Editing Meta-analysis (section)

==Applications in modern science==
[[File:Integrated Molecular Meta-Analysis of 1,000 Pediatric High-Grade and Diffuse Intrinsic Pontine Glioma - graphical abstract.jpg|thumb|300px|Graphical summary of a meta-analysis of over 1,000 cases of [[diffuse intrinsic pontine glioma]] and other pediatric gliomas, in which information about the [[mutation]]s involved as well as generic outcomes were distilled from the underlying [[primary literature]]]]Modern statistical meta-analysis does more than just combine the effect sizes of a set of studies using a weighted average. It can test if the outcomes of studies show more variation than the variation that is expected because of the sampling of different numbers of research participants. Additionally, study characteristics such as measurement instrument used, population sampled, or aspects of the studies' design can be coded and used to reduce variance of the estimator (see statistical models above). Thus some methodological weaknesses in studies can be corrected statistically. Other uses of meta-analytic methods include the development and validation of clinical prediction models, where meta-analysis may be used to combine individual participant data from different research centers and to assess the model's generalisability,<ref name="Individual participant data IPD m">{{cite journal | vauthors = Debray TP, Riley RD, Rovers MM, Reitsma JB, Moons KG | title = Individual participant data (IPD) meta-analyses of diagnostic and prognostic modeling studies: guidance on their use | journal = PLOS Medicine | volume = 12 | issue = 10 | pages = e1001886 | date = October 2015 | pmid = 26461078 | pmc = 4603958 | doi = 10.1371/journal.pmed.1001886 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Debray TP, Moons KG, Ahmed I, Koffijberg H, Riley RD | title = A framework for developing, implementing, and evaluating clinical prediction models in an individual participant data meta-analysis | journal = Statistics in Medicine | volume = 32 | issue = 18 | pages = 3158–3180 | date = August 2013 | pmid = 23307585 | doi = 10.1002/sim.5732 | s2cid = 25308961 | url = https://ris.utwente.nl/ws/files/16298373/A_framework_for_developing.pdf }}</ref> or even to aggregate existing prediction models.<ref>{{cite journal | vauthors = Debray TP, Koffijberg H, Vergouwe Y, Moons KG, Steyerberg EW | title = Aggregating published prediction models with individual participant data: a comparison of different approaches | journal = Statistics in Medicine | volume = 31 | issue = 23 | pages = 2697–2712 | date = October 2012 | pmid = 22733546 | doi = 10.1002/sim.5412 | s2cid = 39439611 | url = https://ris.utwente.nl/ws/files/16299610/Debray_et_al_2012_Statistics_in_Medicine.pdf }}</ref>

Meta-analysis can be done with [[single-subject design]] as well as group research designs.<ref>{{Cite journal |last=Shadish |first=William R. |date=2014 |title=Analysis and meta-analysis of single-case designs: An introduction |url=https://linkinghub.elsevier.com/retrieve/pii/S0022440513001118 |journal=Journal of School Psychology |language=en |volume=52 |issue=2 |pages=109–122 |doi=10.1016/j.jsp.2013.11.009|pmid=24606971 }}</ref> This is important because much research has been done with [[single-subject research]] designs.<ref>{{Cite journal |last1=Zelinsky |first1=Nicole A. M. |last2=Shadish |first2=William |date=2018-05-19 |title=A demonstration of how to do a meta-analysis that combines single-case designs with between-groups experiments: The effects of choice making on challenging behaviors performed by people with disabilities |url=https://www.tandfonline.com/doi/full/10.3109/17518423.2015.1100690 |journal=Developmental Neurorehabilitation |language=en |volume=21 |issue=4 |pages=266–278 |doi=10.3109/17518423.2015.1100690 |pmid=26809945 |s2cid=20442353 |issn=1751-8423}}</ref> Considerable dispute exists for the most appropriate meta-analytic technique for single subject research.<ref>{{cite journal |vauthors=Van den Noortgate W, Onghena P | year = 2007 | title = Aggregating Single-Case Results | journal = The Behavior Analyst Today | volume = 8 | issue = 2 | pages = 196–209 | url = https://www.questia.com/read/1G1-170115042/the-aggregation-of-single-case-results-using-hierarchical | doi=10.1037/h0100613}}</ref>

Meta-analysis leads to a shift of emphasis from single studies to multiple studies. It emphasizes the practical importance of the effect size instead of the statistical significance of individual studies. This shift in thinking has been termed "meta-analytic thinking". The results of a meta-analysis are often shown in a [[forest plot]].

Results from studies are combined using different approaches. One approach frequently used in meta-analysis in health care research is termed '[[Inverse-variance weighting|inverse variance method]]'. The average [[effect size]] across all studies is computed as a ''weighted mean'', whereby the weights are equal to the inverse variance of each study's effect estimator. Larger studies and studies with less random variation are given greater weight than smaller studies. Other common approaches include the [[Cochran–Mantel–Haenszel statistics|Mantel–Haenszel method]]<ref>{{cite journal | vauthors = Mantel N, Haenszel W | title = Statistical aspects of the analysis of data from retrospective studies of disease | journal = Journal of the National Cancer Institute | volume = 22 | issue = 4 | pages = 719–748 | date = April 1959 | pmid = 13655060 | doi = 10.1093/jnci/22.4.719 | s2cid = 17698270 }}</ref> and the [[Richard Peto|Peto method]].<ref>{{cite book | vauthors = Deeks JJ, Higgins JP, Altman DG | collaboration = Cochrane Statistical Methods Group | chapter = Chapter 10: Analysing data and undertaking meta-analyses: 10.4.2 Peto odds ratio method| chapter-url = https://training.cochrane.org/handbook/current/chapter-10#section-10-4-2 | veditors = Higgins J, Thomas J, Chandler J, Cumpston M, Li T, Page M, Welch V | title = Cochrane Handbook for Systematic Reviews of Interventions | edition = Version 6.2 | date = 2021 | publisher = The Cochrane Collaboration }}</ref>

[[Seed-based d mapping]] (formerly signed differential mapping, SDM) is a statistical technique for meta-analyzing studies on differences in brain activity or structure which used neuroimaging techniques such as fMRI, VBM or PET.

Different high throughput techniques such as [[DNA microarray|microarrays]] have been used to understand [[Gene expression]]. [[MicroRNA]] expression profiles have been used to identify differentially expressed microRNAs in particular cell or tissue type or disease conditions or to check the effect of a treatment. A meta-analysis of such expression profiles was performed to derive novel conclusions and to validate the known findings.<ref>{{cite journal | vauthors = Bargaje R, Hariharan M, Scaria V, Pillai B | title = Consensus miRNA expression profiles derived from interplatform normalization of microarray data | journal = RNA | volume = 16 | issue = 1 | pages = 16–25 | date = January 2010 | pmid = 19948767 | pmc = 2802026 | doi = 10.1261/rna.1688110 }}</ref>

Meta-analysis of whole genome sequencing studies provides an attractive solution to the problem of collecting large sample sizes for discovering rare variants associated with complex phenotypes. Some methods have been developed to enable functionally informed rare variant association meta-analysis in biobank-scale cohorts using efficient approaches for summary statistic storage.<ref>{{cite journal |last1=Li |first1=Xihao |last2=Quick |first2=Corbin |last3=Zhou |first3=Hufeng |last4=Gaynor |first4=Sheila M. |last5=Liu |first5=Yaowu |last6=Chen |first6=Han |last7=Selvaraj |first7=Margaret Sunitha |last8=Sun |first8=Ryan |last9=Dey |first9=Rounak |last10=Arnett |first10=Donna K. |last11=Bielak |first11=Lawrence F. |last12=Bis |first12=Joshua C. |last13=Blangero |first13=John |last14=Boerwinkle |first14=Eric |last15=Bowden |first15=Donald W. |last16=Brody |first16=Jennifer A. |last17=Cade |first17=Brian E. |last18=Correa |first18=Adolfo |last19=Cupples |first19=L. Adrienne |last20=Curran |first20=Joanne E. |last21=de Vries |first21=Paul S. |last22=Duggirala |first22=Ravindranath |last23=Freedman |first23=Barry I. |last24=Göring |first24=Harald H. H. |last25=Guo |first25=Xiuqing |last26=Haessler |first26=Jeffrey |last27=Kalyani |first27=Rita R. |last28=Kooperberg |first28=Charles |last29=Kral |first29=Brian G. |last30=Lange |first30=Leslie A. |last31=Manichaikul |first31=Ani |last32=Martin |first32=Lisa W. |last33=McGarvey |first33=Stephen T. |last34=Mitchell |first34=Braxton D. |last35=Montasser |first35=May E. |last36=Morrison |first36=Alanna C. |last37=Naseri |first37=Take |last38=O’Connell |first38=Jeffrey R. |last39=Palmer |first39=Nicholette D. |last40=Peyser |first40=Patricia A. |last41=Psaty |first41=Bruce M. |last42=Raffield |first42=Laura M. |last43=Redline |first43=Susan |last44=Reiner |first44=Alexander P. |last45=Reupena |first45=Muagututi’a Sefuiva |last46=Rice |first46=Kenneth M. |last47=Rich |first47=Stephen S. |last48=Sitlani |first48=Colleen M. |last49=Smith |first49=Jennifer A. |last50=Taylor |first50=Kent D. |last51=Vasan |first51=Ramachandran S. |last52=Willer |first52=Cristen J. |last53=Wilson |first53=James G. |last54=Yanek |first54=Lisa R. |last55=Zhao |first55=Wei 
|last56=NHLBI Trans-Omics for Precision Medicine (TOPMed) Consortium|last57=TOPMed Lipids Working Group
|last58=Rotter |first58=Jerome I. |last59=Natarajan |first59=Pradeep |last60=Peloso |first60=Gina M. |last61=Li |first61=Zilin |last62=Lin |first62=Xihong |title=Powerful, scalable and resource-efficient meta-analysis of rare variant associations in large whole genome sequencing studies |journal=Nature Genetics |date=January 2023 |volume=55 |issue=1 |pages=154–164 |doi=10.1038/s41588-022-01225-6|pmid=36564505 |pmc=10084891 |s2cid=255084231 }}</ref>

Sweeping meta-analyses can also be used to estimate a network of effects. This allows researchers to examine patterns in the fuller panorama of more accurately estimated results and draw conclusions that consider the broader context (e.g., how personality-intelligence relations vary by trait family).<ref>{{Cite book |last1=Stanek |first1=Kevin C. |url=https://umnlibraries.manifoldapp.org/projects/of-anchors-and-sails |title=Of Anchors & Sails: Personality-ability trait constellations |last2=Ones |first2=Deniz S. |publisher=University of Minnesota Libraries Publishing |year=2023 |location=Minneapolis, Minnesota, United States |pages=Chapters 4–7 |doi=10.24926/9781946135988|isbn=978-1-946135-98-8 |s2cid=265335858 }}</ref>