Although dependence in effect sizes is ubiquitous, commonly used meta-analytic methods assume independent effect sizes. We describe and illustrate three-level extensions of a mixed effects meta-analytic model that accounts for various sources of dependence within and across studies, because multilevel extensions of metaanalytic models still are not well known. We also present a three-level model for the common case where, within studies, multiple effect sizes are calculated using the same sample. Whereas this approach is relatively simple and does not require imputing values for the unknown sampling covariances, it has hardly been used, and its performance has not been empirically investigated. Therefore, we set up a simulation study, showing that also in this situation, a threelevel approach yields valid results: Estimates of the treatment effects and the corresponding standard errors are unbiased.Keywords Multilevel . Meta-analysis . Multiple outcomes . Dependence Three-level meta-analysis of dependent effect sizesMeta-analysis refers to the statistical integration of the quantitative results of several studies. For instance, if several experimental studies examine the effect of student coaching on students' achievement, a meta-analysis can be used to investigate how large the effect is on average, whether this effect varies over studies, and whether we can find factors that are related to the size of the effect (for an introduction to meta-analysis, see Borenstein, Hedges, Higgins, & Rothstein, 2009). Most often, the effects that were observed in the primary studies are not exactly the same as the ones predicted on the basis of the meta-analytic model. Most meta-analytic methods assume that these deviations of the observed effect sizes from their expected values are independent. This means, it is assumed that one specific observed effect size does not give information about the direction or size of deviation of another observed effect from the value we would expect on the basis of the metaanalytic model. Nevertheless, in practice, there are numerous sources of effect size dependence, and therefore, metaanalysts are very often confronted with dependent effect sizes. For instance, if several studies were done by the same research group, it is not unlikely that the effect sizes from this research group are more similar than effect sizes from two different research groups, because the effect sizes might be influenced by common factors, including the way the dependent and independent variables were operationalized, the characteristics of the studied population, the way subjects were sampled, and the observers or interviewers who collected the data (Cooper, 2009). In the same way, study results from the same country might be more similar than study results from different countries, again inducing dependence in observed effects.Besides dependence over studies, there also might be dependence within studies. For instance, a specific effect can be investigated for several samples in a single study. In this sit...

Objectives To evaluate the effects on non-specific and all cause mortality, in children under 5, of Bacillus Calmette-Guérin (BCG), diphtheria-tetanus-pertussis (DTP), and standard titre measles containing vaccines (MCV); to examine internal validity of the studies; and to examine any modifying effects of sex, age, vaccine sequence, and co-administration of vitamin A.Design Systematic review, including assessment of risk of bias, and meta-analyses of similar studies.Study eligibility criteria Clinical trials, cohort studies, and case-control studies of the effects on mortality of BCG, whole cell DTP, and standard titre MCV in children under 5.Data sources Searches of Medline, Embase, Global Index Medicus, and the WHO International Clinical Trials Registry Platform, supplemented by contact with experts in the field. To avoid overlap in children studied across the included articles, findings from non-overlapping birth cohorts were identified.Results Results from 34 birth cohorts were identified. Most evidence was from observational studies, with some from short term clinical trials. Most studies reported on all cause (rather than non-specific) mortality. Receipt of BCG vaccine was associated with a reduction in all cause mortality: the average relative risks were 0.70 (95% confidence interval 0.49 to 1.01) from five clinical trials and 0.47 (0.32 to 0.69) from nine observational studies at high risk of bias. Receipt of DTP (almost always with oral polio vaccine) was associated with a possible increase in all cause mortality on average (relative risk 1.38, 0.92 to 2.08) from 10 studies at high risk of bias; this effect seemed stronger in girls than in boys. Receipt of standard titre MCV was associated with a reduction in all cause mortality (relative risks 0.74 (0.51 to 1.07) from four clinical trials and 0.51 (0.42 to 0.63) from 18 observational studies at high risk of bias); this effect seemed stronger in girls than in boys. Seven observational studies, assessed as being at high risk of bias, have compared sequences of vaccines; results of a subset of these suggest that administering DTP with or after MCV may be associated with higher mortality than administering it before MCV.Conclusions Evidence suggests that receipt of BCG and MCV reduce overall mortality by more than would be expected through their effects on the diseases they prevent, and receipt of DTP may be associated with an increase in all cause mortality. Although efforts should be made to ensure that all children are immunised on schedule with BCG, DTP, and MCV, randomised trials are needed to compare the effects of different sequences.

Objective To compare the efficacy, safety, and cost effectiveness of direct acting oral anticoagulants (DOACs) for patients with atrial fibrillation. Design Systematic review, network meta-analysis, and cost effectiveness analysis. Data sources Medline, PreMedline, Embase, and The Cochrane Library. Eligibility criteria for selecting studies Published randomised trials evaluating the use of a DOAC, vitamin K antagonist, or antiplatelet drug for prevention of stroke in patients with atrial fibrillation. Results 23 randomised trials involving 94 656 patients were analysed: 13 compared a DOAC with warfarin dosed to achieve a target INR of 2.0-3.0. Apixaban 5 mg twice daily (odds ratio 0.79, 95% confidence interval 0.66 to 0.94), dabigatran 150 mg twice daily (0.65, 0.52 to 0.81), edoxaban 60 mg once daily (0.86, 0.74 to 1.01), and rivaroxaban 20 mg once daily (0.88, 0.74 to 1.03) reduced the risk of stroke or systemic embolism compared with warfarin. The risk of stroke or systemic embolism was higher with edoxaban 60 mg once daily (1.33, 1.02 to 1.75) and rivaroxaban 20 mg once daily (1.35, 1.03 to 1.78) than with dabigatran 150 mg twice daily. The risk of all-cause mortality was lower with all DOACs than with warfarin. Apixaban 5 mg twice daily (0.71, 0.61 to 0.81), dabigatran 110 mg twice daily (0.80, 0.69 to 0.93), edoxaban 30 mg once daily (0.46, 0.40 to 0.54), and edoxaban 60 mg once daily (0.78, 0.69 to 0.90) reduced the risk of major bleeding compared with warfarin. The risk of major bleeding was higher with dabigatran 150 mg twice daily than apixaban 5 mg twice daily (1.33, 1.09 to 1.62), rivaroxaban 20 mg twice daily than apixaban 5 mg twice daily (1.45, 1.19 to 1.78), and rivaroxaban 20 mg twice daily than edoxaban 60 mg once daily (1.31, 1.07 to 1.59). The risk of intracranial bleeding was substantially lower for most DOACs compared with warfarin, whereas the risk of gastrointestinal bleeding was higher with some DOACs than warfarin. Apixaban 5 mg twice daily was ranked the highest for most outcomes, and was cost effective compared with warfarin. Conclusions The network meta-analysis informs the choice of DOACs for prevention of stroke in patients with atrial fibrillation. Several DOACs are of net benefit compared with warfarin. A trial directly comparing DOACs would overcome the need for indirect comparisons to be made through network meta-analysis. Systematic review registration PROSPERO CRD 42013005324.

In meta-analysis, dependent effect sizes are very common. An example is where in one or more studies the effect of an intervention is evaluated on multiple outcome variables for the same sample of participants. In this paper, we evaluate a three-level meta-analytic model to account for this kind of dependence, extending the simulation results of Van den Noortgate, López-López, Marín-Martínez, and Sánchez-Meca Behavior Research Methods, 45, 576-594 (2013) by allowing for a variation in the number of effect sizes per study, in the between-study variance, in the correlations between pairs of outcomes, and in the sample size of the studies. At the same time, we explore the performance of the approach if the outcomes used in a study can be regarded as a random sample from a population of outcomes. We conclude that although this approach is relatively simple and does not require prior estimates of the sampling covariances between effect sizes, it gives appropriate mean effect size estimates, standard error estimates, and confidence interval coverage proportions in a variety of realistic situations.

Ecosystem recovery from anthropogenic disturbances, either without human intervention or assisted by ecological restoration, is increasingly occurring worldwide. As ecosystems progress through recovery, it is important to estimate any resulting deficit in biodiversity and functions. Here we use data from 3,035 sampling plots worldwide, to quantify the interim reduction of biodiversity and functions occurring during the recovery process (that is, the ‘recovery debt'). Compared with reference levels, recovering ecosystems run annual deficits of 46–51% for organism abundance, 27–33% for species diversity, 32–42% for carbon cycling and 31–41% for nitrogen cycling. Our results are consistent across biomes but not across degrading factors. Our results suggest that recovering and restored ecosystems have less abundance, diversity and cycling of carbon and nitrogen than ‘undisturbed' ecosystems, and that even if complete recovery is reached, an interim recovery debt will accumulate. Under such circumstances, increasing the quantity of less-functional ecosystems through ecological restoration and offsetting are inadequate alternatives to ecosystem protection.