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Summary . We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration. 相似文献
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The Wilcoxon signed rank test is a frequently used nonparametric test for paired data (e.g., consisting of pre- and posttreatment measurements) based on independent units of analysis. This test cannot be used for paired comparisons arising from clustered data (e.g., if paired comparisons are available for each of two eyes of an individual). To incorporate clustering, a generalization of the randomization test formulation for the signed rank test is proposed, where the unit of randomization is at the cluster level (e.g., person), while the individual paired units of analysis are at the subunit within cluster level (e.g., eye within person). An adjusted variance estimate of the signed rank test statistic is then derived, which can be used for either balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, with an exchangeable correlation structure, with or without tied values. The resulting test statistic is shown to be asymptotically normal as the number of clusters becomes large, if the cluster size is bounded. Simulation studies are performed based on simulating correlated ranked data from a signed log-normal distribution. These studies indicate appropriate type I error for data sets with > or =20 clusters and a superior power profile compared with either the ordinary signed rank test based on the average cluster difference score or the multivariate signed rank test of Puri and Sen. Finally, the methods are illustrated with two data sets, (i) an ophthalmologic data set involving a comparison of electroretinogram (ERG) data in retinitis pigmentosa (RP) patients before and after undergoing an experimental surgical procedure, and (ii) a nutritional data set based on a randomized prospective study of nutritional supplements in RP patients where vitamin E intake outside of study capsules is compared before and after randomization to monitor compliance with nutritional protocols. 相似文献
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Informative drop-out arises in longitudinal studies when the subject's follow-up time depends on the unobserved values of the response variable. We specify a semiparametric linear regression model for the repeatedly measured response variable and an accelerated failure time model for the time to informative drop-out. The error terms from the two models are assumed to have a common, but completely arbitrary joint distribution. Using a rank-based estimator for the accelerated failure time model and an artificial censoring device, we construct an asymptotically unbiased estimating function for the linear regression model. The resultant estimator is shown to be consistent and asymptotically normal. A resampling scheme is developed to estimate the limiting covariance matrix. Extensive simulation studies demonstrate that the proposed methods are suitable for practical use. Illustrations with data taken from two AIDS clinical trials are provided. 相似文献
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Summary . The work is motivated by the Cache County Study of Aging, a population-based study in Utah, in which sibship associations in dementia onset are of interest. Complications arise because only a fraction of the population ever develops dementia, with the majority dying without dementia. The application of standard dependence analyses for independently right-censored data may not be appropriate with such multivariate competing risks data, where death may violate the independent censoring assumption. Nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data, as needed with the large sibships in the Cache County Study. Time-dependent association measures are evaluated using these estimators. Large sample inferences are studied rigorously using empirical process techniques. The practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the Cache County Study, where dementia onset clustering among siblings varies strongly by age. 相似文献
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McNemar's test is used to assess the difference between two different procedures (treatments) using independent matched-pair data. For matched-pair data collected in clusters, the tests proposed by Durkalski et al. and Obuchowski are popular and commonly used in practice since these tests do not require distributional assumptions or assumptions on the structure of the within-cluster correlation of the data. Motivated by these tests, this note proposes a modified Obuchowski test and illustrates comparisons of the proposed test with the extant methods. An extensive Monte Carlo simulation study suggests that the proposed test performs well with respect to the nominal size, and has higher power; Obuchowski's test is most conservative, and the performance of the Durkalski's test varies between the modified Obuchowski test and the original Obuchowski's test. These results form the basis for our recommendation that (i) for equal cluster size, the modified Obuchowski test is always preferred; (ii) for varying cluster size Durkalski's test can be used for a small number of clusters (e.g. K < 50), whereas for a large number of clusters (e.g. K ≥ 50) the modified Obuchowski test is preferred. Finally, to illustrate practical application of the competing tests, two real collections of clustered matched-pair data are analyzed. 相似文献
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The Wilcoxon rank sum test is widely used for two-group comparisons of nonnormal data. An assumption of this test is independence of sampling units both within and between groups, which will be violated in the clustered data setting such as in ophthalmological clinical trials, where the unit of randomization is the subject, but the unit of analysis is the individual eye. For this purpose, we have proposed the clustered Wilcoxon test to account for clustering among multiple subunits within the same cluster (Rosner, Glynn, and Lee, 2003, Biometrics 59, 1089-1098; 2006, Biometrics 62, 1251-1259). However, power estimation is needed to plan studies that use this analytic approach. We have recently published methods for estimating power and sample size for the ordinary Wilcoxon rank sum test (Rosner and Glynn, 2009, Biometrics 65, 188-197). In this article we present extensions of this approach to estimate power for the clustered Wilcoxon test. Simulation studies show a good agreement between estimated and empirical power. These methods are illustrated with examples from randomized trials in ophthalmology. Enhanced power is achieved with use of the subunit as the unit of analysis instead of the cluster using the ordinary Wilcoxon rank sum test. 相似文献
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We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration. 相似文献
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Understanding nonparametric estimation for clustered data 总被引:1,自引:0,他引:1
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Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t1j, t2j), the classes of tests are those based on t1j-t2j and those based on log t1j–log t2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t1j — t2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem. For tests based on log t1j — log t2j, the ARE comparisons reduce to the well-known results for the one-sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t1j — log t2j are not complicated by the underlying pairing mechanism. 相似文献
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Semiparametric regression for clustered data 总被引:4,自引:0,他引:4
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Summary The generalized estimating equation (GEE) has been a popular tool for marginal regression analysis with longitudinal data, and its extension, the weighted GEE approach, can further accommodate data that are missing at random (MAR). Model selection methodologies for GEE, however, have not been systematically developed to allow for missing data. We propose the missing longitudinal information criterion (MLIC) for selection of the mean model, and the MLIC for correlation (MLICC) for selection of the correlation structure in GEE when the outcome data are subject to dropout/monotone missingness and are MAR. Our simulation results reveal that the MLIC and MLICC are effective for variable selection in the mean model and selecting the correlation structure, respectively. We also demonstrate the remarkable drawbacks of naively treating incomplete data as if they were complete and applying the existing GEE model selection method. The utility of proposed method is further illustrated by two real applications involving missing longitudinal outcome data. 相似文献
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Rank-based regression for analysis of repeated measures 总被引:1,自引:0,他引:1