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Survey calibration is a widely used method to estimate the population mean or total score of a target variable, particularly in medical research. In this procedure, auxiliary information related to the variable of interest is used to recalibrate the estimation weights. However, when the auxiliary information includes qualitative variables, traditional calibration techniques may be not feasible or the optimisation procedure may fail. In this article, we propose the use of linear calibration in conjunction with a multidimensional scaling-based set of continuous, uncorrelated auxiliary variables along with a suitable metric in a distance-based regression framework. The calibration weights are estimated using a projection of the auxiliary information on a low-dimensional Euclidean space. The approach becomes one of the linear calibration with quantitative variables avoiding the usual computational problems in the presence of qualitative auxiliary information. The new variables preserve the underlying assumption in linear calibration of a linear relationship between the auxiliary and target variables, and therefore the optimal properties of the linear calibration method remain true. The behaviour of this approach is examined using a Monte Carlo procedure and its value is illustrated by analysing real data sets and by comparing its performance with that of traditional calibration procedures.

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Propensity score methods are a widely recommended approach to adjust for confounding and to recover treatment effects with non-experimental, single-level data. This article reviews propensity score weighting estimators for multilevel data in which individuals (level 1) are nested in clusters (level 2) and nonrandomly assigned to either a treatment or control condition at level 1. We address the choice of a weighting strategy (inverse probability weights, trimming, overlap weights, calibration weights) and discuss key issues related to the specification of the propensity score model (fixed-effects model, multilevel random-effects model) in the context of multilevel data. In three simulation studies, we show that estimates based on calibration weights, which prioritize balancing the sample distribution of level-1 and (unmeasured) level-2 covariates, should be preferred under many scenarios (i.e., treatment effect heterogeneity, presence of strong level-2 confounding) and can accommodate covariate-by-cluster interactions. However, when level-1 covariate effects vary strongly across clusters (i.e., under random slopes), and this variation is present in both the treatment and outcome data-generating mechanisms, large cluster sizes are needed to obtain accurate estimates of the treatment effect. We also discuss the implementation of survey weights and present a real-data example that illustrates the different methods.

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BACKGROUND: In rapidly changing fields such as the study of drug use, the need for accurate and timely data is paramount to properly inform policy and intervention decisions. Trends in drug use can change rapidly by month, and using study designs with flexible modules could present advantages. Timely data from online panels can inform proactive interventions against emerging trends, leading to a faster public response. However, threats to validity from using online panels must be addressed to create accurate estimates. OBJECTIVE: The objective of this study was to demonstrate a comprehensive methodological approach that optimizes a nonprobability, online opt-in sample to provide timely, accurate national estimates on prevalence of drug use. METHODS: The Survey of Non-Medical Use of Prescription Drugs Program from the Researched Abuse, Diversion and Addiction Related Surveillance (RADARS) System is an online, cross-sectional survey on drug use in the United States, and several best practices were implemented. To optimize final estimates, two best practices were investigated in detail: exclusion of respondents showing careless or improbable responding patterns and calibration of weights. The approach in this work was to cumulatively implement each method, which improved key estimates during the third quarter 2018 survey launch. Cutoffs for five exclusion criteria were tested. Using a series of benchmarks, average relative bias and changes in bias were calculated for 33 different weighting variable combinations. RESULTS: There were 148,274 invitations sent to panelists, with 40,021 who initiated the survey (26.99%). After eligibility assessment, 20.23% (29,998/148,274) of the completed questionnaires were available for analysis. A total of 0.52% (157/29,998) of respondents were excluded based on careless or improbable responses; however, these exclusions had larger impacts on lower volume drugs. Number of exclusions applied were negatively correlated to total dispensing volume by drug (Spearman ρ=-.88, P<.001). A weighting scheme including three demographic and two health characteristics reduced average relative bias by 31.2%. After weighting, estimates of drug use decreased, reflecting a weighted sample that had healthier benchmarks than the unweighted sample. CONCLUSIONS: Our study illustrates a new approach to using nonprobability online panels to achieve national prevalence estimates for drug abuse. We were able to overcome challenges with using nonprobability internet samples, including misclassification due to improbable responses. Final drug use and health estimates demonstrated concurrent validity to national probability-based drug use and health surveys. Inclusion of multiple best practices cumulatively improved the estimates generated. This method can bridge the information gap when there is a need for prompt, accurate national data.

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BACKGROUND: Sampling bias, like survey participants' nonresponse, needs to be adequately addressed in the analysis of sampling designs. Often survey weights will be calibrated on specific covariates related to the probability of selection and nonresponse to get representative population estimates. However, such calibrated survey (CS) weights are usually constructed for cross-sectional results, but not for longitudinal analyses. For example, when the outcome of interest is time to death, and sampling selection is related to time to death and censoring, sampling is informative. Then, unweighted or CS weighted inferential statistical analyses may be biased. In 2010, Switzerland changed from a decennial full enumeration census to a yearly registry-based (i.e., data from harmonised community registries) and a survey-based census system. In the present study, we investigated the potential bias due to informative sampling when time to death is the outcome of interest, using data from the new Swiss census system. METHODS: We analysed more than 6.5 million individuals aged 15 years or older from registry-based census data from years 2010 to 2013, linked with mortality records up to end of 2014. Out of this population, a target sample of 3.5% was sampled from the Swiss Federal Statistical Office (SFSO) in a stratified yearly micro census. The SFSO calculated CS weights to enable representative population estimates from the micro census. We additionally constructed inverse probability (IP) weights, where we used survival information in addition to known sampling covariates. We compared CS and IP weighted mortality rates (MR) and life expectancy (LE) with estimates from the underlying population. Additionally, we performed a simulation study under different sampling and nonresponse scenarios. RESULTS: We found that individuals who died in 2011, had a 0.67 (95% CI [0.64-0.70]) times lower odds of participating in the 2010 micro census, using a multivariable logistic regression model with covariates age, gender, nationality, civil status, region and survival information. IP weighted MR were comparable to estimates from the total population, whereas CS weighted MR underestimated the population MR in general. The IP weighted LE estimates at age 30 years for men were 50.9 years (95% CI [50.2-51.6] years), whereas the CS weighted overestimated LE by 2.5 years. Our results from the simulation study confirmed that IP weighted models are comparable to population estimates. CONCLUSION: Mortality analyses based on the new Swiss survey-based census system may be biased, because of informative sampling. We conclude that mortality analyses based on census-linked survey data have to be carefully conducted, and if possible, validated by registry information to allow for unbiased interpretation and generalisation.