Rebecca M. Turner

Plasma homocysteine concentrations and risk of coronary heart disease in UK Indian Asian and European men.

BACKGROUND Reasons for the increase in mortality due to coronary heart disease (CHD) in UK Indian Asians are not well understood. In this study, we tested the hypotheses that elevated plasma homocysteine concentrations are a risk factor for CHD in Indian Asians, and explain part of their increased CHD risk, compared with Europeans. METHODS We undertook two parallel case-control studies, one in Europeans and one in Indian Asians. We recruited 551 male cases (294 European, 257 Indian Asian) and 1025 healthy male controls (507 European, 518 Indian Asian). Fasting and post-methionine load homocysteine, vitamin B12 and folate concentrations, and conventional CHD risk factors were measured. FINDINGS Fasting homocysteine concentrations were 8% higher (95% CI 3-14) in cases compared with controls, in both ethnic groups. The odds ratio of CHD for a 5 micromol/L increment in fasting plasma homocysteine was 1.3 (1.1-1.6) in Europeans and 1.2 (1.0-1.4) in Indian Asians. The association between fasting plasma homocysteine and CHD was independent of conventional CHD risk factors in both ethnic groups. Post-load homocysteine concentrations were not significantly different in cases compared with controls. Among the controls, fasting homocysteine concentrations were 6% (2-10) higher in Indian Asians than in Europeans. From the results we estimate that elevated homocysteine may contribute to twice as many CHD deaths in Indian Asians, compared with Europeans. The differences in homocysteine concentrations between the two ethnic groups were explained by lower vitamin B12 and folate levels in Asians. INTERPRETATION Plasma homocysteine is a novel and independent risk factor for CHD in Indian Asians, and may contribute to their increased CHD risk. Raised homocysteine concentrations in Indian Asians may be related to their reduced vitamin B12 and folate levels, implying that the increased CHD risk in this group may be reduced by dietary vitamin supplementation.

Bias modelling in evidence synthesis

Policy decisions often require synthesis of evidence from multiple sources, and the source studies typically vary in rigour and in relevance to the target question. We present simple methods of allowing for differences in rigour (or lack of internal bias) and relevance (or lack of external bias) in evidence synthesis. The methods are developed in the context of reanalysing a UK National Institute for Clinical Excellence technology appraisal in antenatal care, which includes eight comparative studies. Many were historically controlled, only one was a randomized trial and doses, populations and outcomes varied between studies and differed from the target UK setting. Using elicited opinion, we construct prior distributions to represent the biases in each study and perform a bias-adjusted meta-analysis. Adjustment had the effect of shifting the combined estimate away from the null by approximately 10%, and the variance of the combined estimate was almost tripled. Our generic bias modelling approach allows decisions to be based on all available evidence, with less rigorous or less relevant studies downweighted by using computationally simple methods.

A multilevel model framework for meta-analysis of clinical trials with binary outcomes.

In this paper we explore the potential of multilevel models for meta-analysis of trials with binary outcomes for both summary data, such as log-odds ratios, and individual patient data. Conventional fixed effect and random effects models are put into a multilevel model framework, which provides maximum likelihood or restricted maximum likelihood estimation. To exemplify the methods, we use the results from 22 trials to prevent respiratory tract infections; we also make comparisons with a second example data set comprising fewer trials. Within summary data methods, confidence intervals for the overall treatment effect and for the between-trial variance may be derived from likelihood based methods or a parametric bootstrap as well as from Wald methods; the bootstrap intervals are preferred because they relax the assumptions required by the other two methods. When modelling individual patient data, a bias corrected bootstrap may be used to provide unbiased estimation and correctly located confidence intervals; this method is particularly valuable for the between-trial variance. The trial effects may be modelled as either fixed or random within individual data models, and we discuss the corresponding assumptions and implications. If random trial effects are used, the covariance between these and the random treatment effects should be included; the resulting model is equivalent to a bivariate approach to meta-analysis. Having implemented these techniques, the flexibility of multilevel modelling may be exploited in facilitating extensions to standard meta-analysis methods.

The impact of study size on meta-analyses: examination of underpowered studies in Cochrane reviews.

Background Most meta-analyses include data from one or more small studies that, individually, do not have power to detect an intervention effect. The relative influence of adequately powered and underpowered studies in published meta-analyses has not previously been explored. We examine the distribution of power available in studies within meta-analyses published in Cochrane reviews, and investigate the impact of underpowered studies on meta-analysis results. Methods and Findings For 14,886 meta-analyses of binary outcomes from 1,991 Cochrane reviews, we calculated power per study within each meta-analysis. We defined adequate power as ≥50% power to detect a 30% relative risk reduction. In a subset of 1,107 meta-analyses including 5 or more studies with at least two adequately powered and at least one underpowered, results were compared with and without underpowered studies. In 10,492 (70%) of 14,886 meta-analyses, all included studies were underpowered; only 2,588 (17%) included at least two adequately powered studies. 34% of the meta-analyses themselves were adequately powered. The median of summary relative risks was 0.75 across all meta-analyses (inter-quartile range 0.55 to 0.89). In the subset examined, odds ratios in underpowered studies were 15% lower (95% CI 11% to 18%, P<0.0001) than in adequately powered studies, in meta-analyses of controlled pharmacological trials; and 12% lower (95% CI 7% to 17%, P<0.0001) in meta-analyses of controlled non-pharmacological trials. The standard error of the intervention effect increased by a median of 11% (inter-quartile range −1% to 35%) when underpowered studies were omitted; and between-study heterogeneity tended to decrease. Conclusions When at least two adequately powered studies are available in meta-analyses reported by Cochrane reviews, underpowered studies often contribute little information, and could be left out if a rapid review of the evidence is required. However, underpowered studies made up the entirety of the evidence in most Cochrane reviews.

Characteristics of meta-analyses and their component studies in the Cochrane Database of Systematic Reviews: a cross-sectional, descriptive analysis

BackgroundCochrane systematic reviews collate and summarise studies of the effects of healthcare interventions. The characteristics of these reviews and the meta-analyses and individual studies they contain provide insights into the nature of healthcare research and important context for the development of relevant statistical and other methods.MethodsWe classified every meta-analysis with at least two studies in every review in the January 2008 issue of the Cochrane Database of Systematic Reviews (CDSR) according to the medical specialty, the types of interventions being compared and the type of outcome. We provide descriptive statistics for numbers of meta-analyses, numbers of component studies and sample sizes of component studies, broken down by these categories.ResultsWe included 2321 reviews containing 22,453 meta-analyses, which themselves consist of data from 112,600 individual studies (which may appear in more than one meta-analysis). Meta-analyses in the areas of gynaecology, pregnancy and childbirth (21%), mental health (13%) and respiratory diseases (13%) are well represented in the CDSR. Most meta-analyses address drugs, either with a control or placebo group (37%) or in a comparison with another drug (25%). The median number of meta-analyses per review is six (inter-quartile range 3 to 12). The median number of studies included in the meta-analyses with at least two studies is three (inter-quartile range 2 to 6). Sample sizes of individual studies range from 2 to 1,242,071, with a median of 91 participants.DiscussionIt is clear that the numbers of studies eligible for meta-analyses are typically very small for all medical areas, outcomes and interventions covered by Cochrane reviews. This highlights the particular importance of suitable methods for the meta-analysis of small data sets. There was little variation in number of studies per meta-analysis across medical areas, across outcome data types or across types of interventions being compared.

Meta-analysis using multilevel models with an application to the study of class size effects

Meta-analysis is formulated as a special case of a multilevel (hierarchical data) model in which the highest level is that of the study and the lowest level that of an observation on an individual respondent. Studies can be combined within a single model where the responses occur at different levels of the data hierarchy and efficient estimates are obtained. An example is given from studies of class sizes and achievement in schools, where study data are available at the aggregate level in terms of overall mean values for classes of different sizes, and also at the student level.

Bayesian methods of analysis for cluster randomized trials with binary outcome data

We explore the potential of Bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data, and apply the methods to a trial randomized by general practice. An approximate relationship is derived between the intracluster correlation coefficient (ICC) and the between-cluster variance used in a hierarchical logistic regression model. By constructing an informative prior for the ICC on the basis of available information, we are thus able implicitly to specify an informative prior for the between-cluster variance. The approach also provides us with a credible interval for the ICC for binary outcome data. Several approaches to constructing informative priors from empirical ICC values are described. We investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set, while its interval estimate is more sensitive. The Bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering. This enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption. In a model with a more complex variance structure, Bayesian methods can provide credible intervals for a difference between two variance components, in order for example to investigate whether the effect of intervention varies across clusters. We compare our results with those obtained from classical estimation, discuss the relative merits of the Bayesian framework, and conclude that the flexibility of the Bayesian approach offers some substantial advantages, although selection of prior distributions is not straightforward.

Analysing repeated measurements data: a practical comparison of methods.

A variety of methods are available for analysing repeated measurements data where the outcome is continuous. However, there is little information on how established methods, such as summary statistics and repeated measures analysis of variance (RMAOV), compare in practice with methods that have become available to applied statisticians more recently, such as marginal models (based on generalized estimating equation methodology) and multilevel models (that is, hierarchical random effects models). The aim of this paper is to exemplify the use of these methods, and directly compare their results by application to a clinical trial data set. The focus is on practical aspects rather than technical issues. The data considered were taken from a clinical trial of treatments for asthma in 240 children, in which a baseline and four post-randomization measurements of outcomes were taken. The simplicity of the method of summary statistics using the post-randomization mean of observations provided a useful initial analysis. However, fixed time effects or treatment-time interactions cannot be included in such an analysis, and choice of appropriate weighting when there is substantial missing data is problematic. RMAOV, marginal models and multilevel models generally provided similar estimates and standard errors for the treatment effects, although in one example with a relatively complex variance structure the marginal model produced less efficient estimates. Two advantages of multilevel models are that they provide direct estimates of variance components which are often of interest in their own right, and that they can be naturally extended to handle multivariate outcomes.

Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data

Objectives Estimation of between-study heterogeneity is problematic in small meta-analyses. Bayesian meta-analysis is beneficial because it allows incorporation of external evidence on heterogeneity. To facilitate this, we provide empirical evidence on the likely heterogeneity between studies in meta-analyses relating to specific research settings. Study Design and Setting Our analyses included 6,492 continuous-outcome meta-analyses within the Cochrane Database of Systematic Reviews. We investigated the influence of meta-analysis settings on heterogeneity by modeling study data from all meta-analyses on the standardized mean difference scale. Meta-analysis setting was described according to outcome type, intervention comparison type, and medical area. Predictive distributions for between-study variance expected in future meta-analyses were obtained, which can be used directly as informative priors. Results Among outcome types, heterogeneity was found to be lowest in meta-analyses of obstetric outcomes. Among intervention comparison types, heterogeneity was lowest in meta-analyses comparing two pharmacologic interventions. Predictive distributions are reported for different settings. In two example meta-analyses, incorporating external evidence led to a more precise heterogeneity estimate. Conclusion Heterogeneity was influenced by meta-analysis characteristics. Informative priors for between-study variance were derived for each specific setting. Our analyses thus assist the incorporation of realistic prior information into meta-analyses including few studies.

Multilevel models for meta-analysis, and their application to absolute risk differences.

Meta-analysis can be considered a multilevel statistical problem, since information within studies is combined in the presence of potential heterogeneity between studies. Here a general multilevel model framework is developed for meta-analysis to combine either summary data or individual patient outcome data from each study, and to include either study or individual level covariates that might explain heterogeneity. Classical and Bayesian approaches to estimation are contrasted. These methods are applied to a meta-analysis of trials of thrombolytic therapy after myocardial infarction. Subgroups within the trials were available, categorized by the time delay until treatment, so that a three-level random effects model that includes time delay as a covariate is proposed. In addition it was desired to represent the treatment effect as an absolute risk reduction, rather than the conventional odds ratio. We show how this can be achieved within a Bayesian analysis, while still recognizing the binary nature of the original outcome data.