Confidence intervals for the between-study variance in random-effects meta-analysis using generalised heterogeneity statistics: should we use unequal tails?

BACKGROUND: Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative. METHODS: We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained. RESULTS: Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest. CONCLUSIONS: We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the '1-4 % split', where greater tail probability is allocated to the upper confidence bound. The 'width-optimal' interval that we present deserves further investigation

Weighing evidence ‘steampunk’ style via the Meta-Analyser

The funnel plot is a graphical visualization of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modeling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the center of mass of a physical system. We used this analogy to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulas and with a little help from Sherlock Holmes! Following on from the science fair, we have developed an interactive web-application (named the Meta-Analyser) to bring these ideas to a wider audience. We envisage that our application will be a useful tool for researchers when interpreting their data. First, to facilitate a simple understanding of fixed and random effects modeling approaches; second, to assess the importance of outliers; and third, to show the impact of adjusting for small study bias. This final aim is realized by introducing a novel graphical interpretation of the well-known method of Egger regression

A re-evaluation of the ‘quantile approximation method’ for random effects meta-analysis

The quantile approximation method has recently been proposed as a simple method for deriving confidence intervals for the treatment effect in a random effects meta-analysis. Although easily implemented, the quantiles used to construct intervals are derived from a single simulation study. Here it is shown that altering the study parameters, and in particular introducing changes to the distribution of the within-study variances, can have a dramatic impact on the resulting quantiles. This is further illustrated analytically by examining the scenario where all trials are assumed to be the same size. A more cautious approach is therefore suggested, where the conventional standard normal quantile is used in the primary analysis, but where the use of alternative quantiles is also considered in a sensitivity analysis. Copyright © 2008 John Wiley & Sons, Ltd

Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants satisfy the exclusion restriction assumption, or in genetic terms, when there is no pleiotropy. In this scenario, we derive a maximum profile likelihood estimator with provable consistency and asymptotic normality. However, through analyzing real datasets, we find strong evidence of both systematic and idiosyncratic pleiotropy in MR, echoing the omnigenic model of complex traits that is recently proposed in genetics. We model the systematic pleiotropy by a random effects model, where no genetic variant satisfies the exclusion restriction condition exactly. In this case we propose a consistent and asymptotically normal estimator by adjusting the profile score. We then tackle the idiosyncratic pleiotropy by robustifying the adjusted profile score. We demonstrate the robustness and efficiency of the proposed methods using several simulated and real datasets.Comment: 59 pages, 5 figures, 6 table

Accelerated longitudinal designs: An overview of modelling, power, costs and handling missing data.

Longitudinal studies are often used to investigate age-related developmental change. Whereas a single cohort design takes a group of individuals at the same initial age and follows them over time, an accelerated longitudinal design takes multiple single cohorts, each one starting at a different age. The main advantage of an accelerated longitudinal design is its ability to span the age range of interest in a shorter period of time than would be possible with a single cohort longitudinal design. This paper considers design issues for accelerated longitudinal studies. A linear mixed effect model is considered to describe the responses over age with random effects for intercept and slope parameters. Random and fixed cohort effects are used to cope with the potential bias accelerated longitudinal designs have due to multiple cohorts. The impact of other factors such as costs and the impact of dropouts on the power of testing or the precision of estimating parameters are examined. As duration-related costs increase relative to recruitment costs the best designs shift towards shorter duration and eventually cross-sectional design being best. For designs with the same duration but differing interval between measurements, we found there was a cutoff point for measurement costs relative to recruitment costs relating to frequency of measurements. Under our model of 30% dropout there was a maximum power loss of 7%.This work was supported by the Medical Research Council (G0800860