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Major depressive disorder (MDD) is a heterogeneous condition; multiple underlying neurobiological substrates could be associated with treatment response variability. Understanding the sources of this variability and predicting outcomes has been elusive. Machine learning has shown promise in predicting treatment response in MDD, but one limitation has been the lack of clinical interpretability of machine learning models. We analyzed data from six clinical trials of pharmacological treatment for depression (total n = 5438) using the Differential Prototypes Neural Network (DPNN), a neural network model that derives patient prototypes which can be used to derive treatment-relevant patient clusters while learning to generate probabilities for differential treatment response. A model classifying remission and outputting individual remission probabilities for five first-line monotherapies and three combination treatments was trained using clinical and demographic data. Model validity and clinical utility were measured based on area under the curve (AUC) and expected improvement in sample remission rate with model-guided treatment, respectively. Post-hoc analyses yielded clusters (subgroups) based on patient prototypes learned during training. Prototypes were evaluated for interpretability by assessing differences in feature distributions and treatment-specific outcomes. A 3-prototype model achieved an AUC of 0.66 and an expected absolute improvement in population remission rate compared to the sample remission rate. We identified three treatment-relevant patient clusters which were clinically interpretable. It is possible to produce novel treatment-relevant patient profiles using machine learning models; doing so may improve precision medicine for depression. Note: This model is not currently the subject of any active clinical trials and is not intended for clinical use.

In network meta-analysis (NMA), we synthesize all relevant evidence about health outcomes with competing treatments. The evidence may come from randomized controlled trials (RCT) or non-randomized studies (NRS) as individual participant data (IPD) or as aggregate data (AD). We present a suite of Bayesian NMA and network meta-regression (NMR) models allowing for cross-design and cross-format synthesis. The models integrate a three-level hierarchical model for synthesizing IPD and AD into four approaches. The four approaches account for differences in the design and risk of bias in the RCT and NRS evidence. These four approaches variously ignoring differences in risk of bias, using NRS to construct penalized treatment effect priors and bias-adjustment models that control the contribution of information from high risk of bias studies in two different ways. We illustrate the methods in a network of three pharmacological interventions and placebo for patients with relapsing-remitting multiple sclerosis. The estimated relative treatment effects do not change much when we accounted for differences in design and risk of bias. Conducting network meta-regression showed that intervention efficacy decreases with increasing participant age. We re-analysed a network of 431 RCT comparing 21 antidepressants, and we did not observe material changes in intervention efficacy when adjusting for studies high risk of bias. In summary, the described suite of NMA/NMR models enables inclusion of all relevant evidence while incorporating information on the within-study bias in both observational and experimental data and enabling estimation of individualized treatment effects through the inclusion of participant characteristics.

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

Network meta-analysis (NMA) has been used to answer a range of clinical questions about the preferable intervention for a given condition. Although the effectiveness and safety of pharmacological agents depend on the dose administered, NMA applications typically ignore the role that drugs dosage play on the results. This leads to more heterogeneity in the network. In this paper we present a suite of network meta-analysis models that incorporates the dose-effect relationship (DE-NMA) using restricted cubic splines (RCS). We extend the model into a dose-effect network meta-regression to account for study-level covariates and for groups of agents in a class-effect DE-NMA model. We apply the models to a network of aggregate data about the efficacy of 21 antidepressants and placebo for depression. We found that all antidepressants are more efficacious than placebo after a certain dose. We also identify the dose level in which each antidepressant effect exceeds that of placebo and estimate the dose beyond the effect of the antidepressants no longer increases. The DE-NMA model with RCS takes a flexible approach to modelling the dose-effect relationship in multiple interventions, so decision-makers can use them to inform treatment choice.

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the C-statistic. These naive methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (https://github.com/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial.

Dose-response models express the effect of different dose or exposure levels on a specific outcome. In meta-analysis, where aggregated-level data is available, dose-response evidence is synthesized using either one-stage or two-stage models in a frequentist setting. We propose a hierarchical dose-response model implemented in a Bayesian framework. We present the model with cubic dose-response shapes for a dichotomous outcome and take into account heterogeneity due to variability in the dose-response shape. We develop our Bayesian model assuming normal or binomial likelihood and accounting for exposures grouped in clusters. We implement these models in R using JAGS and we compare our approach to the one-stage dose-response meta-analysis model in a simulation study. We found that the Bayesian dose-response model with binomial likelihood has slightly lower bias than the Bayesian model with the normal likelihood and the frequentist one-stage model. However, all three models perform very well and give practically identical results. We also re-analyze the data from 60 randomized controlled trials (15,984 participants) examining the efficacy (response) of various doses of antidepressant drugs. All models suggest that the dose-response curve increases between zero dose and 40 mg of fluoxetine-equivalent dose, and thereafter is constant. We draw the same conclusion when we take into account the fact that five different antidepressants have been studied in the included trials. We show that implementation of the hierarchical model in Bayesian framework has similar performance to, but overcomes some of the limitations of the frequentist approaches and offers maximum flexibility to accommodate features of the data.

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.

Network meta-analysis has been gaining prominence as an evidence synthesis method that enables the comprehensive synthesis and simultaneous comparison of multiple treatments. In many network meta-analyses, some of the constituent studies may have markedly different characteristics from the others, and may be influential enough to change the overall results. The inclusion of these "outlying" studies might lead to biases, yielding misleading results. In this article, we propose effective methods for detecting outlying and influential studies in a frequentist framework. In particular, we propose suitable influence measures for network meta-analysis models that involve missing outcomes and adjust the degree of freedoms appropriately. We propose three influential measures by a leave-one-trial-out cross-validation scheme: (1) comparison-specific studentized residual, (2) relative change measure for covariance matrix of the comparative effectiveness parameters, (3) relative change measure for heterogeneity covariance matrix. We also propose (4) a model-based approach using a likelihood ratio statistic by a mean-shifted outlier detection model. We illustrate the effectiveness of the proposed methods via applications to a network meta-analysis of antihypertensive drugs. Using the four proposed methods, we could detect three potential influential trials involving an obvious outlier that was retracted because of data falsifications. We also demonstrate that the overall results of comparative efficacy estimates and the ranking of drugs were altered by omitting these three influential studies.

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

Meta-analyses of diagnostic test accuracy (DTA) studies have been gaining prominence in research in clinical epidemiology and health technology development. In these DTA meta-analyses, some studies may have markedly different characteristics from the others, and potentially be inappropriate to include. The inclusion of these "outlying" studies might lead to biases, yielding misleading results. In addition, there might be influential studies that have notable impacts on the results. In this article, we propose Bayesian methods for detecting outlying studies and their influence diagnostics in DTA meta-analyses. Synthetic influence measures based on the bivariate hierarchical Bayesian random effects models are developed because the overall influences of individual studies should be simultaneously assessed by the two outcome variables and their correlation information. We propose four synthetic measures for influence analyses: (1) relative distance, (2) standardized residual, (3) Bayesian p-value, and (4) influence statistic on the area under the summary receiver operating characteristic curve. We also show conventional univariate Bayesian influential measures can be applied to the bivariate random effects models, which can be used as marginal influential measures. We illustrate the effectiveness of the proposed methods by applying them to a DTA meta-analysis of ultrasound in screening for vesicoureteral reflux among children with urinary tract infections., Comment: 18 pages, 3 tables, 4 figures

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

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