Robust inference methods for meta-analysis involving influential outlying studies.

Meta-analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence-based medicine. In many meta-analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed-effect and random-effects models of meta-analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta-analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta-analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.

Improved methods to construct prediction intervals for network meta-analysis.

Network meta-analysis has played an important role in evidence-based medicine for assessing the comparative effectiveness of multiple available treatments. The prediction interval has been one of the standard outputs in recent network meta-analysis as an effective measure that enables simultaneous assessment of uncertainties in treatment effects and heterogeneity among studies. To construct the prediction interval, a large-sample approximating method based on the t-distribution has generally been applied in practice; however, recent studies have shown that similar t-approximation methods for conventional pairwise meta-analyses can substantially underestimate the uncertainty under realistic situations. In this article, we performed simulation studies to assess the validity of the current standard method for network meta-analysis, and we show that its validity can also be violated under realistic situations. To address the invalidity issue, we developed two new methods to construct more accurate prediction intervals through bootstrap and Kenward-Roger-type adjustment. In simulation experiments, the two proposed methods exhibited better coverage performance and generally provided wider prediction intervals than the ordinary t-approximation. We also developed an R package, PINMA (https://cran.r-project.org/web/packages/PINMA/), to perform the proposed methods using simple commands. We illustrate the effectiveness of the proposed methods through applications to two real network meta-analyses.

Grouped generalized estimating equations for longitudinal data analysis.

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real data set.

Efficient testing and effect size estimation for set-based genetic association inference via semiparametric multilevel mixture modeling.

In genetic association studies, rare variants with extremely low allele frequencies play a crucial role in complex traits. Therefore, set-based testing methods that jointly assess the effects of groups of single nucleotide polymorphisms (SNPs) were developed to increase the powers of the association tests. However, these powers are still insufficient, and precise estimations of the effect sizes of individual SNPs are largely impossible. In this article, we provide an efficient set-based statistical inference framework that addresses both of these important issues simultaneously using an empirical Bayes method with semiparametric multilevel mixture modeling. We propose to utilize the hierarchical model that incorporates variations in set-specific effects and to apply the optimal discovery procedure (ODP) that achieves the largest overall power in multiple significance testing. In addition, we provide an optimal "set-based" estimator of the empirical distribution of effect sizes. The efficiency of the proposed methods is demonstrated through application to a genome-wide association study of coronary artery disease and through simulation studies. The results demonstrated numerous rare variants with large effect sizes for coronary artery disease, and the number of significant sets detected by the ODP was much greater than those identified by existing methods.

On Selection Criteria for the Tuning Parameter in Robust Divergence.

Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.

Efficient screening of predictive biomarkers for individual treatment selection.

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available treatments. However, due to the large number of candidate biomarkers in the large-scale genetic and molecular studies, and complex relationships among clinical outcome, biomarkers, and treatments, the ordinary statistical tests for the interactions between treatments and covariates have difficulties from their limited statistical powers. In this paper, we propose an efficient method for detecting predictive biomarkers. We employ weighted loss functions of Chen et al. to directly estimate individual treatment scores and propose synthetic posterior inference for effect sizes of biomarkers. We develop an empirical Bayes approach, namely, we estimate unknown hyperparameters in the prior distribution based on data. We then provide efficient screening methods for the candidate biomarkers via optimal discovery procedure with adequate control of false discovery rate. The proposed method is demonstrated in simulation studies and an application to a breast cancer clinical study in which the proposed method was shown to detect the much larger numbers of significant biomarkers than existing standard methods.

A unified method for improved inference in random effects meta-analysis.

Random effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article, we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, meta-analysis of diagnostic test accuracy, and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.

Robust Bayesian Regression with Synthetic Posterior Distributions.

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

Predicting intervention effect for COVID-19 in Japan: state space modeling approach.

Japan has observed a surge in the number of confirmed cases of the coronavirus disease (COVID-19) that has caused a serious impact on the society especially after the declaration of the state of emergency on April 7, 2020. This study analyzes the real time data from March 1 to April 22, 2020 by adopting a sophisticated statistical modeling based on the state space model combined with the well-known susceptible-infected-recovered (SIR) model. The model estimation and forecasting are conducted using the Bayesian methodology. The present study provides the parameter estimates of the unknown parameters that critically determine the epidemic process derived from the SIR model and prediction of the future transition of the infectious proportion including the size and timing of the epidemic peak with the prediction intervals that naturally accounts for the uncertainty. Even though the epidemic appears to be settling down during this intervention period, the prediction results under various scenarios using the data up to May 18 reveal that the temporary reduction in the infection rate would still result in a delayed the epidemic peak unless the long-term reproduction number is controlled.

Estimating individual treatment effects by gradient boosting trees.

The development of molecular diagnostic tools to achieve individualized medicine requires accurate estimation of individual treatment effects (ITEs). Although several effective data analytic strategies have been proposed for this purpose, they have limitations when it comes to flexibly capturing the complex relationships between clinical outcome and possibly high-dimensional covariates. In this article, we propose an effective machine learning method to estimate ITEs using the gradient boosting trees (GBT). GBT is a powerful nonparametric regression tool in machine learning, and its outstanding performance has been widely recognized for various applications. We use GBT to develop an estimation method for the ITE that is formulated under the potential outcome model framework. Our method can flexibly capture the relationship between clinical outcome and possibly high-dimensional covariates, and it would also be useful for identifying subpopulations of patients who would benefit from the treatment. Results of simulation studies and a real-data analysis of a breast cancer clinical study show that the proposed method can precisely estimate ITEs, and these estimates possibly identify the subgroup of patients who can benefit from treatment.

Exploring predictive biomarkers from clinical genome-wide association studies via multidimensional hierarchical mixture models.

Although the detection of predictive biomarkers is of particular importance for the development of accurate molecular diagnostics, conventional statistical analyses based on gene-by-treatment interaction tests lack sufficient statistical power for this purpose, especially in large-scale clinical genome-wide studies that require an adjustment for multiplicity of a huge number of tests. Here we demonstrate an alternative efficient multi-subgroup screening method using multidimensional hierarchical mixture models developed to overcome this issue, with application to stroke and breast cancer randomized clinical trials with genomic data. We show that estimated effect size distributions of single nucleotide polymorphisms (SNPs) associated with outcomes, which could provide clues for exploring predictive biomarkers, optimizing individualized treatments, and understanding biological mechanisms of diseases. Furthermore, using this method we detected three new SNPs that are associated with blood homocysteine levels, which are strongly associated with the risk of stroke. We also detected six new SNPs that are associated with progression-free survival in breast cancer patients.

An efficient and flexible test for rare variant effects.

Since it has been claimed that rare variants with extremely small allele frequency play a crucial role in complex traits, there is great demand for the development of a powerful test for detecting these variants. However, due to the extremely low frequencies of rare variants, common statistical testing methods do not work well, which has motivated recent extensive research on developing an efficient testing procedure for rare variant effects. Many studies have suggested effective testing procedures with reasonably high power under some presumed assumptions of parametric statistical models. However, if the parametric assumptions are violated, these tests are possibly under-powered. In this paper, we develop an optimal, powerful statistical test called the aggregated conditional score test (ACST) for simultaneously testing M rare variant effects without restrictive parametric assumptions. The proposed test uses a test statistic aggregating the conditional score statistics of effect sizes of M rare variants. In simulation studies, ACST generally performed well compared with the two most commonly used tests, the optimal sequence kernel association test (SKAT-O) and Kullback-Leibler distance test. Finally, we demonstrate the performance and practical utility of ACST using the Dallas Heart Study data.