Trim and fill: A simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis

We study recently developed nonparametric methods for estimating the number of missing studies that might exist in a meta-analysis and the effect that these studies might have had on its outcome. These are simple rank-based data augmentation techniques, which formalize the use of funnel plots. We show that they provide effective and relatively powerful tests for evaluating the existence of such publication bias. After adjusting for missing studies, we find that the point estimate of the overall effect size is approximately correct and coverage of the effect size confidence intervals is substantially improved, in many cases recovering the nominal confidence levels entirely. We illustrate the trim and fill method on existing meta-analyses of studies in clinical trials and psychometrics.     

Chimpanzee right-handedness reconsidered: Evaluating the evidence with funnel plots

Evidence for population-level right-handedness in nonhuman primates seems inconsistent and contradictory, and many hypotheses have been advanced to account for this volatility. Funnel plots (scatter plots of percent right-hand use vs. sample size) offer a straightforward graphical technique for assessing: 1) the strength and consistency of handedness, 2) whether variability is consistent with normal sampling variation, and 3) how likely reports of statistically significant handedness might have arisen due to chance (i.e., type I error). They are informative for both within- and among-population variation. Reexamination of within-population variation from a detailed and widely cited study reporting significant population-level right-handedness in 140 individual captive chimpanzees (Hopkins [1994] Dev. Psychobiol. 27:395-407) revealed several puzzling patterns: 1) funnel plots showed higher percent right-hand use among individuals for which fewer observations were recorded, 2) when individuals with fewer than 25 observations were excluded, statistical support for population-level right-handedness either became marginal (P = 0.043, when computed as average percent use of the right hand) or disappeared (P = 0.62, when computed as proportion of individuals using the right hand more than the left, whether they did so significantly or not), and 3) the proportion of statistically ambilateral chimpanzees actually increased with increasing number of observations per individual, rather than decreased as would be expected for true population-level right-handedness. In addition, funnel plots of among-population variation from an earlier meta-analysis (McGrew and Marchant [1997] Yrbk. Phys. Anthropol. 40:201-232) suggested that the four reports of significant right-handedness, out of 37 estimates from 14 studies, were likely those that achieved statistical significance simply due to chance. Funnel plots, and the more refined statistical tests they suggest, confirm that the current evidence for population-level right-handedness in chimpanzees remains equivocal.     

Assessing the sensitivity of meta-analysis to selection bias: a multiple imputation approach

Evidence synthesis, both qualitatively and quantitatively through meta-analysis, is central to the development of evidence-based medicine. Unfortunately, meta-analysis is often complicated by the suspicion that the available studies represent a biased subset of the evidence, possibly due to publication bias or other systematically different effects in small studies. A number of statistical methods have been proposed to address this, among which the trim-and-fill method and the Copas selection model are two of the most widely discussed. However, both methods have drawbacks: the trim-and-fill method is based on strong assumptions about the symmetry of the funnel plot; the Copas selection model is less accessible to systematic reviewers, and sometimes encounters estimation problems. In this article, we adopt a logistic selection model, and show how treatment effects can be rapidly estimated via multiple imputation. Specifically, we impute studies under a missing at random assumption, and then reweight to obtain estimates under nonrandom selection. Our proposal is computationally straightforward. It allows users to increase selection while monitoring the extent of remaining funnel plot asymmetry, and also visualize the results using the funnel plot. We illustrate our approach using a small meta-analysis of benign prostatic hyperplasia.     

Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy

PurposeBiological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2) are needed for treatment planning and plan evaluation in carbon ion therapy. We present a model-independent, Monte Carlo based sensitivity analysis (SA) approach to quantify the impact of different uncertainties on the biological models.Methods and materialsThe Monte Carlo based SA is used for the evaluation of variations in biological parameters. The key property of this SA is the high number of simulation runs, each with randomized input parameters, allowing for a statistical variance-based ranking of the input variations. The potential of this SA is shown in a simplified one-dimensional treatment plan optimization. Physical properties of carbon ion beams (e.g. fragmentation) are simulated using the Monte Carlo code FLUKA. To estimate biological effects of ion beams compared to X-rays, we use the Local Effect Model (LEM) in the framework of the linear-quadratic (LQ) model. Currently, only uncertainties in the output of the biological models are taken into account.Results/conclusionsThe presented SA is suitable for evaluation of the impact of variations in biological parameters. Major advantages are the possibility to access and display the sensitivity of the evaluated quantity on several parameter variations at the same time. Main challenges for later use in three-dimensional treatment plan evaluation are computational time and memory usage. The presented SA can be performed with any analytical or numerical function and hence be applied to any biological model used in carbon ion therapy.     

A study on long-term salt-marsh succession using permanent plots

Succession of plant communities on a salt marsh at the Boschplaat, Terschelling (The Netherlands) is described on the basis of relevés from permanent plots in three transects, covering a period of almost 30 years. All relevés were clustered, using a hierarchical fusion technique. Succession has been quantified in terms of transitions between clusters over time in all plots. Analysis of the results showed four clearly distinct successional trends, each restricted to a particular altitudinal zone of the salt marsh. Between zones there were only few interconnections. This implies that zonation does not represent succession, at least not on the time scale of this study. It is suggested that initial differences between zones in the processes that change the abiotic environment, form the basis of vegetation zonation at the Boschplaat.The study was financially supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).     

An error in interpretation of double-reciprocal plots and Scatchard plots in studies of binding of fluorescent probes to proteins,and alternative proposals for determining binding parameters

One of the objects of experiments in which a fluorochrome is added to suspensions of cell membranes is to determine the parameters n and K _D , the capacity of unit mass of protein to bind fluorochrome and the dissociation constant, respectively. Currently, these are estimated from Scatchard plots, construction of which first requires that observed fluorescence intensity be converted to moles of bound fluorochrome. This in turn is said to be possible by analysis of the intercept of a plot of reciprocal fluorescence intensity against reciprocal protein concentration. However, analysis of the classical mass action equilibrium equation, upon which the foregoing procedures are said to be based, reveals that the intercept of the double-reciprocal plot always underestimates the desired value. The error is formalized and shown to increase without bound with fluorochrome concentration. The error in turn leads to erroneous assessment of n and K _D . Alternative methods for calculating the desired parameters are proposed, based on direct plots of fluorescence intensity.     

Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.     

A sensitivity analysis to methodological variation in indicator-based urban sustainability assessment: a Quebec case study

Methodological factors are often acknowledged for their impact on the urban sustainability assessment outcomes. The significance of this impact, however, divides those who assign it great importance; to the point of compromising any attempt at sustainability benchmarking using indicators, from those who regard it as having a relatively limited role. In this paper, we aim to contribute to this debate by assessing how methodological choices could influence the variation in the outcomes of indicator-based urban sustainability benchmarking. The paper starts with a literature review outlining the evolution of the approaches adopted since the pioneering experiences in the ‘90s to show a convergence in indicators and data over time. Subsequently, by using the data of the 25 most populous cities in Quebec, we empirically analyse the sensitivity of the cities’ sustainability scores to 18 combinations of estimation techniques, and observe consistency within the outcomes while maintaining general patterns regardless of the approach used. The results suggest that methodological choices play a limited role in the urban sustainability assessment outcomes. Thus, other determinants beyond the evaluation methods are most likely involved and therefore should be a major focus in future research agendas.     

Regression survival analysis with an assumed copula for dependent censoring: a sensitivity analysis approach

SUMMARY: In clinical studies, when censoring is caused by competing risks or patient withdrawal, there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring. Because dependent censoring is nonidentifiable without additional information, the best we can do is a sensitivity analysis to assess the changes of parameter estimates under different assumptions about the association between failure and censoring. This analysis is especially useful when knowledge about such association is available through literature review or expert opinions. In a regression analysis setting, the consequences of falsely assuming independent censoring on parameter estimates are not clear. Neither the direction nor the magnitude of the potential bias can be easily predicted. We provide an approach to do sensitivity analysis for the widely used Cox proportional hazards models. The joint distribution of the failure and censoring times is assumed to be a function of their marginal distributions. This function is called a copula. Under this assumption, we propose an iteration algorithm to estimate the regression parameters and marginal survival functions. Simulation studies show that this algorithm works well. We apply the proposed sensitivity analysis approach to the data from an AIDS clinical trial in which 27% of the patients withdrew due to toxicity or at the request of the patient or investigator.     

Statistical issues in a metaregression analysis of randomized trials: impact on the dietary sodium intake and blood pressure relationship

In a meta-analysis of randomized trials of the effects of dietary sodium interventions on blood pressure, we found substantial heterogeneity among the studies. We were interested in evaluating whether measurement error, known to be a problem for dietary sodium measures, publication bias, or confounding factors could be responsible for the heterogeneity. A measurement error correction was developed that corrects both the slope and the intercept and takes into account the sample size of each study and the number of measurements taken on an individual. The measurement error correction had a minimal effect on the estimates, although it performed well in simulated data. A smoothed scatter plot was used to assess publication bias. Metaregressions provide a convenient way to jointly assess the effects of several factors, but care must be taken to fit an appropriate model.     

GENESIS: a simulation model of phylogeny 2. A sensitivity analysis

In a former paper (Heijerman 1988) a simulation model of phylogeny, GENESIS, was presented. This paer describes the results of a sensitivity analysis of GENESIS. The analysis is performed by cganging the input parameter values and estimating the relative effects on the model's output, as summarized by several tree statistics. The results show that none of the statistics tested can be classified as an unambiguous estimator of accuracy of methods for estimating hylogenetic trees. The sensitivity analysis increases the insight into the behaviour and applicability of the model. This is a prerequisite for a correct interpretation of the results of the evaluation experiments that will be carried out using GENESIS.     

Biodiesel production from waste cooking oil: 2. Economic assessment and sensitivity analysis

The economic feasibilities of four continuous processes to produce biodiesel, including both alkali- and acid-catalyzed processes, using waste cooking oil and the ‘standard’ process using virgin vegetable oil as the raw material, were assessed. Although the alkali-catalyzed process using virgin vegetable oil had the lowest fixed capital cost, the acid-catalyzed process using waste cooking oil was more economically feasible overall, providing a lower total manufacturing cost, a more attractive after-tax rate of return and a lower biodiesel break-even price. On the basis of these economic calculations, sensitivity analyses for these processes were carried out. Plant capacity and prices of feedstock oils and biodiesel were found to be the most significant factors affecting the economic viability of biodiesel manufacture.     

Meta-analysis in applied ecology

This overview examines research synthesis in applied ecology and conservation. Vote counting and pooling unweighted averages are widespread despite the superiority of syntheses based on weighted combination of effects. Such analyses allow exploration of methodological uncertainty in addition to consistency of effects across species, space and time, but exploring heterogeneity remains controversial. Meta-analyses are required to generalize in ecology, and to inform evidence-based decision-making, but the more sophisticated statistical techniques and registers of research used in other disciplines must be employed in ecology to fully realize their benefits.     

A novel interpretation of structural dot plots of genomes derived from the analysis of two strains of Neisseria meningitidis

Neisseria meningitidis is the agent of invasive meningococcal disease, including cerebral meningitis and septicemia. Because the diseases caused by different clonal groups (sequence types) have their own epidemiological characteristics, it is important to understand the differences among the genomes of the N. meningitidis clonal groups. To this end, a novel interpretation of a structural dot plot of genomes was devised and applied; exact nucleotide matches between the genomes of N. meningitidis serogroup A strain Z2491 and serogroup B strain MC58 were identified, leading to the specification of various structural regions. Known and putative virulence genes for each N. meningitidis strain were then classified into these regions. We found that virulence genes of MC58 tend more to the translocated regions (chromosomal segments in new sequence contexts) than do those of Z2491, notably tending towards the interface between one of the translocated regions and the collinear region. Within the col-linear region, virulence genes tend to occur within 16 kb of gaps in the exact matches. Verification of these tendencies using genes clustered in the cps locus was sufficiently supportive to suggest that these tendencies can be used to focus the search for and understanding of virulence genes and mechanisms of pathogenicity in these two organisms.     

Missing covariates in longitudinal data with informative dropouts: bias analysis and inference

We consider estimation in generalized linear mixed models (GLMM) for longitudinal data with informative dropouts. At the time a unit drops out, time-varying covariates are often unobserved in addition to the missing outcome. However, existing informative dropout models typically require covariates to be completely observed. This assumption is not realistic in the presence of time-varying covariates. In this article, we first study the asymptotic bias that would result from applying existing methods, where missing time-varying covariates are handled using naive approaches, which include: (1) using only baseline values; (2) carrying forward the last observation; and (3) assuming the missing data are ignorable. Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology.     

女性生殖道支原体感染与不孕症的关系及药敏分析

目的探讨女性生殖道支原体感染与不孕症之间的关系及对11种抗生素的敏感率,指导临床明确诊断,合理用药。方法随机选择2007年至2009年来长治市妇幼保健院就诊的女性不孕症患者360例,进行宫颈分泌物支原体培养和药敏试验。结果 360例宫颈分泌物标本中检出解脲支原体(Uu)阳性者161例、人型支原体(Mh)阳性者3例、解脲支原体(Uu)+人型支原体(Mh)混合阳性者29例;对阳性标本都做了11种抗生素的药敏试验,其中交沙霉素敏感率为93.47%、美满霉素敏感率为92.00%、强力霉素敏感率为90.21%、克拉霉素敏感率为83.69%、甲砜霉素敏感率为73.91%、环脂红霉素敏感率为61.95%和阿奇霉素敏感率为53.26%等。结论女性不孕症伴随高发的生殖道支原体感染,支原体感染与不孕症可能有关;长治地区生殖道支原体对交沙霉素、美满霉素、强力霉素、克拉霉素、甲砜霉素敏感性较高,环脂红霉素、阿奇霉素次之,对红霉素、罗红霉素敏感性较低,对环丙沙星、左氧氟沙星敏感性很低。     

Confidence intervals and P-values for meta-analysis with publication bias

We study publication bias in meta-analysis by supposing there is a population (y, sigma) of studies which give treatment effect estimates y approximately N(theta, sigma(2)). A selection function describes the probability that each study is selected for review. The overall estimate of theta depends on the studies selected, and hence on the (unknown) selection function. Our previous paper, Copas and Jackson (2004, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small sigma) are as likely, or more likely, to be selected than small studies (large sigma). This led to a worst-case sensitivity analysis, controlling for the overall fraction of studies selected. However, no account was taken of the effect of selection on the uncertainty in estimation. This article extends the previous work by finding corresponding confidence intervals and P-values, and hence a new sensitivity analysis for publication bias. Two examples are discussed.     

Floristic composition, structure, and diversity of four forest plots in the Sierra Maigualida, Venezuelan Guayana

A phytosociological study was carried out in four 1-ha forest plots in the Sierra Maigualida region, Venezuelan Guayana. Density, dominance, and frequency values were calculated as well as the species and family importance values (FIVs) in each plot. A total of 65 families, 232 genera and 533 species were represented in the 4ha of forest. The number of stems 10cmdbh varied from 355 to 563, the number of species from 133 to 191, the genera from 76 to 120, the families from 38 to 51, and the basal area from 20.56 to 40.83m² per hectare. Overall the most species rich family was Fabaceae (38 species), the most numerous in total stems was Burseraceae (165 individuals), and the most dominant in terms of basal area was Sapotaceae (1367.13cm²). The most conspicuous families, as represented among the top five FIV, include Burseraceae in all four plots, Moraceae in three of the plots, and Sapotaceae in two plots. Less than 20% of the total inventory of species are represented in two or more plots. The percentages of species which are unique to a single plot range from 56 to 67%. The within-plot diversities recorded in the present study indicate that the Sierra Maiguailida harbors the richest forests thus far documented in Venezuelan Guayana. Meanwhile, the low between-plot similarity indices reinforce the notion that the species richness of this region is unusually high and suggest the need to extend collections and inventory studies.