RESEARCH: Potential Perils Associated with Complex Sampling Designs

Most large-scale secondary data sets used in higher education research (e.g., NPSAS or BPS) are constructed using complex survey sample designs where the population of interest is stratified on a number of dimensions and oversampled within certain of these strata. Moreover, these complex sample designs often cluster lower level units (e.g., students) within higher level units (e.g., colleges) to achieve efficiencies in the sampling process. Ignoring oversampling (unequal probability of selection) in complex survey designs presents problems when trying to make inferences—data from these designs are, in their raw form, admittedly nonrepresentative of the population to which they are designed to generalize. Ignoring the clustering of observations in these sampling designs presents a second set of problems when making inferences about variability in the population and testing hypotheses and usually leads to an increased likelihood of committing Type I errors (declaring something as an effect when in fact it is not). This article presents an extended example using complex sample survey data to demonstrate how researchers can address problems associated with oversampling and clustering of observations in these designs.

Exogenous corticosteroids and major depression in the general population

Objective: An existing literature suggests that corticosteroid exposures are associated with an elevated level of depressive symptoms in various clinical populations. The objective of this study was to evaluate this association in a general population sample. Methods: Data from a large-scale Canadian health survey were used in this analysis. The survey sample included 73,402 subjects over the age of 12 from the general Canadian population. The survey interview included a short-form version of the Composite International Diagnostic Interview (CIDI) section evaluating major depressive episodes. All estimates were weighted to account for unequal selection probabilities, and variance estimates were calculated using methods accounting for the survey design. Results: A statistically significant elevation in major depression prevalence was observed in corticosteroid-treated subjects. The estimated 12-month period prevalence of major depression was approximately three times as high in corticosteroid treated vs. non-treated subjects irrespective of age, gender and perceived health. Conclusions: In the general population, persons taking corticosteroids have a higher frequency of major depression than non-exposed subjects. Because this was an analysis of cross-sectional survey data, causal inference is not possible. However, the existence of an epidemiological association, in conjunction with information from the broader literature, suggests that corticosteroid exposure may be a determinant of depressive disorders in the general population.

Stature Prediction Equations for Elderly non-Hispanic White, non-Hispanic black, and Mexican-American Persons Developed from NHANES III Data

Objective To develop new, nationally representative equations to predict stature for racial/ethnic groups of the elderly population in the United States. Design Anthropometric data for stature, knee height, and sitting height for adults aged 60 years or older were collected from a sample of persons in the third National Health and Nutrition Examination Survey (1988-1994), a national probability sample of the US population. Subjects A gender- and racial/ethnic-stratified sample of 4,750 persons from the US population (1,369 non-Hispanic white men, 1,472 non-Hispanic white women, 474 non-Hispanic black men, 481 non-Hispanic black women, 497 Mexican-American men, 457 Mexican-American women) aged 60 years or older participated in this study. Statistical analyses Sampling weights were used to adjust the individual data to account for unequal probabilities of selection, nonresponse, and coverage errors so that all individual data used in these analyses represented national probability estimates. Regression analysis was performed to predict stature in each gender and ethnic group, and the results were cross-validated. Results Stature prediction models using knee height and age and sitting height and age were evaluated for each gender and racial/ethnic group. The equations with knee height and age were selected on the basis of root mean square error and pure errors in cross-validation and on the accuracy and validity of measures of knee height over sitting height. Results of these regressions, including regression coefficients, standard errors of the coefficients, multiple correlation coefficients, root mean square error, and the standard error for the individual for the final equations, are presented. Conclusions New stature prediction equations using knee height and age are presented for non-Hispanic white, non-Hispanic black and Mexican-American elderly persons from current nationally representative data. These equations should be applied when a measure of stature cannot be obtained, for example, for persons with amputations of the leg, or with spinal curvature or who are confined to bed. Predicted stature values are acceptable surrogates in nutritional indexes. J Am Diet Assoc. 1998;98:137-142.

Weighting for Unequal Selection Probabilities in Multilevel Models

Summary When multilevel models are estimated from survey data derived using multistage sampling, unequal selection probabilities at any stage of sampling may induce bias in standard estimators, unless the sources of the unequal probabilities are fully controlled for in the covariates. This paper proposes alternative ways of weighting the estimation of a two-level model by using the reciprocals of the selection probabilities at each stage of sampling. Consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase. Scaling of the weights is proposed to improve the properties of the estimators and to simplify computation. Variance estimators are also proposed. In a limited simulation study the scaled weighted estimators are found to perform well, although non-negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small. The variance estimators perform extremely well. The procedures are illustrated using data from the survey of psychiatric morbidity.

Improving on Probability Weighting for Household Size

In survey sampling, inverse-probability weights are used to correct for unequal selection probabilities, and poststratification weights are used to correct for known or expected discrepancies between the sample and the population (see, e.g., Kish 1992). In this research note, we consider the effects of these adjustments for household size in telephone polling. In a survey in which households are sampled at random, and then a single individual is sampled from each sampled household, individuals in larger households have a smaller probability of being selected. The probability of an individual being included in the survey is inversely proportional to the size of the household in a simple random sample of households if individuals within a household are selected with equal probability and there is no nonresponse. However, composition of the sample is also affected by nonresponse. One source of nonresponse is nonavailabilityno one answers the phone, or no one receives the message on the answering machine. It seems reasonable to suppose that in a larger household it is more likely that someone will be home to receive the phone call. Another source of nonresponse is refusal to participate in the survey.

Stature Prediction Equations Using Knee Height for Elderly Americans from NHANES III (1988–94)

LEARNING OUTCOME: To present nationally representative equations for predicting stature in eldery non-hispanic whites, blacks and Mexican Americans for use in nutritional indices. Predicted values for stature are frequently needed for elderly persons in order to apply equations for estimating basal energy expenditure, subsequent nutrient needs and to calculate indices of nutritional status such as BMI. Anthropometric data for stature, knee height (knht) and sitting height were collected from a sex- and racial/ethnic-stratified sample of 4750 persons from the U.S. population (1369 non-Hispanic White men, 1472 non-Hispanic White women; 474 non-Hispanic Black men, 481 non-Hispanic Black women; 497 Mexican American men, 457 Mexican American women) 60 years of age or older in the NHANES III (1988-94). Sampling weights were used to adjust the individual data to account for unequal probabilities of selection, for non response and coverage errors to represent national probability estimates. Regression analysis was performed to predict stature in each sex and ethnic group, and the results cross validated. In the development of the new equations, the statistical model with knee height and age as predictor variables was chosen the best stature prediction equation in each sex-and racial/ethnic group. Significant regression estimates (p<.05) including regression coefficients, standard errors of the coefficients, R 2, RMSE, and the standard error for the individual (SEI) for the equations are presented in each sex- and racial/ethnic-specific group. This study presents new stature prediction equations for non-Hispanic White, non-Hispanic Black and Mexican American elderly persons developed from current nationally representative data. Supported by Ross Products Division, Abbott Laboratories, Columbus, OH, and by NIH grants HD-12252, HD-27023 and HL53404.