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Register a new userTesting small study effects in multivariate meta-analysis
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Chuan Hong
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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Small study effects occur when smaller studies show different, often larger, treatment effects than large ones, which may threaten the validity of systematic reviews and meta-analyses. The most well-known reasons for small study effects include publication bias, outcome reporting bias and clinical heterogeneity. Methods to account for small study effects in univariate meta-analysis have been extensively studied. However, detecting small study effects in a multivariate meta-analysis setting remains an untouched research area. One of the complications is that different types of selection processes can be involved in the reporting of multivariate outcomes. For example, some studies may be completely unpublished while others may selectively report multiple outcomes. In this paper, we propose a score test as an overall test of small study effects in multivariate meta-analysis. Two detailed case studies are given to demonstrate the advantage of the proposed test over various naive applications of univariate tests in practice. Through simulation studies, the proposed test is found to retain nominal Type I error with considerable power in moderate sample size settings. Finally, we also evaluate the concordance between the proposed test with the naive application of univariate tests by evaluating 44 systematic reviews with multiple outcomes from the Cochrane Database.
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Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.
In meta-analyses, publication bias is a well-known, important and challenging issue because the validity of the results from a meta-analysis is threatened if the sample of studies retrieved for review is biased. One popular method to deal with publication bias is the Copas selection model, which provides a flexible sensitivity analysis for correcting the estimates with considerable insight into the data suppression mechanism. However, rigorous testing procedures under the Copas selection model to detect bias are lacking. To fill this gap, we develop a score-based test for detecting publication bias under the Copas selection model. We reveal that the behavior of the standard score test statistic is irregular because the parameters of the Copas selection model disappear under the null hypothesis, leading to an identifiability problem. We propose a novel test statistic and derive its limiting distribution. A bootstrap procedure is provided to obtain the p-value of the test for practical applications. We conduct extensive Monte Carlo simulations to evaluate the performance of the proposed test and apply the method to several existing meta-analyses.
Meta-analysis combines pertinent information from existing studies to provide an overall estimate of population parameters/effect sizes, as well as to quantify and explain the differences between studies. However, testing the between-study heterogeneity is one of the most troublesome topics in meta-analysis research. Additionally, no methods have been proposed to test whether the size of the heterogeneity is larger than a specific level. The existing methods, such as the Q test and likelihood ratio (LR) tests, are criticized for their failure to control the Type I error rate and/or failure to attain enough statistical power. Although better reference distribution approximations have been proposed in the literature, the expression is complicated and the application is limited. In this article, we propose bootstrap based heterogeneity tests combining the restricted maximum likelihood (REML) ratio test or Q test with bootstrap procedures, denoted as B-REML-LRT and B-Q respectively. Simulation studies were conducted to examine and compare the performance of the proposed methods with the regular LR tests, the regular Q test, and the improved Q test in both the random-effects meta-analysis and mixed-effects meta-analysis. Based on the results of Type I error rates and statistical power, B-Q is recommended. An R package mathtt{boot.heterogeneity} is provided to facilitate the implementation of the proposed method.
As the most important tool to provide high-level evidence-based medicine, researchers can statistically summarize and combine data from multiple studies by conducting meta-analysis. In meta-analysis, mean differences are frequently used effect size measurements to deal with continuous data, such as the Cohens d statistic and Hedges g statistic values. To calculate the mean difference based effect sizes, the sample mean and standard deviation are two essential summary measures. However, many of the clinical reports tend not to directly record the sample mean and standard deviation. Instead, the sample size, median, minimum and maximum values and/or the first and third quartiles are reported. As a result, researchers have to transform the reported information to the sample mean and standard deviation for further compute the effect size. Since most of the popular transformation methods were developed upon the normality assumption of the underlying data, it is necessary to perform a pre-test before transforming the summary statistics. In this article, we had introduced test statistics for three popular scenarios in meta-analysis. We suggests medical researchers to perform a normality test of the selected studies before using them to conduct further analysis. Moreover, we applied three different case studies to demonstrate the usage of the newly proposed test statistics. The real data case studies indicate that the new test statistics are easy to apply in practice and by following the recommended path to conduct the meta-analysis, researchers can obtain more reliable conclusions.
According to Davey et al. (2011) with a total of 22,453 meta-analyses from the January 2008 Issue of the Cochrane Database of Systematic Reviews, the median number of studies included in each meta-analysis is only three. In other words, about a half or more of meta-analyses conducted in the literature include only two or three studies. While the common-effect model (also referred to as the fixed-effect model) may lead to misleading results when the heterogeneity among studies is large, the conclusions based on the random-effects model may also be unreliable when the number of studies is small. Alternatively, the fixed-effects model avoids the restrictive assumption in the common-effect model and the need to estimate the between-study variance in the random-effects model. We note, however, that the fixed-effects model is under appreciated and rarely used in practice until recently. In this paper, we compare all three models and demonstrate the usefulness of the fixed-effects model when the number of studies is small. In addition, we propose a new estimator for the unweighted average effect in the fixed-effects model. Simulations and real examples are also used to illustrate the benefits of the fixed-effects model and the new estimator.
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