Generalized inferences on the overall treatment effect in meta-analysis with normally distributed outcomes

This paper focuses on inferences about the overall treatment effect in meta-analysis with normally distributed responses based on the concepts of generalized inference. A refined generalized pivotal quantity based on t distribution is presented and simulation study shows that it can provide confidence intervals with satisfactory coverage probabilities and perform hypothesis testing with satisfactory type-I error control at very small sample sizes.     

Variance matters: The shape of a datum

In the quantitative analysis of behaviour, choice data are most often plotted and analyzed as logarithmic transforms of ratios of responses and of ratios of reinforcers according to the generalized-matching relation, or its derivatives such as conditional-discrimination models. The relation between log choice ratios and log reinforcer ratios has normally been found using ordinary linear regression, which minimizes the sums of the squares of the y deviations from the fitted line. However, linear regression of this type requires that the log choice data be normally distributed, of equal variance for each log reinforcer ratio, and that the x (log reinforcer ratio) measures be fixed with no variance. We argue that, while log transformed choice data may be normally distributed, log reinforcer ratios do have variance, and because these measures derive from a binomial process, log reinforcer ratio distributions will be non-normal and skewed to more extreme values. These effects result in ordinary linear regression systematically underestimating generalized-matching sensitivity values, and in faulty parameter estimates from non-linear regression to assume hyperbolic and exponential decay processes. They also lead to model comparisons, which assume equal normally distributed error around every data point, being incorrect. We describe an alternative approach that can be used if the variance in choice is measured.     

Assessing the implications of publication bias for two popular estimates of between-study variance in meta-analysis

Perhaps the greatest threat to the validity of a meta-analysis is the possibility of publication bias, where studies with interesting or statistically significant results are more likely to be published. This obviously impacts on inference concerning the treatment effect but also has implications for estimates of between-study variance. Two popular and established estimation methods are considered and formulae for assessing the implications of the bias are provided in terms of a general process for selecting studies. Meta-analysts, concerned that publication bias may be present, can use these as part of a sensitivity analysis to assess the robustness of their estimates of between-study variance using any selection process that is likely to be used in practice. The procedure is illustrated using a meta-analysis of clinical trials concerning the effectiveness of endoscopic sclerotherapy for preventing death in patients with cirrhosis and oesophagogastric varices.     

A unification of models for meta-analysis of diagnostic accuracy studies

Studies of diagnostic accuracy require more sophisticated methods for their meta-analysis than studies of therapeutic interventions. A number of different, and apparently divergent, methods for meta-analysis of diagnostic studies have been proposed, including two alternative approaches that are statistically rigorous and allow for between-study variability: the hierarchical summary receiver operating characteristic (ROC) model (Rutter and Gatsonis, 2001) and bivariate random-effects meta-analysis (van Houwelingen and others, 1993), (van Houwelingen and others, 2002), (Reitsma and others, 2005). We show that these two models are very closely related, and define the circumstances in which they are identical. We discuss the different forms of summary model output suggested by the two approaches, including summary ROC curves, summary points, confidence regions, and prediction regions.     

Meta-analysis of genetic-linkage analysis of quantitative-trait loci

Meta-analysis is an important tool in linkage analysis. The pooling of results across primary linkage studies allows greater statistical power to detect quantitative-trait loci (QTLs) and more-precise estimation of their genetic effects and, hence, yields conclusions that are stronger relative to those of individual studies. Previous methods for the meta-analysis of linkage studies have been proposed, and, although some methods address the problem of between-study heterogeneity, most methods still require linkage analysis at the same marker or set of markers across studies, whereas others do not result in an estimate of genetic variance. In this study, we present a meta-analytic procedure to evaluate evidence from several studies that report Haseman-Elston statistics for linkage to a QTL at multiple, possibly distinct, markers on a chromosome. This technique accounts for between-study heterogeneity and estimates both the location of the QTL and the magnitude of the genetic effect more precisely than does an individual study. We also provide standard errors for the genetic effect and for the location (in cM) of the QTL, using a resampling method. The approach can be applied under other conditions, provided that the various studies use the same linkage statistic.     

Multiple outputation: inference for complex clustered data by averaging analyses from independent data

This article applies a simple method for settings where one has clustered data, but statistical methods are only available for independent data. We assume the statistical method provides us with a normally distributed estimate, theta, and an estimate of its variance sigma. We randomly select a data point from each cluster and apply our statistical method to this independent data. We repeat this multiple times, and use the average of the associated theta's as our estimate. An estimate of the variance is given by the average of the sigma2's minus the sample variance of the theta's. We call this procedure multiple outputation, as all "excess" data within each cluster is thrown out multiple times. Hoffman, Sen, and Weinberg (2001, Biometrika 88, 1121-1134) introduced this approach for generalized linear models when the cluster size is related to outcome. In this article, we demonstrate the broad applicability of the approach. Applications to angular data, p-values, vector parameters, Bayesian inference, genetics data, and random cluster sizes are discussed. In addition, asymptotic normality of estimates based on all possible outputations, as well as a finite number of outputations, is proven given weak conditions. Multiple outputation provides a simple and broadly applicable method for analyzing clustered data. It is especially suited to settings where methods for clustered data are impractical, but can also be applied generally as a quick and simple tool.     

An alternative model for bivariate random-effects meta-analysis when the within-study correlations are unknown

Multivariate meta-analysis models can be used to synthesize multiple, correlated endpoints such as overall and disease-free survival. A hierarchical framework for multivariate random-effects meta-analysis includes both within-study and between-study correlation. The within-study correlations are assumed known, but they are usually unavailable, which limits the multivariate approach in practice. In this paper, we consider synthesis of 2 correlated endpoints and propose an alternative model for bivariate random-effects meta-analysis (BRMA). This model maintains the individual weighting of each study in the analysis but includes only one overall correlation parameter, rho, which removes the need to know the within-study correlations. Further, the only data needed to fit the model are those required for a separate univariate random-effects meta-analysis (URMA) of each endpoint, currently the common approach in practice. This makes the alternative model immediately applicable to a wide variety of evidence synthesis situations, including studies of prognosis and surrogate outcomes. We examine the performance of the alternative model through analytic assessment, a realistic simulation study, and application to data sets from the literature. Our results show that, unless rho is very close to 1 or -1, the alternative model produces appropriate pooled estimates with little bias that (i) are very similar to those from a fully hierarchical BRMA model where the within-study correlations are known and (ii) have better statistical properties than those from separate URMAs, especially given missing data. The alternative model is also less prone to estimation at parameter space boundaries than the fully hierarchical model and thus may be preferred even when the within-study correlations are known. It also suitably estimates a function of the pooled estimates and their correlation; however, it only provides an approximate indication of the between-study variation. The alternative model greatly facilitates the utilization of correlation in meta-analysis and should allow an increased application of BRMA in practice.     

Variance stabilization and normalization for one-color microarray data using a data-driven multiscale approach

MOTIVATION: Many standard statistical techniques are effective on data that are normally distributed with constant variance. Microarray data typically violate these assumptions since they come from non-Gaussian distributions with a non-trivial mean-variance relationship. Several methods have been proposed that transform microarray data to stabilize variance and draw its distribution towards the Gaussian. Some methods, such as log or generalized log, rely on an underlying model for the data. Others, such as the spread-versus-level plot, do not. We propose an alternative data-driven multiscale approach, called the Data-Driven Haar-Fisz for microarrays (DDHFm) with replicates. DDHFm has the advantage of being 'distribution-free' in the sense that no parametric model for the underlying microarray data is required to be specified or estimated; hence, DDHFm can be applied very generally, not just to microarray data. RESULTS: DDHFm achieves very good variance stabilization of microarray data with replicates and produces transformed intensities that are approximately normally distributed. Simulation studies show that it performs better than other existing methods. Application of DDHFm to real one-color cDNA data validates these results. AVAILABILITY: The R package of the Data-Driven Haar-Fisz transform (DDHFm) for microarrays is available in Bioconductor and CRAN.     

Evaluating the Quality of Evidence from a Network Meta-Analysis

Systematic reviews that collate data about the relative effects of multiple interventions via network meta-analysis are highly informative for decision-making purposes. A network meta-analysis provides two types of findings for a specific outcome: the relative treatment effect for all pairwise comparisons, and a ranking of the treatments. It is important to consider the confidence with which these two types of results can enable clinicians, policy makers and patients to make informed decisions. We propose an approach to determining confidence in the output of a network meta-analysis. Our proposed approach is based on methodology developed by the Grading of Recommendations Assessment, Development and Evaluation (GRADE) Working Group for pairwise meta-analyses. The suggested framework for evaluating a network meta-analysis acknowledges (i) the key role of indirect comparisons (ii) the contributions of each piece of direct evidence to the network meta-analysis estimates of effect size; (iii) the importance of the transitivity assumption to the validity of network meta-analysis; and (iv) the possibility of disagreement between direct evidence and indirect evidence. We apply our proposed strategy to a systematic review comparing topical antibiotics without steroids for chronically discharging ears with underlying eardrum perforations. The proposed framework can be used to determine confidence in the results from a network meta-analysis. Judgements about evidence from a network meta-analysis can be different from those made about evidence from pairwise meta-analyses.     

Inferences on the common mean of several log-normal populations: the generalized variable approach

This paper proposes a novel approach for the confidence interval estimation and hypothesis testing of the common mean of several log-normal populations using the concept of generalized variable. Simulation studies demonstrate that the proposed approach can provide confidence intervals with satisfying coverage probabilities and can perform hypothesis testing with satisfying type-I error control even at small sample sizes. Overall, it is superior to the large sample approach. The proposed method is illustrated using two examples.     

An association between − 866G/A polymorphism in the promoter of UCP2 and obesity: A meta-analysis

− 866G/A polymorphism in the promoter of UCP2 gene has been reported to be associated with obesity, but the results remain inconclusive. To assess the relation of UCP2 − 866G/A polymorphism and obesity susceptibility, a meta-analysis was performed. PubMed, ISI, Wanfang database, VIP and CBM were searched to identify relevant studies up to July 31, 2012. Odds ratios (OR) and 95% confidence interval (95% CI) were pooled using fixed or random effect models. Subgroup analysis was performed by ethnicity (categorized as Asian and European). Heterogeneity and publication bias evaluation were performed to validate the credibility. Meta-regression and the ‘leave one out’ sensitive analysis were used to explore the potential sources of between-study heterogeneity. 14 studies were included in this meta-analysis. After exclusion of articles that deviated from the HWE in controls, and were the key contributors to between-study heterogeneity, the meta-analysis showed a significant association of the A allele with reduced risk of obesity in overall analysis and in European in the dominant, codominant and additional models. In Asian, no significant association was found between the − 866G/A in UCP2 gene and obesity susceptibility. The meta-analysis suggested that UCP2 − 866G/A polymorphism was associated with obesity. The A allele may be an important protective factor for obesity in European, but not in Asian. Further studies are needed to elucidate the relationship.     

Issues of cost and efficiency in the design of reliability studies

Reliability of continuous and dichotomous responses is usually assessed by means of the intraclass correlation coefficient (ICC). We derive the optimal allocation of the number of subjects k and the number of repeated measurements n that minimize the variance of the estimated ICC. Cost constraints are discussed for the case of normally distributed responses. Tables showing optimal choices of k and n are given, along with guidelines for the design of reliability studies in light of our results and those reported by others.     

Analysis of Matched Case–Control Data in Presence of Nonignorable Missing Exposure

Summary.   The present article deals with informative missing (IM) exposure data in matched case–control studies. When the missingness mechanism depends on the unobserved exposure values, modeling the missing data mechanism is inevitable. Therefore, a full likelihood-based approach for handling IM data has been proposed by positing a model for selection probability, and a parametric model for the partially missing exposure variable among the control population along with a disease risk model. We develop an EM algorithm to estimate the model parameters. Three special cases: (a) binary exposure variable, (b) normally distributed exposure variable, and (c) lognormally distributed exposure variable are discussed in detail. The method is illustrated by analyzing a real matched case–control data with missing exposure variable. The performance of the proposed method is evaluated through simulation studies, and the robustness of the proposed method for violation of different types of model assumptions has been considered.     

Interval estimation of the mean difference in the analysis of over‐dispersed count data

This paper focuses on the development and study of the confidence interval procedures for mean difference between two treatments in the analysis of over‐dispersed count data in order to measure the efficacy of the experimental treatment over the standard treatment in clinical trials. In this study, two simple methods are proposed. One is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations (GEEs) approach of Zeger and Liang (1986) and the other is based on an estimator of the variance of a ratio estimator (1977). We also develop three other procedures following the procedures studied by Newcombe (1998) and the procedure studied by Beal (1987). As assessed by Monte Carlo simulations, all the procedures have reasonably well coverage properties. Moreover, the interval procedure based on GEEs outperforms other interval procedures in the sense that it maintains the coverage very close to the nominal coverage level and that it has the shortest interval length, a satisfactory location property, and a very simple form, which can be easily implemented in the applied fields. Illustrative applications in the biological studies for these confidence interval procedures are also presented.     

Mixture generalized linear models for multiple interval mapping of quantitative trait Loci in experimental crosses

Summary .  Quantitative trait loci mapping in experimental organisms is of great scientific and economic importance. There has been a rapid advancement in statistical methods for quantitative trait loci mapping. Various methods for normally distributed traits have been well established. Some of them have also been adapted for other types of traits such as binary, count, and categorical traits. In this article, we consider a unified mixture generalized linear model (GLIM) for multiple interval mapping in experimental crosses. The multiple interval mapping approach was proposed by Kao, Zeng, and Teasdale (1999, Genetics 152, 1203–1216) for normally distributed traits. However, its application to nonnormally distributed traits has been hindered largely by the lack of an efficient computation algorithm and an appropriate mapping procedure. In this article, an effective expectation–maximization algorithm for the computation of the mixture GLIM and an epistasis-effect-adjusted multiple interval mapping procedure is developed. A real data set, Radiata Pine data, is analyzed and the data structure is used in simulation studies to demonstrate the desirable features of the developed method.     

Multiple contrast tests in the presence of heteroscedasticity

This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison-specific degrees of freedom and a correlation matrix depending on sample variances maintains the alpha-level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment.     

The Youden Index and the optimal cut-point corrected for measurement error

Random measurement error can attenuate a biomarker's ability to discriminate between diseased and non-diseased populations. A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1-specificity, the probability of incorrectly classifying health individuals. We present an approach for estimating the Youden index and associated optimal cut-point for a normally distributed biomarker that corrects for normally distributed random measurement error. We also provide confidence intervals for these corrected estimates using the delta method and coverage probability through simulation over a variety of situations. Applying these techniques to the biomarker thiobarbituric acid reaction substance (TBARS), a measure of sub-products of lipid peroxidation that has been proposed as a discriminating measurement for cardiovascular disease, yields a 50% increase in diagnostic effectiveness at the optimal cut-point. This result may lead to biomarkers that were once naively considered ineffective becoming useful diagnostic devices.     

A random effects model for multivariate failure time data from multicenter clinical trials

A random effects model for analyzing multivariate failure time data is proposed. The work is motivated by the need for assessing the mean treatment effect in a multicenter clinical trial study, assuming that the centers are a random sample from an underlying population. An estimating equation for the mean hazard ratio parameter is proposed. The proposed estimator is shown to be consistent and asymptotically normally distributed. A variance estimator, based on large sample theory, is proposed. Simulation results indicate that the proposed estimator performs well in finite samples. The proposed variance estimator effectively corrects the bias of the naive variance estimator, which assumes independence of individuals within a group. The methodology is illustrated with a clinical trial data set from the Studies of Left Ventricular Dysfunction. This shows that the variability of the treatment effect is higher than found by means of simpler models.     

The impact of imputation on meta-analysis of genome-wide association studies

Genotype imputation is often used in the meta-analysis of genome-wide association studies (GWAS), for combining data from different studies and/or genotyping platforms, in order to improve the ability for detecting disease variants with small to moderate effects. However, how genotype imputation affects the performance of the meta-analysis of GWAS is largely unknown. In this study, we investigated the effects of genotype imputation on the performance of meta-analysis through simulations based on empirical data from the Framingham Heart Study. We found that when fix-effects models were used, considerable between-study heterogeneity was detected when causal variants were typed in only some but not all individual studies, resulting in up to ～25% reduction of detection power. For certain situations, the power of the meta-analysis can be even less than that of individual studies. Additional analyses showed that the detection power was slightly improved when between-study heterogeneity was partially controlled through the random-effects model, relative to that of the fixed-effects model. Our study may aid in the planning, data analysis, and interpretation of GWAS meta-analysis results when genotype imputation is necessary.     

Random-effects models for serial observations with binary response

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.