Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcomes: a simulation study

Abstract: The objective of this simulation study is to compare the accuracy and efficiency of population-averaged (i.e. generalized estimating equations (GEE)) and cluster-specific (i.e. random-effects logistic regression (RELR)) models for analyzing data from cluster randomized trials (CRTs) with missing binary responses. In this simulation study, clustered responses were generated from a beta-binomial distribution. The number of clusters per trial arm, the number of subjects per cluster, intra-cluster correlation coefficient, and the percentage of missing data were allowed to vary. Under the assumption of covariate dependent missingness, missing outcomes were handled by complete case analysis, standard multiple imputation (MI) and within-cluster MI strategies. Data were analyzed using GEE and RELR. Performance of the methods was assessed using standardized bias, empirical standard error, root mean squared error (RMSE), and coverage probability. GEE performs well on all four measures — provided the downward bias of the standard error (when the number of clusters per arm is small) is adjusted appropriately — under the following scenarios: complete case analysis for CRTs with a small amount of missing data; standard MI for CRTs with variance inflation factor (VIF) 50. RELR performs well only when a small amount of data was missing, and complete case analysis was applied. GEE performs well as long as appropriate missing data strategies are adopted based on the design of CRTs and the percentage of missing data. In contrast, RELR does not perform well when either standard or within-cluster MI strategy is applied prior to the analysis.

Orthodox BLUP versus h-likelihood methods for inferences about random effects in Tweedie mixed models

Abstract: Recently, the orthodox best linear unbiased predictor (BLUP) method was introduced for inference about random effects in Tweedie mixed models. With the use of h-likelihood, we illustrate that the standard likelihood procedures, developed for inference about fixed unknown parameters, can be used for inference about random effects. We show that the necessary standard error for the prediction interval of the random effect can be computed from the Hessian matrix of the h-likelihood. We also show numerically that the h-likelihood provides a prediction interval that maintains a more precise coverage probability than the BLUP method.

Regression analysis for long-term survival rate via empirical likelihood

Abstract: In recent years, regression models have been shown to be useful for predicting the long-term survival probabilities of patients in clinical trials. For inference on the vector of regression parameters, there are semiparametric procedures based on normal approximations. However, the accuracy of such procedures in terms of coverage probability can be quite low when the censoring rate is heavy. In this paper, we apply an empirical likelihood ratio (ELR) method to the regression model and derive the limiting distribution of the ELR. On the basis of the result, we develop a confidence region for the vector of regression parameters. Furthermore, we use a simulation study to compare the proposed method with the normal approximation-based method proposed by Jung [Jung, S., 1996, Regression analysis for long-term survival rate. Biometrika, 83, 227–232.]. Finally, the proposed procedure is illustrated with data from a clinical trial.

Exact confidence coefficients of confidence intervals for a binomial proportion

Abstract: Let X have a binomial distribution B(n; p). For a condence interval (L(X); U(X)) of a binomial proportion p, the coverage probability is a variable function of p. The condence coecien t of the condence interval is the inm um of the coverage probabilities, inf0 p 1 Pp(p 2 (L(X); U(X))). Usually, the exact condence coecien t is unknown since the inm um of the coverage probabilities may occur at any point p 2 (0; 1). In this paper, a methodology to compute the exact condence coecien t is proposed. With this methodology, the point where the inm um of the coverage probabilities occurs, as well as the condence coecien t, can be precisely derived.

Interval estimation of a normal process standard deviation from rounded data

Abstract: In standard statistical analyses, data are typically assumed to be essentially exact. It is increasingly evident with the proliferation of digital readouts that this assumption can in practice be a poor one. We consider the analysis of data for which observed variation is potentially small in comparison to the finest unit of recording. In particular, we focus discussion on interval estimation of the parameter σ when a rounded sample comes from the N(μ, σ2) distribution with both parameters unknown. The traditional method and a (modified) rounded-data likelihood-based method are compared. We find that the likelihood-based method provides a reliable means of estimating σ, even in the face of the possibility that it is small.