Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative.
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ABSTRACT:
SUBMITTER: Innocenti F
PROVIDER: S-EPMC8172256 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:In multilevel populations, there are two types of population means of an outcome variable ie, the average of all individual outcomes ignoring cluster membership and the average of cluster-specific means. To estimate the first mean, individuals can be sampled directly with simple random sampling or with two-stage sampling (TSS), that is, sampling clusters first, and then individuals within the sampled clusters. When cluster size varies in the population, three TSS schemes can be considered, ie, sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster; sampling clusters with equal probability and then sampling the same percentage of individuals per cluster; and sampling clusters with equal probability and then sampling the same number of individuals per cluster. Unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative. Furthermore, the three TSS schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size. The relative efficiency of the sampling schemes is shown to vary across different cluster size distributions. However, sampling clusters with probability proportional to size is the most efficient TSS scheme for many cluster size distributions. Model-based and design-based inference are compared and are shown to give similar results. The results are applied to the distribution of high school size in Italy and the distribution of patient list size for general practices in England.
| S-EPMC6590157 | biostudies-literature
Project description:In the analysis of clustered data, inverse cluster size weighting has been shown to be resistant to the potentially biasing effects of informative cluster size, where the number of observations within a cluster is associated with the outcome variable of interest. The method of inverse cluster size reweighting has been implemented to establish clustered data analogues of common tests for independent data, but the method has yet to be extended to tests of categorical data. Many variance estimators have been implemented across established cluster-weighted tests, but potential effects of differing methods on test performance has not previously been explored. Here, we develop cluster-weighted estimators of marginal proportions that remain unbiased under informativeness, and derive analogues of three popular tests for clustered categorical data, the one-sample proportion, goodness of fit, and independence chi square tests. We construct these tests using several variance estimators and show substantial differences in the performance of cluster-weighted tests based on variance estimation technique, with variance estimators constructed under the null hypothesis maintaining size closest to nominal. We illustrate the proposed tests through an application to a data set of functional measures from patients with spinal cord injuries participating in a rehabilitation program.
| S-EPMC11220780 | biostudies-literature
Project description:Measuring the overlap between two populations is, in principle, straightforward. Upon fully sampling both populations, the number of shared objects-species, taxonomical units, or gene variants, depending on the context-can be directly counted. In practice, however, only a fraction of each population's objects are likely to be sampled due to stochastic data collection or sequencing techniques. Although methods exists for quantifying population overlap under subsampled conditions, their bias is well documented and the uncertainty of their estimates cannot be quantified. Here we derive and validate a method to rigorously estimate the population overlap from incomplete samples when the total number of objects, species, or genes in each population is known, a special case of the more general β-diversity problem that is particularly relevant in the ecology and genomic epidemiology of malaria. By solving a Bayesian inference problem, this method takes into account the rates of subsampling and produces unbiased and Bayes-optimal estimates of overlap. In addition, it provides a natural framework for computing the uncertainty of its estimates, and can be used prospectively in study planning by quantifying the tradeoff between sampling effort and uncertainty.
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Project description:To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two-phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean 'importance-weighted' breadth (Y) of the T-cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design-estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost-standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y?|?W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method.
| S-EPMC4021041 | biostudies-literature
Project description:Clustered data commonly arise in epidemiology. We assume each cluster member has an outcome Y and covariates X. When there are missing data in Y, the distribution of Y given X in all cluster members ("complete clusters") may be different from the distribution just in members with observed Y ("observed clusters"). Often the former is of interest, but when data are missing because in a fundamental sense Y does not exist (e.g., quality of life for a person who has died), the latter may be more meaningful (quality of life conditional on being alive). Weighted and doubly weighted generalized estimating equations and shared random-effects models have been proposed for observed-cluster inference when cluster size is informative, that is, the distribution of Y given X in observed clusters depends on observed cluster size. We show these methods can be seen as actually giving inference for complete clusters and may not also give observed-cluster inference. This is true even if observed clusters are complete in themselves rather than being the observed part of larger complete clusters: here methods may describe imaginary complete clusters rather than the observed clusters. We show under which conditions shared random-effects models proposed for observed-cluster inference do actually describe members with observed Y. A psoriatic arthritis dataset is used to illustrate the danger of misinterpreting estimates from shared random-effects models.
| S-EPMC4312901 | biostudies-other
Project description:Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.
| S-EPMC6026085 | biostudies-literature
Project description:BackgroundRecent work has shown that cluster-randomised trials can estimate two distinct estimands: the participant-average and cluster-average treatment effects. These can differ when participant outcomes or the treatment effect depends on the cluster size (termed informative cluster size). In this case, estimators that target one estimand (such as the analysis of unweighted cluster-level summaries, which targets the cluster-average effect) may be biased for the other. Furthermore, commonly used estimators such as mixed-effects models or generalised estimating equations with an exchangeable correlation structure can be biased for both estimands. However, there has been little empirical research into whether informative cluster size is likely to occur in practice.MethodWe re-analysed a cluster-randomised trial comparing two different thresholds for red blood cell transfusion in patients with acute upper gastrointestinal bleeding to explore whether estimates for the participant- and cluster-average effects differed, to provide empirical evidence for whether informative cluster size may be present. For each outcome, we first estimated a participant-average effect using independence estimating equations, which are unbiased under informative cluster size. We then compared this to two further methods: (1) a cluster-average effect estimated using either weighted independence estimating equations or unweighted cluster-level summaries, and (2) estimates from a mixed-effects model or generalised estimating equations with an exchangeable correlation structure. We then performed a small simulation study to evaluate whether observed differences between cluster- and participant-average estimates were likely to occur even if no informative cluster size was present.ResultsFor most outcomes, treatment effect estimates from different methods were similar. However, differences of >10% occurred between participant- and cluster-average estimates for 5 of 17 outcomes (29%). We also observed several notable differences between estimates from mixed-effects models or generalised estimating equations with an exchangeable correlation structure and those based on independence estimating equations. For example, for the EQ-5D VAS score, the independence estimating equation estimate of the participant-average difference was 4.15 (95% confidence interval: -3.37 to 11.66), compared with 2.84 (95% confidence interval: -7.37 to 13.04) for the cluster-average independence estimating equation estimate, and 3.23 (95% confidence interval: -6.70 to 13.16) from a mixed-effects model. Similarly, for thromboembolic/ischaemic events, the independence estimating equation estimate for the participant-average odds ratio was 0.43 (95% confidence interval: 0.07 to 2.48), compared with 0.33 (95% confidence interval: 0.06 to 1.77) from the cluster-average estimator.ConclusionIn this re-analysis, we found that estimates from the various approaches could differ, which may be due to the presence of informative cluster size. Careful consideration of the estimand and the plausibility of assumptions underpinning each estimator can help ensure an appropriate analysis methods are used. Independence estimating equations and the analysis of cluster-level summaries (with appropriate weighting for each to correspond to either the participant-average or cluster-average treatment effect) are a desirable choice when informative cluster size is deemed possible, due to their unbiasedness in this setting.
| S-EPMC10638852 | biostudies-literature
Project description:Clustered data are often encountered in biomedical studies, and to date, a number of approaches have been proposed to analyze such data. However, the phenomenon of informative cluster size (ICS) is a challenging problem, and its presence has an impact on the choice of a correct analysis methodology. For example, Dutta and Datta (2015, Biometrics) presented a number of marginal distributions that could be tested. Depending on the nature and degree of informativeness of the cluster size, these marginal distributions may differ, as do the choices of the appropriate test. In particular, they applied their new test to a periodontal data set where the plausibility of the informativeness was mentioned, but no formal test for the same was conducted. We propose bootstrap tests for testing the presence of ICS. A balanced bootstrap method is developed to successfully estimate the null distribution by merging the re-sampled observations with closely matching counterparts. Relying on the assumption of exchangeability within clusters, the proposed procedure performs well in simulations even with a small number of clusters, at different distributions and against different alternative hypotheses, thus making it an omnibus test. We also explain how to extend the ICS test to a regression setting and thereby enhancing its practical utility. The methodologies are illustrated using the periodontal data set mentioned earlier. Copyright © 2017 John Wiley & Sons, Ltd.
| S-EPMC5461221 | biostudies-literature
Project description:The issue of informative cluster size (ICS) often arises in the analysis of dental data. ICS describes a situation where the outcome of interest is related to cluster size. Much of the work on modeling marginal inference in longitudinal studies with potential ICS has focused on continuous outcomes. However, periodontal disease outcomes, including clinical attachment loss, are often assessed using ordinal scoring systems. In addition, participants may lose teeth over the course of the study due to advancing disease status. Here we develop longitudinal cluster-weighted generalized estimating equations (CWGEE) to model the association of ordinal clustered longitudinal outcomes with participant-level health-related covariates, including metabolic syndrome and smoking status, and potentially decreasing cluster size due to tooth-loss, by fitting a proportional odds logistic regression model. The within-teeth correlation coefficient over time is estimated using the two-stage quasi-least squares method. The motivation for our work stems from the Department of Veterans Affairs Dental Longitudinal Study in which participants regularly received general and oral health examinations. In an extensive simulation study, we compare results obtained from CWGEE with various working correlation structures to those obtained from conventional GEE which does not account for ICS. Our proposed method yields results with very low bias and excellent coverage probability in contrast to a conventional generalized estimating equations approach.
| S-EPMC6838778 | biostudies-literature
Project description:BackgroundClustered data arise in research when patients are clustered within larger units. Generalised Estimating Equations (GEE) and Generalised Linear Models (GLMM) can be used to provide marginal and cluster-specific inference and predictions, respectively.MethodsConfounding by Cluster (CBC) and Informative cluster size (ICS) are two complications that may arise when modelling clustered data. CBC can arise when the distribution of a predictor variable (termed 'exposure'), varies between clusters causing confounding of the exposure-outcome relationship. ICS means that the cluster size conditional on covariates is not independent of the outcome. In both situations, standard GEE and GLMM may provide biased or misleading inference, and modifications have been proposed. However, both CBC and ICS are routinely overlooked in the context of risk prediction, and their impact on the predictive ability of the models has been little explored. We study the effect of CBC and ICS on the predictive ability of risk models for binary outcomes when GEE and GLMM are used. We examine whether two simple approaches to handle CBC and ICS, which involve adjusting for the cluster mean of the exposure and the cluster size, respectively, can improve the accuracy of predictions.ResultsBoth CBC and ICS can be viewed as violations of the assumptions in the standard GLMM; the random effects are correlated with exposure for CBC and cluster size for ICS. Based on these principles, we simulated data subject to CBC/ICS. The simulation studies suggested that the predictive ability of models derived from using standard GLMM and GEE ignoring CBC/ICS was affected. Marginal predictions were found to be mis-calibrated. Adjusting for the cluster-mean of the exposure or the cluster size improved calibration, discrimination and the overall predictive accuracy of marginal predictions, by explaining part of the between cluster variability. The presence of CBC/ICS did not affect the accuracy of conditional predictions. We illustrate these concepts using real data from a multicentre study with potential CBC.ConclusionIgnoring CBC and ICS when developing prediction models for clustered data can affect the accuracy of marginal predictions. Adjusting for the cluster mean of the exposure or the cluster size can improve the predictive accuracy of marginal predictions.
| S-EPMC8254921 | biostudies-literature