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Abstract Background The heterogeneity statistic I2, interpreted as the percentage of variability due to heterogeneity between studies rather than sampling error, depends on precision, that is, the size of the studies included. Methods Based on a real meta-analysis, we simulate artificially 'inflating' the sample size under the random effects model. For a given inflation factor M = 1, 2, 3,... and for each trial i, we create a M-inflated trial by drawing a treatment effect estimate from the random effects model, using si2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4Cam3aa0baaSqaaiabdMgaPbqaaiabikdaYaaaaaa@2FBE@/M as within-trial sampling variance. Results As precision increases, while estimates of the heterogeneity variance τ2 remain unchanged on average, estimates of I2 increase rapidly to nearly 100%. A similar phenomenon is apparent in a sample of 157 meta-analyses. Conclusion When deciding whether or not to pool treatment estimates in a meta-analysis, the yard-stick should be the clinical relevance of any heterogeneity present. τ2, rather than I2, is the appropriate measure for this purpose.

Abstract Background Simpson's paradox is sometimes referred to in the areas of epidemiology and clinical research. It can also be found in meta-analysis of randomized clinical trials. However, though readers are able to recalculate examples from hypothetical as well as real data, they may have problems to easily figure where it emerges from. Method First, two kinds of plots are proposed to illustrate the phenomenon graphically, a scatter plot and a line graph. Subsequently, these can be overlaid, resulting in a overlay plot. The plots are applied to the recent large meta-analysis of adverse effects of rosiglitazone on myocardial infarction and to an example from the literature. A large set of meta-analyses is screened for further examples. Results As noted earlier by others, occurrence of Simpson's paradox in the meta-analytic setting, if present, is associated with imbalance of treatment arm size. This is well illustrated by the proposed plots. The rosiglitazone meta-analysis shows an effect reversion if all trials are pooled. In a sample of 157 meta-analyses, nine showed an effect reversion after pooling, though non-significant in all cases. Conclusion The plots give insight on how the imbalance of trial arm size works as a confounder, thus producing Simpson's paradox. Readers can see why meta-analytic methods must be used and what is wrong with simple pooling.

Abstract Background Citation counts are often regarded as a measure of the utilization and contribution of published articles. The objective of this study is to assess whether statistical reporting and statistical errors in the analysis of the primary outcome are associated with the number of citations received. Methods We evaluated all original research articles published in 1996 in four psychiatric journals. The statistical and reporting quality of each paper was assessed and the number of citations received up to 2005 was obtained from the Web of Science database. We then examined whether the number of citations was associated with the quality of the statistical analysis and reporting. Results A total of 448 research papers were included in the citation analysis. Unclear or inadequate reporting of the research question and primary outcome were not statistically significantly associated with the citation counts. After adjusting for journal, extended description of statistical procedures had a positive effect on the number of citations received. Inappropriate statistical analysis did not affect the number of citations received. Adequate reporting of the primary research question, statistical methods and primary findings were all associated with the journal visibility and prestige. Conclusion In this cohort of published research, measures of reporting quality and appropriate statistical analysis were not associated with the number of citations. The journal in which a study is published appears to be as important as the statistical reporting quality in ensuring dissemination of published medical science.

Background: The heterogeneity statistic I(2), interpreted as the percentage of variability due to heterogeneity between studies rather than sampling error, depends on precision, that is, the size of the studies included.Methods: Based on a real meta-analysis, we simulate artificially 'inflating' the sample size under the random effects model. For a given inflation factor M = 1, 2, 3,... and for each trial i, we create a M-inflated trial by drawing a treatment effect estimate from the random effects model, using s(i)(2)/M as within-trial sampling variance.Results: As precision increases, while estimates of the heterogeneity variance tau(2) remain unchanged on average, estimates of I(2) increase rapidly to nearly 100%. A similar phenomenon is apparent in a sample of 157 meta-analyses.Conclusion: When deciding whether or not to pool treatment estimates in a meta-analysis, the yard-stick should be the clinical relevance of any heterogeneity present. tau(2), rather than I(2), is the appropriate measure for this purpose. [ABSTRACT FROM AUTHOR]

Background: Simpson's paradox is sometimes referred to in the areas of epidemiology and clinical research. It can also be found in meta-analysis of randomized clinical trials. However, though readers are able to recalculate examples from hypothetical as well as real data, they may have problems to easily figure where it emerges from.Method: First, two kinds of plots are proposed to illustrate the phenomenon graphically, a scatter plot and a line graph. Subsequently, these can be overlaid, resulting in a overlay plot. The plots are applied to the recent large meta-analysis of adverse effects of rosiglitazone on myocardial infarction and to an example from the literature. A large set of meta-analyses is screened for further examples.Results: As noted earlier by others, occurrence of Simpson's paradox in the meta-analytic setting, if present, is associated with imbalance of treatment arm size. This is well illustrated by the proposed plots. The rosiglitazone meta-analysis shows an effect reversion if all trials are pooled. In a sample of 157 meta-analyses, nine showed an effect reversion after pooling, though non-significant in all cases.Conclusion: The plots give insight on how the imbalance of trial arm size works as a confounder, thus producing Simpson's paradox. Readers can see why meta-analytic methods must be used and what is wrong with simple pooling. [ABSTRACT FROM AUTHOR]

Background: Network meta-analysis (NMA) allows estimating and ranking the effects of several interventions for a clinical condition. Component network meta-analysis (CNMA) is an extension of NMA which considers the individual components of multicomponent interventions. CNMA allows to "reconnect" a disconnected network with common components in subnetworks. An additive CNMA assumes that component effects are additive. This assumption can be relaxed by including interaction terms in the CNMA., Methods: We evaluate a forward model selection strategy for component network meta-analysis to relax the additivity assumption that can be used in connected or disconnected networks. In addition, we describe a procedure to create disconnected networks in order to evaluate the properties of the model selection in connected and disconnected networks. We apply the methods to simulated data and a Cochrane review on interventions for postoperative nausea and vomiting in adults after general anaesthesia. Model performance is compared using average mean squared errors and coverage probabilities., Results: CNMA models provide good performance for connected networks and can be an alternative to standard NMA if additivity holds. For disconnected networks, we recommend to use additive CNMA only if strong clinical arguments for additivity exist., Conclusions: CNMA methods are feasible for connected networks but questionable for disconnected networks., (© 2023. The Author(s).)

Background: Network meta-analysis estimates all relative effects between competing treatments and can produce a treatment hierarchy from the most to the least desirable option according to a health outcome. While about half of the published network meta-analyses present such a hierarchy, it is rarely the case that it is related to a clinically relevant decision question., Methods: We first define treatment hierarchy and treatment ranking in a network meta-analysis and suggest a simulation method to estimate the probability of each possible hierarchy to occur. We then propose a stepwise approach to express clinically relevant decision questions as hierarchy questions and quantify the uncertainty of the criteria that constitute them. The steps of the approach are summarized as follows: a) a question of clinical relevance is defined, b) the hierarchies that satisfy the defined question are collected and c) the frequencies of the respective hierarchies are added; the resulted sum expresses the certainty of the defined set of criteria to hold. We then show how the frequencies of all possible hierarchies relate to common ranking metrics., Results: We exemplify the method and its implementation using two networks. The first is a network of four treatments for chronic obstructive pulmonary disease where the most probable hierarchy has a frequency of 28%. The second is a network of 18 antidepressants, among which Vortioxetine, Bupropion and Escitalopram occupy the first three ranks with frequency 19%., Conclusions: The developed method offers a generalised approach of producing treatment hierarchies in network meta-analysis, which moves towards attaching treatment ranking to a clear decision question, relevant to all or a subset of competing treatments., (© 2022. The Author(s).)

Background: Network meta-analysis (NMA) has attracted growing interest in evidence-based medicine. Consistency between different sources of evidence is fundamental to the reliability of the NMA results. The purpose of the present study was to estimate the prevalence of evidence of inconsistency and describe its association with different NMA characteristics., Methods: We updated our collection of NMAs with articles published up to July 2018. We included networks with randomised clinical trials, at least four treatment nodes, at least one closed loop, a dichotomous primary outcome, and available arm-level data. We assessed consistency using the design-by-treatment interaction (DBT) model and testing all the inconsistency parameters globally through the Wald-type chi-squared test statistic. We estimated the prevalence of evidence of inconsistency and its association with different network characteristics (e.g., number of studies, interventions, intervention comparisons, loops). We evaluated the influence of the network characteristics on the DBT p-value via a multivariable regression analysis and the estimated Pearson correlation coefficients. We also evaluated heterogeneity in NMA (consistency) and DBT (inconsistency) random-effects models., Results: We included 201 published NMAs. The p-value of the design-by-treatment interaction (DBT) model was lower than 0.05 in 14% of the networks and lower than 0.10 in 20% of the networks. Networks including many studies and comparing few interventions were more likely to have small DBT p-values (less than 0.10), which is probably because they yielded more precise estimates and power to detect differences between designs was higher. In the presence of inconsistency (DBT p-value lower than 0.10), the consistency model displayed higher heterogeneity than the DBT model., Conclusions: Our findings show that inconsistency was more frequent than what would be expected by chance, suggesting that researchers should devote more resources to exploring how to mitigate inconsistency. The results of this study highlight the need to develop strategies to detect inconsistency (because of the relatively high prevalence of evidence of inconsistency in published networks), and particularly in cases where the existing tests have low power., (© 2021. The Author(s).)

Background: Healthcare decisions are ideally based on clinical trial results, published in study registries, as journal articles or summarized in secondary research articles. In this research project, we investigated the impact of academically and commercially sponsored clinical trials on medical practice by measuring the proportion of trials published and cited by systematic reviews and clinical guidelines., Methods: We examined 691 multicenter, randomized controlled trials that started in 2005 or later and were completed by the end of 2016. To determine whether sponsorship/funding and place of conduct influence a trial's impact, we created four sub-cohorts of investigator initiated trials (IITs) and industry sponsored trials (ISTs): 120 IITs and 171 ISTs with German contribution compared to 200 IITs and 200 ISTs without German contribution. We balanced the groups for study phase and place of conduct. German IITs were funded by the German Research Foundation (DFG), the Federal Ministry of Education and Research (BMBF), or by another non-commercial research organization. All other trials were drawn from the German Clinical Trials Register or ClinicalTrials.gov. We investigated, to what extent study characteristics were associated with publication and impact using multivariable logistic regressions., Results: For 80% of the 691 trials, results were published as result articles in a medical journal and/or study registry, 52% were cited by a systematic review, and 26% reached impact in a clinical guideline. Drug trials and larger trials were associated with a higher probability to be published and to have an impact than non-drug trials and smaller trials. Results of IITs were more often published as a journal article while results of ISTs were more often published in study registries. International ISTs less often gained impact by inclusion in systematic reviews or guidelines than IITs., Conclusion: An encouraging high proportion of the clinical trials were published, and a considerable proportion gained impact on clinical practice. However, there is still room for improvement. For publishing study results, study registries have become an alternative or complement to journal articles, especially for ISTs. IITs funded by governmental bodies in Germany reached an impact that is comparable to international IITs and ISTs., (© 2021. The Author(s).)

Background: In pairwise meta-analysis, the contribution of each study to the pooled estimate is given by its weight, which is based on the inverse variance of the estimate from that study. For network meta-analysis (NMA), the contribution of direct (and indirect) evidence is easily obtained from the diagonal elements of a hat matrix. It is, however, not fully clear how to generalize this to the percentage contribution of each study to a NMA estimate., Methods: We define the importance of each study for a NMA estimate by the reduction of the estimate's variance when adding the given study to the others. An equivalent interpretation is the relative loss in precision when the study is left out. Importances are values between 0 and 1. An importance of 1 means that the study is an essential link of the pathway in the network connecting one of the treatments with another., Results: Importances can be defined for two-stage and one-stage NMA. These numbers in general do not add to one and thus cannot be interpreted as 'percentage contributions'. After briefly discussing other available approaches, we question whether it is possible to obtain unique percentage contributions for NMA., Conclusions: Importances generalize the concept of weights in pairwise meta-analysis in a natural way. Moreover, they are uniquely defined, easily calculated, and have an intuitive interpretation. We give some real examples for illustration.

Background: Length of stay evaluations are very common to determine the burden of nosocomial infections. However, there exist fundamentally different methods to quantify the prolonged length of stay associated with nosocomial infections. Previous methodological studies emphasized the need to account for the timing of infection in order to differentiate the length of stay before and after the infection., Methods: We derive four different approaches in a simple multi-state framework, display their mathematical relationships in a multiplicative as well as additive way and apply them to a real cohort study (n=756 German intensive-care unit patients of whom 124 patients acquired a nosocomial infection)., Results: The first approach ignores the timing of infection and quantifies the difference of eventually infected and eventually uninfected; it is 12.31 days in the real data. The second approach compares the average sojourn time with infection with the average sojourn time of being hypothetically uninfected; it is 2.12 days. The third one compares the average length of stay of a population in a world with nosocomial infections with a population in a hypothetical world without nosocomial infections; it is 0.35 days. Finally, approach four compares the mean residual length of stay between currently infected and uninfected patients on a daily basis; the difference is 1.77 days per infected patient., Conclusions: The first approach should be avoided because it compares the eventually infected with the eventually uninfected, but has no prospective interpretation. The other approaches differ in their interpretation but are suitable because they explicitly distinguish between the pre- and post-time of the nosocomial infection.

Background: In meta-analyses of diagnostic test accuracy, routinely only one pair of sensitivity and specificity per study is used. However, for tests based on a biomarker or a questionnaire often more than one threshold and the corresponding values of true positives, true negatives, false positives and false negatives are known., Methods: We present a new meta-analysis approach using this additional information. It is based on the idea of estimating the distribution functions of the underlying biomarker or questionnaire within the non-diseased and diseased individuals. Assuming a normal or logistic distribution, we estimate the distribution parameters in both groups applying a linear mixed effects model to the transformed data. The model accounts for across-study heterogeneity and dependence of sensitivity and specificity. In addition, a simulation study is presented., Results: We obtain a summary receiver operating characteristic (SROC) curve as well as the pooled sensitivity and specificity at every specific threshold. Furthermore, the determination of an optimal threshold across studies is possible through maximization of the Youden index. We demonstrate our approach using two meta-analyses of B type natriuretic peptide in heart failure and procalcitonin as a marker for sepsis., Conclusions: Our approach uses all the available information and results in an estimation not only of the performance of the biomarker but also of the threshold at which the optimal performance can be expected.

Background: Network meta-analysis is used to compare three or more treatments for the same condition. Within a Bayesian framework, for each treatment the probability of being best, or, more general, the probability that it has a certain rank can be derived from the posterior distributions of all treatments. The treatments can then be ranked by the surface under the cumulative ranking curve (SUCRA). For comparing treatments in a network meta-analysis, we propose a frequentist analogue to SUCRA which we call P-score that works without resampling., Methods: P-scores are based solely on the point estimates and standard errors of the frequentist network meta-analysis estimates under normality assumption and can easily be calculated as means of one-sided p-values. They measure the mean extent of certainty that a treatment is better than the competing treatments., Results: Using case studies of network meta-analysis in diabetes and depression, we demonstrate that the numerical values of SUCRA and P-Score are nearly identical., Conclusions: Ranking treatments in frequentist network meta-analysis works without resampling. Like the SUCRA values, P-scores induce a ranking of all treatments that mostly follows that of the point estimates, but takes precision into account. However, neither SUCRA nor P-score offer a major advantage compared to looking at credible or confidence intervals.

Background: Statisticians investigate new methods in simulations to evaluate their properties for future real data applications. Results are often presented in a number of figures, e.g., Trellis plots. We had conducted a simulation study on six statistical methods for estimating the treatment effect in binary outcome meta-analyses, where selection bias (e.g., publication bias) was suspected because of apparent funnel plot asymmetry. We varied five simulation parameters: true treatment effect, extent of selection, event proportion in control group, heterogeneity parameter, and number of studies in meta-analysis. In combination, this yielded a total number of 768 scenarios. To present all results using Trellis plots, 12 figures were needed., Methods: Choosing bias as criterion of interest, we present a 'nested loop plot', a diagram type that aims to have all simulation results in one plot. The idea was to bring all scenarios into a lexicographical order and arrange them consecutively on the horizontal axis of a plot, whereas the treatment effect estimate is presented on the vertical axis., Results: The plot illustrates how parameters simultaneously influenced the estimate. It can be combined with a Trellis plot in a so-called hybrid plot. Nested loop plots may also be applied to other criteria such as the variance of estimation., Conclusion: The nested loop plot, similar to a time series graph, summarizes all information about the results of a simulation study with respect to a chosen criterion in one picture and provides a suitable alternative or an addition to Trellis plots.