Jack Bowden

Methods to estimate the between-study variance and its uncertainty in meta-analysis

Meta‐analyses are typically used to estimate the overall/mean of an outcome of interest. However, inference about between‐study variability, which is typically modelled using a between‐study variance parameter, is usually an additional aim. The DerSimonian and Laird method, currently widely used by default to estimate the between‐study variance, has been long challenged. Our aim is to identify known methods for estimation of the between‐study variance and its corresponding uncertainty, and to summarise the simulation and empirical evidence that compares them. We identified 16 estimators for the between‐study variance, seven methods to calculate confidence intervals, and several comparative studies. Simulation studies suggest that for both dichotomous and continuous data the estimator proposed by Paule and Mandel and for continuous data the restricted maximum likelihood estimator are better alternatives to estimate the between‐study variance. Based on the scenarios and results presented in the published studies, we recommend the Q‐profile method and the alternative approach based on a ‘generalised Cochran between‐study variance statistic’ to compute corresponding confidence intervals around the resulting estimates. Our recommendations are based on a qualitative evaluation of the existing literature and expert consensus. Evidence‐based recommendations require an extensive simulation study where all methods would be compared under the same scenarios.

Unbiased estimation of selected treatment means in two-stage trials.

Straightforward estimation of a treatments effect in an adaptive clinical trial can be severely hindered when it has been chosen from a larger group of potential candidates. This is because selection mechanisms that condition on the rank order of treatment statistics introduce bias. Nevertheless, designs of this sort are seen as a practical and efficient way to fast track the most promising compounds in drug development. In this paper we extend the method of Cohen and Sackrowitz (1989) who proposed a two-stage unbiased estimate for the best performing treatment at interim. This enables their estimate to work for unequal stage one and two sample sizes, and also when the quantity of interest is the best, second best, or j -th best treatment out of k. The implications of this new flexibility are explored via simulation.

Sensitivity Analyses for Robust Causal Inference from Mendelian Randomization Analyses with Multiple Genetic Variants.

Mendelian randomization investigations are becoming more powerful and simpler to perform, due to the increasing size and coverage of genome-wide association studies and the increasing availability of summarized data on genetic associations with risk factors and disease outcomes. However, when using multiple genetic variants from different gene regions in a Mendelian randomization analysis, it is highly implausible that all the genetic variants satisfy the instrumental variable assumptions. This means that a simple instrumental variable analysis alone should not be relied on to give a causal conclusion. In this article, we discuss a range of sensitivity analyses that will either support or question the validity of causal inference from a Mendelian randomization analysis with multiple genetic variants. We focus on sensitivity analyses of greatest practical relevance for ensuring robust causal inferences, and those that can be undertaken using summarized data. Aside from cases in which the justification of the instrumental variable assumptions is supported by strong biological understanding, a Mendelian randomization analysis in which no assessment of the robustness of the findings to violations of the instrumental variable assumptions has been made should be viewed as speculative and incomplete. In particular, Mendelian randomization investigations with large numbers of genetic variants without such sensitivity analyses should be treated with skepticism.

On Instrumental Variables Estimation of Causal Odds Ratios

Inference for causal effects can benefit from the availability of an instrumental variable (IV) which, by definition, is associated with the given exposure, but not with the outcome of interest other than through a causal exposure effect. Estimation methods for instrumental variables are now well established for continuous outcomes, but much less so for dichotomous outcomes. In this article we review IV estimation of so-called conditional causal odds ratios which express the effect of an arbitrary exposure on a dichotomous outcome conditional on the exposure level, instrumental variable and measured covariates. In addition, we propose IV estimators of so-called marginal causal odds ratios which express the effect of an arbitrary exposure on a dichotomous outcome at the population level, and are therefore of greater public health relevance. We explore interconnections between the different estimators and support the results with extensive simulation studies and three applications.

A framework for the investigation of pleiotropy in two-sample summary data Mendelian randomization

Mendelian randomization (MR) uses genetic data to probe questions of causality in epidemiological research, by invoking the Instrumental Variable (IV) assumptions. In recent years, it has become commonplace to attempt MR analyses by synthesising summary data estimates of genetic association gleaned from large and independent study populations. This is referred to as two‐sample summary data MR. Unfortunately, due to the sheer number of variants that can be easily included into summary data MR analyses, it is increasingly likely that some do not meet the IV assumptions due to pleiotropy. There is a pressing need to develop methods that can both detect and correct for pleiotropy, in order to preserve the validity of the MR approach in this context. In this paper, we aim to clarify how established methods of meta‐regression and random effects modelling from mainstream meta‐analysis are being adapted to perform this task. Specifically, we focus on two contrastin g approaches: the Inverse Variance Weighted (IVW) method which assumes in its simplest form that all genetic variants are valid IVs, and the method of MR‐Egger regression that allows all variants to violate the IV assumptions, albeit in a specific way. We investigate the ability of two popular random effects models to provide robustness to pleiotropy under the IVW approach, and propose statistics to quantify the relative goodness‐of‐fit of the IVW approach over MR‐Egger regression.

Genome-wide association analyses of sleep disturbance traits identify new loci and highlight shared genetics with neuropsychiatric and metabolic traits

Chronic sleep disturbances, associated with cardiometabolic diseases, psychiatric disorders and all-cause mortality, affect 25–30% of adults worldwide. Although environmental factors contribute substantially to self-reported habitual sleep duration and disruption, these traits are heritable and identification of the genes involved should improve understanding of sleep, mechanisms linking sleep to disease and development of new therapies. We report single- and multiple-trait genome-wide association analyses of self-reported sleep duration, insomnia symptoms and excessive daytime sleepiness in the UK Biobank (n = 112,586). We discover loci associated with insomnia symptoms (near MEIS1, TMEM132E, CYCL1 and TGFBI in females and WDR27 in males), excessive daytime sleepiness (near AR–OPHN1) and a composite sleep trait (near PATJ (INADL) and HCRTR2) and replicate a locus associated with sleep duration (at PAX8). We also observe genetic correlation between longer sleep duration and schizophrenia risk (rg = 0.29, P = 1.90 × 10−13) and between increased levels of excessive daytime sleepiness and increased measures for adiposity traits (body mass index (BMI): rg = 0.20, P = 3.12 × 10−9; waist circumference: rg = 0.20, P = 2.12 × 10−7).

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%.

Unbiased estimation of odds ratios: combining genomewide association scans with replication studies

Odds ratios or other effect sizes estimated from genome scans are upwardly biased, because only the top‐ranking associations are reported, and moreover only if they reach a defined level of significance. No unbiased estimate exists based on data selected in this fashion, but replication studies are routinely performed that allow unbiased estimation of the effect sizes. Estimation based on replication data alone is inefficient in the sense that the initial scan could, in principle, contribute information on the effect size. We propose an unbiased estimator combining information from both the initial scan and the replication study, which is more efficient than that based just on the replication. Specifically, we adjust the standard combined estimate to allow for selection by rank and significance in the initial scan. Our approach explicitly allows for multiple associations arising from a scan, and is robust to mis‐specification of a significance threshold. We require replication data to be available but argue that, in most applications, estimates of effect sizes are only useful when associations have been replicated. We illustrate our approach on some recently completed scans and explore its efficiency by simulation. Genet. Epidemiol. 33:406–418, 2009.

Collaborative pooled analysis of data on C-reactive protein gene variants and coronary disease: judging causality by Mendelian randomisation

Many prospective studies have reported associations between circulating C-reactive protein (CRP) levels and risk of coronary heart disease (CHD), but causality remains uncertain. Studies of CHD are being conducted that involve measurement of common polymorphisms of the CRP gene known to be associated with circulating concentrations, thereby utilising these variants as proxies for circulating CRP levels. By analysing data from several studies examining the association between relevant CRP polymorphisms and CHD risk, the present collaboration will undertake a Mendelian randomisation analysis to help assess the likelihood of any causal relevance of CRP levels to CHD risk. A central database is being established containing individual data on CRP polymorphisms, circulating CRP levels, and major coronary outcomes as well as age, sex and other relevant characteristics. Associations between CRP polymorphisms or haplotypes and CHD will be evaluated under different circumstances. This collaboration comprises, at present, about 37,000 CHD outcomes and about 120,000 controls, which should yield suitably precise findings to help judge causality. This work should advance understanding of the relevance of low-grade inflammation to CHD and indicate whether or not CRP itself is involved in long-term pathogenesis.

BMI as a Modifiable Risk Factor for Type 2 Diabetes: Refining and Understanding Causal Estimates Using Mendelian Randomization

This study focused on resolving the relationship between BMI and type 2 diabetes. The availability of multiple variants associated with BMI offers a new chance to resolve the true causal effect of BMI on type 2 diabetes; however, the properties of these associations and their validity as genetic instruments need to be considered alongside established and new methods for undertaking Mendelian randomization (MR). We explore the potential for pleiotropic genetic variants to generate bias, revise existing estimates, and illustrate value in new analysis methods. A two-sample MR approach with 96 genetic variants was used with three different analysis methods, two of which (MR-Egger and the weighted median) have been developed specifically to address problems of invalid instrumental variables. We estimate an odds ratio for type 2 diabetes per unit increase in BMI (kg/m2) of between 1.19 and 1.38, with the most stable estimate using all instruments and a weighted median approach (1.26 [95% CI 1.17, 1.34]). TCF7L2(rs7903146) was identified as a complex effect or pleiotropic instrument, and removal of this variant resulted in convergence of causal effect estimates from different causal analysis methods. This indicated the potential for pleiotropy to affect estimates and differences in performance of alternative analytical methods. In a real type 2 diabetes–focused example, this study demonstrates the potential impact of invalid instruments on causal effect estimates and the potential for new approaches to mitigate the bias caused.