Coverage probability

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

Exact one‐sided confidence limits for the difference between two correlated proportions

Abstract: We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.

Coverage Probabilities of Bootstrap-Confidence Intervals for Quantiles

Abstract: An asymptotic expansion of length 2 is established for the coverage probabilities of confidence intervals for the underlying $q$-quantile which are derived by bootstrapping the sample $q$-quantile. The corresponding level error turns out to be of order $O(n^{-1/2})$ which is unexpectedly low. A confidence interval of even more practical use is derived by using backward critical points. The resulting confidence interval is of the same length as the one derived by ordinary bootstrap but it is distribution free and has higher coverage probability.

Comparisons of measures of interclass correlations : The general case of unequal group size

Abstract: A problem often encountered in epidemiology is the evaluation of the validity of a short questionnaire for diet or physical activity administered to large numbers of subjects, where the gold standard is a diet record or physical activity diary. It is well known that random measurement error can attenuate the interclass correlation coefficient (validity coefficient) between these two variables. Several authors have proposed a de-attenuated (or corrected) correlation coefficient which is an estimate of the true correlation between the two variables after removing the effect of random measurement error. By true correlation we mean the correlation between the questionnaire and the mean of a large or 'infinite' number of diaries (representing the truth). In this paper the authors propose three methods (two ad hoc methods, the pairwise and weighted sib-mean estimators, and the maximum likelihood with confidence limits computed using the Wald statistic and profile likelihood approaches) to estimate the true correlation between a single questionnaire and the mean of an infinite number of follow-up diaries, in the general case where an unequal number of diaries are available for each individual. A simulation study is done under the assumption that the measured variables are normally distributed. Under the null hypothesis of no correlation between the questionnaires and the diaries, all methods had negligible biases. In cases closer to what is usually seen in practice (true correlation between 0.4 and 0.6), the degree of bias and coverage probability depends heavily on the reliability (intraclass correlation) of the diaries. The maximum likelihood estimator with confidence intervals computed by the profile likelihood approach, while not systematically outperforming the other methods, is shown to be the best of the three proposed approaches.

Laplace approximation, penalized quasi-likelihood, and adaptive Gauss-Hermite quadrature for generalized linear mixed models: towards meta-analysis of binary outcome with sparse data.

Abstract: In meta-analyses of a binary outcome, double zero events in some studies cause a critical methodology problem. The generalized linear mixed model (GLMM) has been proposed as a valid statistical tool for pooling such data. Three parameter estimation methods, including the Laplace approximation (LA), penalized quasi-likelihood (PQL) and adaptive Gauss–Hermite quadrature (AGHQ) were frequently used in the GLMM. However, the performance of GLMM via these estimation methods is unclear in meta-analysis with zero events. A simulation study was conducted to compare the performance. We fitted five random-effects GLMMs and estimated the results through the LA, PQL and AGHQ methods, respectively. Each scenario conducted 20,000 simulation iterations. The data from Cochrane Database of Systematic Reviews were collected to form the simulation settings. The estimation methods were compared in terms of the convergence rate, bias, mean square error, and coverage probability. Our results suggested that when the total events were insufficient in either of the arms, the GLMMs did not show good point estimation to pool studies of rare events. The AGHQ method did not show better properties than the LA estimation in terms of convergence rate, bias, coverage, and possibility to produce very large odds ratios. In addition, although the PQL had some advantages, it was not the preferred option due to its low convergence rate in some situations, and the suboptimal point and variance estimation compared to the LA. The GLMM is an alternative for meta-analysis of rare events and is especially useful in the presence of zero-events studies, while at least 10 total events in both arms is recommended when employing GLMM for meta-analysis. The penalized quasi-likelihood and adaptive Gauss–Hermite quadrature are not superior to the Laplace approximation for rare events and thus they are not recommended.