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The prediction interval is gaining prominence in meta-analysis as it enables the assessment of uncertainties in treatment effects and heterogeneity between studies. However, coverage probabilities of the current standard method for constructing prediction intervals cannot retain their nominal levels in general, particularly when the number of synthesized studies is moderate or small, because their validities depend on large sample approximations. Recently, several methods have developed been to address this issue. This paper briefly summarizes the recent developments in methods of prediction intervals and provides readable examples using R for multiple types of data with simple code. The pimeta package is an R package that provides these improved methods to calculate accurate prediction intervals and graphical tools to illustrate these results. The pimeta package is listed in ``CRAN Task View: Meta-Analysis.'' The analysis is easily performed in R using a series of R packages., Comment: 15 pages, 2 figures

In pharmacogenomic studies, biomedical researchers commonly analyze the association between genotype and biological response by using the Kruskal--Wallis test or one-way analysis of variance (ANOVA) after logarithmic transformation of the obtained data. However, because these methods detect unexpected biological response patterns, the power for detecting the expected pattern is reduced. Previously, we proposed a combination of the maximum contrast method and the permuted modified maximum contrast method for unequal sample sizes in pharmacogenomic studies. However, we noted that the distribution of the permuted modified maximum contrast statistic depends on a nuisance parameter $\sigma^2$, which is the population variance. In this paper, we propose a modified maximum contrast method with a statistic that does not depend on the nuisance parameter. Furthermore, we compare the performance of these methods via simulation studies. The simulation results showed that the modified maximum contrast method gave the lowest false-positive rate; therefore, this method is powerful for detecting the true response patterns in some conditions. Further, it is faster and more accurate than the permuted modified maximum contrast method. On the basis of these results, we suggest a rule of thumb to select the appropriate method in a given situation., Comment: 22 pages, 10 figures

In single-arm clinical trials with survival outcomes, the Kaplan-Meier estimator and its confidence interval are widely used to assess survival probability and median survival time. Since the asymptotic normality of the Kaplan-Meier estimator is a common result, the sample size calculation methods have not been studied in depth. An existing sample size calculation method is founded on the asymptotic normality of the Kaplan-Meier estimator using the log transformation. However, the small sample properties of the log transformed estimator are quite poor in small sample sizes (which are typical situations in single-arm trials), and the existing method uses an inappropriate standard normal approximation to calculate sample sizes. These issues can seriously influence the accuracy of results. In this paper, we propose alternative methods to determine sample sizes based on a valid standard normal approximation with several transformations that may give an accurate normal approximation even with small sample sizes. In numerical evaluations via simulations, some of the proposed methods provided more accurate results, and the empirical power of the proposed method with the arcsine square-root transformation tended to be closer to a prescribed power than the other transformations. These results were supported when methods were applied to data from three clinical trials., Comment: 22 pages

In meta-analysis, the random-effects models are standard tools to address between-study heterogeneity in evidence synthesis analyses. For the random-effects distribution models, the normal distribution model has been adopted in most systematic reviews due to its computational and conceptual simplicity. However, the restrictive model assumption might have serious influences on the overall conclusions in practices. In this article, we first provide two examples of real-world evidence that clearly show that the normal distribution assumption is unsuitable. To address the model restriction problem, we propose alternative flexible random-effects models that can flexibly regulate skewness, kurtosis and tailweight: skew normal distribution, skew t-distribution, asymmetric Subbotin distribution, Jones-Faddy distribution, and sinh-arcsinh distribution. We also developed a R package, flexmeta, that can easily perform these methods. Using the flexible random-effects distribution models, the results of the two meta-analyses were markedly altered, potentially influencing the overall conclusions of these systematic reviews. The flexible methods and computational tools can provide more precise evidence, and these methods would be recommended at least as sensitivity analysis tools to assess the influence of the normal distribution assumption of the random-effects model.

The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the Higgins-Thompson-Spiegelhalter method is used most often in practice, it might not have adequate coverage probability for the true treatment effect of a future study under realistic situations. An effective alternative candidate is the Bayesian prediction interval, which has also been widely used in general prediction problems. However, these prediction intervals are constructed based on the Bayesian philosophy, and their frequentist validities are only justified by large-sample approximations even if non-informative priors are adopted. There has been no certain evidence that evaluated their frequentist performances under realistic situations of meta-analyses. In this study, we conducted extensive simulation studies to assess the frequentist coverage performances of Bayesian prediction intervals with 11 non-informative prior distributions under general meta-analysis settings. Through these simulation studies, we found that frequentist coverage performances strongly depended on what prior distributions were adopted. In addition, when the number of studies was smaller than 10, there were no prior distributions that retained accurate frequentist coverage properties. We also illustrated these methods via applications to eight real meta-analysis datasets. The resultant prediction intervals also differed according to the adopted prior distributions. Inaccurate prediction intervals may provide invalid evidence and misleading conclusions. Thus, if frequentist accuracy is required, Bayesian prediction intervals should be used cautiously in practice., Comment: 23 pages, 4 figures, 1 table

Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies heterogeneities. However, coverage probabilities of confidence regions or intervals for standard inference methods for random-effects models (e.g., restricted maximum likelihood estimation) cannot retain their nominal confidence levels in general, especially when the number of synthesized studies is small because their validities depend on large sample approximations. In this article, we provide permutation-based inference methods that enable exact joint inferences for average outcome measures without large sample approximations. We also provide accurate marginal inference methods under general settings of multivariate meta-analyses. We propose effective approaches for permutation inferences using optimal weighting based on the efficient score statistic. The effectiveness of the proposed methods is illustrated via applications to bivariate meta-analyses of diagnostic accuracy studies for airway eosinophilia in asthma and a network meta-analysis for antihypertensive drugs on incident diabetes, as well as through simulation experiments. In numerical evaluations performed via simulations, our methods generally provided accurate confidence regions or intervals under a broad range of settings, whereas the current standard inference methods exhibited serious undercoverage properties., Comment: 20 pages, 2 figures, 2 table

Powerful array-based single-nucleotide polymorphism--typing platforms have recently heralded a new era in which genome-wide studies are conducted with increasing frequency. A genetic polymorphism associated with population pharmacokinetics (PK) is typically analyzed using nonlinear mixed-effect models (NLMM). Applying NLMM to large-scale data, such as those generated by genome-wide studies, raises several issues related to the assumption of random effects, as follows: (i) Computation time: it takes a long time to compute the marginal likelihood. (ii) Convergence of iterative calculation: an adaptive Gauss-Hermite quadrature is generally used to estimate NLMM; however, iterative calculations may not converge in complex models. (iii) Random-effects misspecification leads to slightly inflated type-I error rates. As an alternative effective approach to resolving these issues, in this article we propose a generalized estimating equation (GEE) approach for analyzing population PK data. In general, GEE analysis does not account for inter-individual variability in PK parameters; therefore, the usual GEE estimators cannot be interpreted straightforwardly, and their validities have not been justified. Here, we propose valid inference methods for using GEE even under conditions of inter-individual variability, and provide theoretical justifications of the proposed GEE estimators for population PK data. In numerical evaluations by simulations, the proposed GEE approach exhibited high computational speed and stability relative to the NLMM approach. Furthermore, the NLMM analysis was sensitive to the misspecification of the random-effects distribution, and the proposed GEE inference is valid for any distributional form. An illustration is provided using data from a genome-wide pharmacogenomic study of an anticancer drug., Comment: 26 pages, 1 figure

For the inference of random-effects models in meta-analysis, the prediction interval was proposed as a summary measure of the treatment effects that explains the heterogeneity in the target population. While the Higgins-Thompson-Spiegelhalter (HTS) plug-in-type prediction interval has been widely used, in which the heterogeneity parameter is replaced with its point estimate, its validity depends on a large sample approximation. Most meta-analyses, however, include less than 20 studies. It has been revealed that the validity of the HTS method is not assured under realistic situations, but no solution to this problem has been proposed in literature. Therefore, in this article, we describe our proposed prediction interval. Instead of using the plug-in scheme, we developed a bootstrap approach using an exact confidence distribution to account for the uncertainty in estimation of the heterogeneity parameter. Compared to the HTS method, the proposed method provides an accurate prediction interval that adequately explains the heterogeneity of treatment effects and the statistical error. Simulation studies demonstrated that the HTS method had poor coverage performance; by contrast, the coverage probabilities for the proposed method satisfactorily retained the nominal level. Applications to three published random-effects meta-analyses are presented., Comment: 14 pages, 3 figures