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At least 19 recordsLinked to original sources
PubMed2002

Issues in the selection of a summary statistic for meta-analysis of clinical trials with binary outcomes.

Meta-analysis of binary data involves the computation of a weighted average of summary statistics calculated for each trial. The selection of the appropriate summary statistic is a subject of debate due to conflicts in the relative importance of mathematical properties and the ability to intuitively interpret results. This paper explores the process of identifying a summary statistic most likely to be consistent across trials when there is variation in control group event rates. Four summary statistics are considered: odds ratios (OR); risk differences (RD) and risk ratios of beneficial (RR(B)); and harmful outcomes (RR(H)). Each summary statistic corresponds to a different pattern of predicted absolute benefit of treatment with variation in baseline risk, the greatest difference in patterns of prediction being between RR(B) and RR(H). Selection of a summary statistic solely based on identification of the best-fitting model by comparing tests of heterogeneity is problematic, principally due to low numbers of trials. It is proposed that choice of a summary statistic should be guided by both empirical evidence and clinically informed debate as to which model is likely to be closest to the expected pattern of treatment benefit across baseline risks. Empirical investigations comparing the four summary statistics on a sample of 551 systematic reviews provide evidence that the RR and OR models are on average more consistent than RD, there being no difference on average between RR and OR. From a second sample of 114 meta-analyses evidence indicates that for interventions aimed at preventing an undesirable event, greatest absolute benefits are observed in trials with the highest baseline event rates, corresponding to the model of constant RR(H). The appropriate selection for a particular meta-analysis may depend on understanding reasons for variation in control group event rates; in some situations uncertainty about the choice of summary statistic will remain.

Anti-Inflammatory Agents, Non-Steroidal↗
PubMed2001

Efficiency comparisons of rank and permutation tests based on summary statistics computed from repeated measures data.

A popular method of using repeated measures data to compare treatment groups in a clinical trial is to summarize each individual's outcomes with a scalar summary statistic, and then to perform a two-group comparison of the resulting statistics using a rank or permutation test. Many different types of summary statistics are used in practice, including discrete and continuous functions of the underlying repeated measures data. When the repeated measures processes of the comparison groups differ by a location shift at each time point, the asymptotic relative efficiency of (continuous) summary statistics that are linear functions of the repeated measures has been determined and used to compare tests in this class. However, little is known about the non-null behaviour of discrete summary statistics, about continuous summary statistics when the groups differ in more complex ways than location shifts or where the summary statistics are not linear functions of the repeated measures. Indeed, even simple distributional structures on the repeated measures variables can lead to complex differences between the distribution of common summary statistics of the comparison groups. The presence of left censoring of the repeated measures, which can arise when these are laboratory markers with lower limits of detection, further complicates the distribution of, and hence the ability to compare, summary statistics. This paper uses recent theoretical results for the non-null behaviour of rank and permutation tests to examine the asymptotic relative efficiencies of several popular summary statistics, both discrete and continuous, under a variety of common settings. We assume a flexible linear growth curve model to describe the repeated measures responses and focus on the types of settings that commonly arise in HIV/AIDS and other diseases.

Acquired Immunodeficiency Syndrome↗
PubMed1994

Stratification of summary statistic tests according to missing data patterns.

Summary statistics, such as slope or area under the time-response curve, reduce the dimensionality of repeated measures data and can thereby simplify the comparison of groups in longitudinal studies. Since summary statistic distributions vary according to the amount, timing, and type of any missingness that occurs, one must choose between analysing the data unconditionally or conditionally on the missingness patterns. This paper uses simulations to compare such unstratified and stratified summary statistic analyses with respect to their size and power under models that allow for both non-informative and informative missingness mechanisms. Of particular interest is the robustness of these methods to violations of the assumptions that one must make if they are to have proper test size. It is found that stratification of the analysis tends to result in an increase of power, and improves the robustness to violations of missing data assumptions.

Computer Simulation↗
PubMed1999

Visit-driven endpoints in randomized HIV/AIDS clinical trials: impact of missing data on treatment difference measured on summary statistics.

In randomized HIV/AIDS clinical trials, CD4 lymphocyte counts and plasma HIV-1 RNA measurements are often used as endpoints. The comparison between treatment groups is mainly based on a summary measure of outcome, so-called summary statistic. Such analyses are often complicated by missing data occurring as drop-outs. For the most currently used summary statistics in these trials, we examined the impact of missing data occurring as drop-outs on test size, in order to help choosing between these statistics. A simulation of missing-data patterns was performed, using HIV-1 plasma RNA measurements as the main endpoint, to compare the effect of three plausible informative patterns, depending on treatment group, and on baseline or current plasma viral load, on eight different summary statistics. Missing data resulted in test sizes over the nominal value for the area under the curve minus baseline, the least-squares slope, the slope estimated with use of a mixed effects linear model, assuming a linear trend over the entire study, the difference between baseline and nadir, and the difference between baseline and week 24. The difference between baseline and week 8 was an acceptable summary with respect to the test size, but did not reflect accurately the durability of the effect of treatment. Two criteria appeared as the best summary statistics: the slope estimated by a mixed effects model, with a change of slope after two weeks of treatment, and to a lesser degree, the area under the curve after carrying forward the last observation.

Acquired Immunodeficiency Syndrome↗
PubMed2006

Comparative phylogeographic summary statistics for testing simultaneous vicariance.

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.

Classification↗
PubMed2005

Likelihoods from summary statistics: recent divergence between species.

We describe an importance-sampling method for approximating likelihoods of population parameters based on multiple summary statistics. In this first application, we address the demographic history of closely related members of the Drosophila pseudoobscura group. We base the maximum-likelihood estimation of the time since speciation and the effective population sizes of the extant and ancestral populations on the pattern of nucleotide variation at DPS2002, a noncoding region tightly linked to a paracentric inversion that strongly contributes to reproductive isolation. Consideration of summary statistics rather than entire nucleotide sequences permits a compact description of the genealogy of the sample. We use importance sampling first to propose a genealogical and mutational history consistent with the observed array of summary statistics and then to correct the likelihood with the exact probability of the history determined from a system of recursions. Analysis of a subset of the data, for which recursive computation of the exact likelihood was feasible, indicated close agreement between the approximate and exact likelihoods. Our results for the complete data set also compare well with those obtained through Metropolis-Hastings sampling of fully resolved genealogies of entire nucleotide sequences.

Animals↗
PubMed1998

Sample size calculations based on slopes and other summary statistics.

Sample size calculations based on two-sample comparisons of slopes have been reported by many. This paper extends such discussions to include summary statistics other than slopes, such as post-baseline means, change scores, and final observations. Specifically, sample size formulas for analyses based on a broad class of summary statistics are presented, with modifications proposed to allow for missing data caused by staggered entry and random dropouts. The formulas developed are used to illustrate how required sample size is affected by summary statistic choice, variance parameters, the type of treatment difference of interest, and the manner in which incomplete observations are used in the analysis. An example based on longitudinal data from the Muscatine Study is presented.

Adolescent↗
PubMed1997

Linearly divergent treatment effects in clinical trials with repeated measures: efficient analysis using summary statistics.

In many randomized clinical trials with repeated measures of a response variable one anticipates a linear divergence over time in the difference between treatments. This paper explores how to make an efficient choice of analysis based on individual patient summary statistics. With the objective of estimating the mean rate of treatment divergence the simplest choice of summary statistic is the regression coefficient of response on time for each subject (SLOPE). The gains in statistical efficiency imposed by adjusting for the observed pre-treatment levels, or even better the estimated intercepts, are clarified. In the process, we develop the optimal linear summary statistic for any repeated measures design with assumed known covariance structure and shape of true mean treatment difference over time. Statistical power considerations are explored and an example from an asthma trial is used to illustrate the main points.

Analysis of Variance↗
PubMed1992

Repeated measures in clinical trials: analysis using mean summary statistics and its implications for design.

This paper explores the use of simple summary statistics for analysing repeated measurements in randomized clinical trials with two treatments. Quite often the data for each patient may be effectively summarized by a pre-treatment mean and a post-treatment mean. Analysis of covariance is the method of choice and its superiority over analysis of post-treatment means or analysis of mean changes is quantified, as regards both reduced variance and avoidance of bias, using a simple model for the covariance structure between time points. Quantitative consideration is also given to practical issues in the design of repeated measures studies: the merits of having more than one pre-treatment measurement are demonstrated, and methods for determining sample sizes in repeated measures designs are provided. Several examples from clinical trials are presented, and broad practical recommendations are made. The examples support the value of the compound symmetry assumption as a realistic simplification in quantitative planning of repeated measures trials. The analysis using summary statistics makes no such assumption. However, allowance in design for alternative non-equal correlation structures can and should be made when necessary.

Analysis of Variance↗
PubMed2003

Exploring the relationship between surrogates and clinical outcomes: analysis of individual patient data vs. meta-regression on group-level summary statistics.

There has been an increasing interest in exploring the relationship between a surrogate and a clinical outcome. Two different statistical approaches have been taken by researchers to quantify the treatment effect on the clinical outcome explained by the surrogate endpoint: 1) analysis based on individual patient data (IPD), and 2) meta-regression based on summary statistics from published literature. An analysis based on IPD models the associations between the surrogate and clinical outcome for patients directly and is able to adjust for patient-level covariates. A meta-regression models the trial-level associations using group-level summary statistics and trial-level covariates. The results from these two approaches can be quite disparate and researchers may reach different conclusions on scientific questions that they wish to answer. We demonstrate that the typical summary statistics, such as group means and event counts, do not provide a set of sufficient statistics for estimating the underlying relationship between the surrogate and clinical outcome for patients. Consequently, the associations derived from meta-regression do not necessarily reflect the causal relationship for patients and should be interpreted with caution. A meta-analysis of antiresorptive agents for osteoporosis serves to illustrate the magnitude of differences between the two approaches.

Humans↗
PubMed2026

A Guide for Exploring Pleiotropic Associations in Genome-Wide Association Studies Using Summary Statistics.

Genome-wide association studies (GWAS) have shown that pleiotropy, whereby a single genetic variant or gene influences multiple traits, is common in complex human diseases. Detecting cross-phenotype associations from GWAS summary statistics remains challenging because of small effect sizes, extensive multiple testing, heterogeneous effects, and possible differences in effect direction across traits. Methods that jointly analyze multiple traits can improve the ability to detect pleiotropic signals while retaining the practical advantages of summary statistic-based analyses. Although a range of statistical approaches has been developed for this purpose, practical guidance on their application, assumptions, and interpretation remains limited. This tutorial reviews several widely used methods for pleiotropy detection from GWAS summary statistics, including ASSET, PLACO, GPA, CPBayes, and GCPBayes, and demonstrates their application using breast and thyroid cancer datasets. We also highlight the importance of accounting for effect heterogeneity, correlation, and biological group structure at the gene and pathway levels in the detection and interpretation of pleiotropic association signals.

Genome-Wide Association Study↗
PubMed2025

Meta-analysis models with group structure for pleiotropy detection at gene and variant level using summary statistics from multiple datasets.

Genome-wide association studies (GWASs) have highlighted the importance of pleiotropy in human diseases, where one gene can impact 2 or more unrelated traits. Examining shared genetic risk factors across multiple diseases can enhance our understanding of these conditions by pinpointing new genes and biological pathways involved. Furthermore, with an increasing wealth of GWAS summary statistics available to the scientific community, leveraging these findings across multiple phenotypes could unveil novel pleiotropic associations. Existing selection methods examine pleiotropic associations one by one at a scale of either the genetic variant or the gene, and thus cannot consider all the genetic information at the same time. To address this limitation, we propose a new approach called MPSG (Meta-analysis model adapted for Pleiotropy Selection with Group structure). This method performs a penalized multivariate meta-analysis method adapted for pleiotropy and takes into account the group structure information nested in the data to select relevant variants and genes (or pathways) from all the genetic information. To do so, we implemented an alternating direction method of multipliers algorithm. We compared the performance of the method with other benchmark meta-analysis approaches such as GCPBayes, PLACO, and ASSET by considering as inputs different kinds of summary statistics. We provide an application of our method to the identification of potential pleiotropic genes between breast and thyroid cancers.

Humans↗
PubMed2026

STABIX: summary-statistic-based GWAS indexing and compression.

MOTIVATION: Genome-wide association studies (GWAS) are widely used to investigate the role of genetics in disease traits, but the resulting file sizes from these studies are large, posing barriers to efficient storage, sharing, and querying. This issue is especially important for biobanks like the UK Biobank that publish GWAS for thousands of traits, increasing the volume of data that must be effectively managed. Current compression and query methods reduce file sizes and allow for quick genomic position-based queries but do not provide utility for quickly finding loci based on their summary statistics. For example, finding all SNVs in a particular p-value range would require decompressing and scanning the whole file. We propose a new tool, STABIX, which introduces summary-statistic-based queries and improves upon the standard bgzip compression and Tabix query tool in both compression ratio and decompression speed. RESULTS: When applied to 10 GWAS files from PanUKBB, STABIX created smaller compressed data and indices than Tabix for all files, where bgzip and tbi files were an average of 1.2 times the size of STABIX compressed files and indexes. In the same 10 files, STABIX per gene decompression was, on average 7× faster than Tabix per gene decompression, and achieved faster per gene decompression times for over 99% of nearly 20,000 genes. AVAILABILITY AND IMPLEMENTATION: Software freely available for download at GitHub: https://github.com/kristen-schneider/stabix/.

Genome-Wide Association Study↗
PubMed2005

Group sequential clinical trials for longitudinal data with analyses using summary statistics.

Longitudinal endpoints are used in clinical trials, and the analysis of the results is often conducted using within-individual summary statistics. When these trials are monitored, interim analyses that include subjects with incomplete follow-up can give incorrect decisions due to bias by non-linearity in the true time trajectory of the treatment effect. Linear mixed-effects models can be used to remove this bias, but there is a lack of software to support both the design and implementation of monitoring plans in this setting. This paper considers a clinical trial in which the measurement time schedule is fixed (at least for pre-trial design), and the scientific question is parameterized by a contrast across these measurement times. This setting assures generalizable inference in the presence of non-linear time trajectories. The distribution of the treatment effect estimate at the interim analyses using the longitudinal outcome measurements is given, and software to calculate the amount of information at each interim analysis is provided. The interim information specifies the analysis timing thereby allowing standard group sequential design software packages to be used for trials with longitudinal outcomes. The practical issues with implementation of these designs are described; in particular, methods are presented for consistent estimation of treatment effects at the interim analyses when outcomes are not measured according to the pre-trial schedule. Splus/R functions implementing this inference using appropriate linear mixed-effects models are provided. These designs are illustrated using a clinical trial of statin treatment for the symptoms of peripheral arterial disease.

Humans↗
PubMed2006

Estimating recombination rates from single-nucleotide polymorphisms using summary statistics.

We describe a novel method for jointly estimating crossing-over and gene-conversion rates from population genetic data using summary statistics. The performance of our method was tested on simulated data sets and compared with the composite-likelihood method of R. R. Hudson. For several realistic parameter values, the new method performed similarly to the composite-likelihood approach for estimating crossing-over rates and better when estimating gene-conversion rates. We used our method to analyze a human data set recently genotyped by Perlegen Sciences.

Computer Simulation↗
PubMed2026

Shared genetic architecture of smoking dependence and Crohn's disease: A cross-trait analysis of GWAS summary statistics.

INTRODUCTION: Smoking dependence (SD) and Crohn's disease (CD) are epidemiologically associated, but whether this relationship reflects shared genetic susceptibility remains unclear. METHODS: We conducted a cross-trait genetic analysis of SD and CD using publicly available genome-wide association study (GWAS) summary statistics from European-ancestry populations. Genome-wide genetic correlation was estimated using linkage disequilibrium score regression (LDSC) and high-definition likelihood (HDL). Pleiotropic variants were identified using PLACO and mapped to genomic loci using FUMA. Regional signal sharing was assessed by Bayesian colocalization. Functional analyses included stratified LDSC, Multi-marker Analysis of GenoMic Annotation (MAGMA), GTEx tissue analysis, and Metascape. Expression-linked candidate genes were prioritized using expression quantitative trait locus (eQTL)-based summary-data-based Mendelian randomization (SMR) with heterogeneity in dependent instruments (HEIDI) testing. Genetically informed spatial mapping of cells for complex traits (gsMap) was used for spatial mapping. RESULTS: SD and CD showed positive genetic correlation by LDSC (rg=0.2090, p=0.0008) and HDL (rg=0.3817, p=0.00106). PLACO identified 81 genome-wide significant pleiotropic SNPs, which were mapped by FUMA to three loci at 1p31.3, 5p13.1, and 12q12, represented by rs11209031, rs1395152, and rs17467116, respectively. MAGMA identified 22 FDR-significant genes, four of which remained Bonferroni significant: LRRK2, TNFRSF6B, ZGPAT, and RP4-583P15.15. Cross-trait tissue analysis showed significant enrichment of the shared genetic signal in whole blood and small intestine, while gene-set analysis highlighted inflammatory response (pbon=1.86×10-5) and T-helper 17 cell differentiation (pbon=7.37×10-4). SMR/HEIDI analysis further prioritized RPS6KB1 as a shared expression-linked candidate. Spatial mapping revealed a prominent signal in the embryonic gastrointestinal tract and gene-specific regional patterns involving LRRK2 and SLC2A13 in the adult mouse brain. CONCLUSIONS: SD and CD showed measurable shared genetic susceptibility, with convergent evidence from pleiotropic loci, immune-inflammatory pathway enrichment, tissue-level associations, and spatial transcriptomic mapping.

Crohn's disease↗
PubMed1997

Effects of beta-adrenoceptor agonists and antagonists on heart-rate variability in normal subjects assessed using summary statistics and nonlinear procedures.

The influence of celiprolol (beta1- and beta2-adrenoceptor partial agonist), propranolol (beta1- and beta2-adrenoceptor antagonist), and atenolol (beta1-adrenoceptor antagonist) on heart-rate variability (HRV) was assessed from Holter records in 12 normal volunteers. A combination of summary statistics and nonlinear procedures was used to assess HRV and autonomic balance. Under double-blind and randomised conditions (Latin-square design), subjects received placebo, celiprolol (200 and 800 mg), propranolol (160 mg), atenolol (50 mg), and combinations of these agents. Single oral doses of medication (at weekly intervals) were administered at 22:30 h with sleeping heart rates (HRs) recorded overnight. Compared with placebo, celiprolol (200 and 800 mg) increased the sleeping HR, the HR effect of celiprolol was different from the bradycardia after propranolol, 160 mg, and atenolol, 50 mg. Dose-response effects on HR with celiprolol were evident in the presence of atenolol, unlike those with propranolol that abolished the HR increase between celiprolol, 200 mg and 800 mg. These data were consistent with beta1-selective adrenoceptor agonism with 200 mg but agonism at both the beta1- and beta2-adrenoceptor with celiprolol, 800 mg. The action of the drugs on short-term HRV indices (rMSSD and pNN50) closely followed their effects on HR. The longer-term HRV indices (global SD, SDANN) were reduced by celiprolol but increased by propranolol and atenolol. At a fixed HR, the data dispersion (SDNN5) was higher with propranolol compared with celiprolol; however, the dispersion was not merely an HR-dependent phenomenon. A novel nonlinear approach (quadrant analysis) revealed the sequencing of cardiac accelerations and decelerations after the high correlation between adjacent intervals had been removed. Celiprolol increased the frequency of consecutive cardiac accelerations; the duration between and variance of these beat-to-beat differences shortened after celiprolol but lengthened with increased variance after propranolol and atenolol. These results demonstrated reduced HRV indices and a shift toward sympathetic dominance after the beta-adrenoceptor agonist celiprolol contrasting with increased HRV indices and parasympathetic dominance after the beta-adrenoceptor antagonists propranolol and atenolol. The implications of these findings for the treatment of patients with cardiovascular disease warrant further study.

Adrenergic beta-Agonists↗