Approximate confidence intervals for moment-based estimators of the between-study variance in random effects meta-analysis.
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ABSTRACT:
SUBMITTER: Jackson D
PROVIDER: S-EPMC4839498 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Meta-regression is becoming increasingly used to model study level covariate effects. However this type of statistical analysis presents many difficulties and challenges. Here two methods for calculating confidence intervals for the magnitude of the residual between-study variance in random effects meta-regression models are developed. A further suggestion for calculating credible intervals using informative prior distributions for the residual between-study variance is presented.Two recently proposed and, under the assumptions of the random effects model, exact methods for constructing confidence intervals for the between-study variance in random effects meta-analyses are extended to the meta-regression setting. The use of Generalised Cochran heterogeneity statistics is extended to the meta-regression setting and a Newton-Raphson procedure is developed to implement the Q profile method for meta-analysis and meta-regression. WinBUGS is used to implement informative priors for the residual between-study variance in the context of Bayesian meta-regressions.Results are obtained for two contrasting examples, where the first example involves a binary covariate and the second involves a continuous covariate. Intervals for the residual between-study variance are wide for both examples.Statistical methods, and R computer software, are available to compute exact confidence intervals for the residual between-study variance under the random effects model for meta-regression. These frequentist methods are almost as easily implemented as their established counterparts for meta-analysis. Bayesian meta-regressions are also easily performed by analysts who are comfortable using WinBUGS. Estimates of the residual between-study variance in random effects meta-regressions should be routinely reported and accompanied by some measure of their uncertainty. Confidence and/or credible intervals are well-suited to this purpose.
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Project description:We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well-approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedure. Our proof uses operator-valued free probability theory, and we establish a general asymptotic freeness result for families of rectangular orthogonally-invariant random matrices, which is of independent interest. Our work is motivated in part by the estimation of components of covariance between multiple phenotypic traits in quantitative genetics, and we specialize our results to common experimental designs that arise in this application.
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Project description:The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions.
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Project description:BackgroundWhile the use of standard errors and confidence intervals is common in regression-based studies in the population sciences, it is far less common in studies using formal demographic measures and methods, including demographic decompositions.ObjectiveThis article describes and provides explicit instructions for using four different approaches for computing standard errors for complex demographic estimators.MethodsStandard errors for Arriaga's decomposition of life expectancy differences are computed using the delta method, the Poisson bootstrap, the binomial bootstrap, and the Monte Carlo approaches. The methods are demonstrated using a 50% sample of vital statistics data on age-specific mortality among urban women in the Pacific region of the United States in 1990 and 2019.ResultsAll four methods for computing standard errors returned similar estimates, with the delta method, Poisson bootstrap, and Monte Carlo approaches being the most consistent. The Monte Carlo approach is recommended for general use, while the delta method is recommended for specific cases.ContributionThis study documents multiple ways of estimating statistical uncertainty for complex demographic estimators and describes in detail how to apply these various methods to nearly any rate-based demographic measure. It also provides advice on when the use of standard errors is and is not appropriate in demographic studies. Explicit formulae for computing standard errors for Arriaga's decomposition using the delta method approach are derived.
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Project description:With the abundance of large data, sparse penalized regression techniques are commonly used in data analysis due to the advantage of simultaneous variable selection and estimation. A number of convex as well as non-convex penalties have been proposed in the literature to achieve sparse estimates. Despite intense work in this area, how to perform valid inference for sparse penalized regression with a general penalty remains to be an active research problem. In this paper, by making use of state-of-the-art optimization tools in stochastic variational inequality theory, we propose a unified framework to construct confidence intervals for sparse penalized regression with a wide range of penalties, including convex and non-convex penalties. We study the inference for parameters under the population version of the penalized regression as well as parameters of the underlying linear model. Theoretical convergence properties of the proposed method are obtained. Several simulated and real data examples are presented to demonstrate the validity and effectiveness of the proposed inference procedure.
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Project description:BACKGROUND:Percentiles are widely used as reference limits for determining the relative magnitude and substantial importance of quantitative measurements. An important application is the advocated Bland-Altman limits of agreement. METHODS:To contribute to the data analysis and design planning of reference limit or percentile research, the purpose of this paper is twofold. The first is to clarify the statistical features of interval estimation procedures for normal percentiles. The second goal is to provide sample size procedures for precise interval estimation of normal percentiles. RESULTS:The delineation demonstrates the theoretical connections between different pivotal quantities for obtaining exact confidence intervals. Moreover, the seemingly accurate approximate methods with equidistant from the principal estimators are shown to have undesirable confidence limits. It is found that the optimal sample size has a minimum for median or mean, and increases as the percentile approaches the extremes. CONCLUSIONS:The exact interval procedure should be used in preference to the approximate methods. Computer algorithms are presented to implement the suggested interval precision and sample size calculations for planning percentile research.
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Project description:Network meta-analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta-analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between-study heterogeneity. Models for network meta-analysis with random inconsistency effects have the dual aim of allowing for inconsistencies and estimating average treatment effects across the whole network. To date, two classical estimation methods for fitting this type of model have been developed: a method of moments that extends DerSimonian and Laird's univariate method and maximum likelihood estimation. However, the Paule and Mandel estimator is another recommended classical estimation method for univariate meta-analysis. In this paper, we extend the Paule and Mandel method so that it can be used to fit models for network meta-analysis with random inconsistency effects. We apply all three estimation methods to a variety of examples that have been used previously and we also examine a challenging new dataset that is highly heterogenous. We perform a simulation study based on this new example. We find that the proposed Paule and Mandel method performs satisfactorily and generally better than the previously proposed method of moments because it provides more accurate inferences. Furthermore, the Paule and Mandel method possesses some advantages over likelihood-based methods because it is both semiparametric and requires no convergence diagnostics. Although restricted maximum likelihood estimation remains the gold standard, the proposed methodology is a fully viable alternative to this and other estimation methods.
| S-EPMC5720360 | biostudies-literature
Project description:The pooled estimate of the average effect is of primary interest when fitting the random-effects model for meta-analysis. However estimates of study specific effects, for example those displayed on forest plots, are also often of interest. In this tutorial, we present the case, with the accompanying statistical theory, for estimating the study specific true effects using so called 'empirical Bayes estimates' or 'Best Unbiased Linear Predictions' under the random-effects model. These estimates can be accompanied by prediction intervals that indicate a plausible range of study specific true effects. We coalesce and elucidate the available literature and illustrate the methodology using two published meta-analyses as examples. We also perform a simulation study that reveals that coverage probability of study specific prediction intervals are substantially too low if the between-study variance is small but not negligible. Researchers need to be aware of this defect when interpreting prediction intervals. We also show how empirical Bayes estimates, accompanied with study specific prediction intervals, can embellish forest plots. We hope that this tutorial will serve to provide a clear theoretical underpinning for this methodology and encourage its widespread adoption.
| S-EPMC8361666 | biostudies-literature
Project description:Genome-wide association studies (GWAS) provide an important approach to identifying common genetic variants that predispose to human disease. A typical GWAS may genotype hundreds of thousands of single nucleotide polymorphisms (SNPs) located throughout the human genome in a set of cases and controls. Logistic regression is often used to test for association between a SNP genotype and case versus control status, with corresponding odds ratios (ORs) typically reported only for those SNPs meeting selection criteria. However, when these estimates are based on the original data used to detect the variant, the results are affected by a selection bias sometimes referred to the "winner's curse" (Capen and others, 1971). The actual genetic association is typically overestimated. We show that such selection bias may be severe in the sense that the conditional expectation of the standard OR estimator may be quite far away from the underlying parameter. Also standard confidence intervals (CIs) may have far from the desired coverage rate for the selected ORs. We propose and evaluate 3 bias-reduced estimators, and also corresponding weighted estimators that combine corrected and uncorrected estimators, to reduce selection bias. Their corresponding CIs are also proposed. We study the performance of these estimators using simulated data sets and show that they reduce the bias and give CI coverage close to the desired level under various scenarios, even for associations having only small statistical power.
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Project description:BACKGROUND:With the rapid development of high-throughput sequencing technologies, many datasets on the same biological subject are generated. A meta-analysis is an approach that combines results from different studies on the same topic. The random-effects model in a meta-analysis enables the modeling of differences between studies by incorporating the between-study variance. RESULTS:This paper proposes a moments estimator of the between-study variance that represents the across-study variation. A new random-effects method (DSLD2), which involves two-step estimation starting with the DSL estimate and the [Formula: see text] in the second step, is presented. The DSLD2 method is compared with 6 other meta-analysis methods based on effect sizes across 8 aspects under three hypothesis settings. The results show that DSLD2 is a suitable method for identifying differentially expressed genes under the first hypothesis. The DSLD2 method is also applied to Alzheimer's microarray datasets. The differentially expressed genes detected by the DSLD2 method are significantly enriched in neurological diseases. CONCLUSIONS:The results from both simulationes and an application show that DSLD2 is a suitable method for detecting differentially expressed genes under the first hypothesis.
| S-EPMC7014785 | biostudies-literature