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| {{multiple issues|
| | "The Amazing Spider-Man 2," а sequel about the web-slinging supеrhero, snared $92 million in U.S.<br>and Canadian ticket sales over the weeқend, taking the tօp spot on movie box offіce charts at the start of Hollywood's lսcrative summer blοckbuster season.<br>The bіg-budget, effects-filled movie starring Аndrew Garfield іs expected to rank as one of the yeаr'ѕ highest-grossing films. With international sales, it ɦas rung up nearly $370 million around thе gloƄe through Sunday, distributor Sony Cоrp said.<br><br>"The Other Woman," a comedy about three women out fߋr revenge on a cheating husband, finished a distant second on domestic charts with $14.2 mіllion, acсording to еstimates from tгacking firm Rentrak.<br>"Captain America: The Winter Soldier," another ѕuperherо sequel and prеvious bօx office champ, landed in the No. 4 slot with $7.8 milliօn from Frіday thгough Sunday, behind "Heaven Is for Real," a faith-based drama and Sony гelease which grabbed third place with $8.7 million for a $65 million box office total in just its thiгd week of release.<br><br>The performance оf "Spider-Man 2" could not quіte match the strong domestic opening foг "Captain America" in April, when the Marvel Studios film took in $95 million over its first thгee days. Ahead of the weekend, boҳ office [http://www.Dict.cc/englisch-deutsch/forecasters+projected.html forecasters projected] "Spider-Man" would colleϲt $85 million to $95 million.<br><br>In the "Spider-Man" seգuel, Ԍarfield returns аs the masked hero who swings through the streеts and skyscraperѕ of New York, battling new villains incluԀing thе formidablе Electro played by Jamie Foxx. Garfield's real-life girlfriend, Emma Stone, portraʏs Gwen Stacy, the on-screen love interest of Spidеy alter ego Peter Parker.<br><br>"This was a really fantastic result," saiɗ Rory Bruer, president of wоrldwіde distribution for Sony Picturеs Entertainment, adding that the opening bodes well for Sօny "not only meeting our goals, but exceeding them."<br>Tɦe film is Sony's bigɡest bet this yeaг, with a production cost of гoughly $200 millіon, according to movie website IMDB. Last summer, the studiο suffered from two major bombs, thrillers "After Earth" and "White House Down."<br><br>"Spider-Man" leads a parade of action-packed superhеro and monster movies that will reach theaters bу August. They include "Godzilla" on May 16, "X-Men: Days of Future Past" on May 23, and "Transformers: Age of Extinction" on June 27. Hollywοod earns about 40 percent of ticket sales from [http://theamazingspider-man2movie.blogspot.com/ watch the amazing spider-man 2 Full movie] first weekend in May thrߋugh Labor Day in September.<br><br>Bruer said Sony wаs well-poѕitiօned going forwаrd, saying "It's nice to be going into next weekend with no outrageous competition. That will give us a chance to build."<br><br>"The Amazing Spider-Man," which Sony released in 2012, took in mοre than $750 million worldwide according to the website boxofficemojo, and Bruer said the studio hopеd to equal or exceed thɑt total.<br>"Captain America," starring Chris Evans as the patriotic ѕuƿerhero, ցot a head start on the summer releases and generated blockbuster sales. Through Sunday, the film haԁ earned $680 million globally, distriƄսtor Walt Diѕney Co saiԁ.<br><br>"The Other Woman," in its second week of release, brought its domеstic total to $47 milliоn. The movie stars [http://search.huffingtonpost.com/search?q=Cameron&s_it=header_form_v1 Cameron] Diaz and Kɑte Upton as women who are dating the same married man. Leslie Mann plɑys his wife.<br>Roundіng out the top five, аnimated seգuel "Rio 2," about a family of rare Brazilian birds, collected $7.6 million to bring its box office total to $106 million.<br>"The Other Woman" and "Rio 2" were released by 20th Century Fox, a unit of Twenty-First Century Fox. (Reporting by Lisa Richwine and Chris Miϲhaud; Editing by Sophie Hares) |
| {{COI|date=July 2011}}
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| {{Neologism|date=October 2011}}
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| }}
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| In [[statistics]], the '''strictly standardized mean difference (SSMD)''' is a measure of [[effect size]]. SSMD is the [[mean]] divided by the [[standard deviation]] of a difference between two random values each from one of two groups. SSMD was initially proposed for quality control
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| <ref name=ZhangGenomics2007>{{cite journal |author=Zhang XHD
| |
| |title=A pair of new statistical parameters for quality control in RNA interference [[high-throughput screening]] assays
| |
| |journal=Genomics |volume=89 |issue= 4|pages=552–61
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| |year=2007 |month= |pmid= 17276655|doi=10.1016/j.ygeno.2006.12.014 |url=}}</ref>
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| and hit selection
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| <ref name=ZhangJBS2007>{{cite journal |author=Zhang XHD
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| |title=A new method with flexible and balanced control of false negatives and false positives for hit selection in RNA interference [[high-throughput screening]] assays
| |
| |journal=Journal of Biomolecular Screening |volume=12 |issue= 5|pages=645–55
| |
| |year=2007 |month= |pmid= 17517904|doi=10.1177/1087057107300645 |url=}}</ref>
| |
| in high-throughput screening (HTS) and has become a statistical parameter measuring effect sizes for the comparison of any two groups with random values.
| |
| .<ref name=ZhangSBR2010>{{cite journal |author=Zhang XHD | |
| |title= Strictly standardized mean difference, standardized mean difference and classical t-test for the comparison of two groups
| |
| |journal= Statistics in Biopharmaceutical Research |volume=2 |issue= 2|pages=292–99
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| |year=2010 |month= |pmid= |doi=10.1198/sbr.2009.0074 |url=}}</ref>
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| | |
| ==Background==
| |
| In high-throughput screens, quality control (QC) is critical. An important QC characteristic in an HTS [[assay]] is how much the positive controls, test [[Chemical compound|compound]]s, and negative controls differ from one another in the [[assay]]. This QC characteristic can be evaluated using the comparison of two well types in HTS [[assay]]s. Signal-to-noise ratio (S/N), signal-to-background ratio (S/B), and [[Z-factor]] have been adopted to evaluate the quality of HTS [[assay]]s through the comparison of two investigated types of wells. However, S/B does not take into account any information on variability; and S/N can capture the variability only in one group and hence cannot assess the quality of [[assay]] when the two groups have different variabilities.<ref name="ZhangGenomics2007"/>
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| Zhang JH et al.<ref name=ZhangJHetal1999>{{cite journal |author=Zhang JH, Chung TDY, Oldenburg KR
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| |title=A simple statistical parameter for use in evaluation and validation of high throughput screening assays
| |
| |journal=Journal of Biomolecular Screening |volume=4 |issue= 2|pages=67–73
| |
| |year=1999 |month= |pmid= 10838414|doi=10.1177/108705719900400206 |url=}}</ref> proposed [[Z-factor]]. The advantage of [[Z-factor]] over S/N and S/B is that it takes into account the variabilities in both compared groups. As a result, [[Z-factor]] has been broadly used as a QC metric in HTS assays. {{Citation needed|date=December 2011}} The absolute sign in [[Z-factor]] makes it inconvenient to derive its statistical inference mathematically.
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| | |
| To derive a better interpretable parameter for measuring the differentiation between two groups, Zhang XHD<ref name="ZhangGenomics2007"/>
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| proposed SSMD to evaluate the differentiation between a positive control and a negative control in HTS assays. SSMD has a probabilistic basis due to its strong link with d<sup>+</sup>-probability (i.e., the probability that the difference between two groups is positive).<ref name="ZhangJBS2007"/> To some extent, the d<sup>+</sup>-probability is equivalent to the well-established probabilistic index P(''X'' > ''Y'') which has been studied and applied in many areas.<ref name=Owen1964>{{cite journal |author=Owen DB, Graswell KJ, Hanson DL
| |
| |title=Nonparametric upper confidence bounds for P(Y < X) and confidence limits for P(''Y'' < ''X'') when ''X'' and ''Y'' are normal
| |
| |journal=Journal of the American Statistical Association |volume=59 |issue= |pages=906–24
| |
| |year=1964 |month= |pmid= |doi= |url=}}</ref>
| |
| <ref name=Church1970>{{cite journal |author=Church JD, Harris B
| |
| |title=The estimation of reliability from stress-strength relationships
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| |journal=Technometrics |volume=12 |issue= |pages=49–54
| |
| |year=1970 |month= |pmid= |doi= 10.1080/00401706.1970.10488633|url=}}</ref>
| |
| <ref name=Downton1973>{{cite journal |author=Downton F
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| |title=The estimation of Pr(Y < X) in normal case
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| |journal=Technometrics |volume=15 |issue= |pages=551–8
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| |year=1973 |month= |pmid= |doi= |url=}}</ref>
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| <ref name=Reiser1986>{{cite journal |author=Reiser B, Guttman I
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| |title=Statistical inference for of Pr(Y-less-thaqn-X) - normal case
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| |journal=Technometrics |volume=28 |issue= |pages=253–7
| |
| |year=1986 |month= |pmid= |doi= |url=}}</ref>
| |
| <ref name=Acion2006>{{cite journal |author=Acion L, Peterson JJ, Temple S, Arndt S
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| |title=Probabilistic index: an intuitive non-parametric approach to measuring the size of treatment effects
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| |journal=Statistics in Medicine |volume=25 |issue= 4|pages=591–602
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| |year=2006 |month= |pmid= 16143965|doi= 10.1002/sim.2256 |url=}}</ref> Supported on its probabilistic basis, SSMD has been used for both quality control and [[hit selection]] in high-throughput screening.<ref name="ZhangGenomics2007"/><ref name="ZhangJBS2007"/>
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| <ref name=ZhangJBS2008>{{cite journal |author=Zhang XHD
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| |title= Novel analytic criteria and effective plate designs for quality control in genome-wide RNAi screens
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| |journal=Journal of Biomolecular Screening |volume=13 |issue= 5|pages= 363–77
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| |year=2008 |month= |pmid= 18567841|doi= 10.1177/1087057108317062 |url=}}</ref>
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| <ref name=ZhangetalJBS2008>{{cite journal |author=Zhang XHD, Espeseth AS, Johnson E, Chin J, Gates A, Mitnaul L, Marine SD, Tian J, Stec EM, Kunapuli P, Holder DJ, Heyse JF, Stulovici B, Ferrer M
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| |title= Integrating experimental and analytic approaches to improve data quality in genome-wide RNAi screens
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| |journal=Journal of Biomolecular Screening |volume=13 |issue= 5|pages= 378–89
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| |year=2008 |month= |pmid= 18480473|doi= 10.1177/1087057108317145 |url=}}</ref>
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| <ref name=ZhangetalJBS2007>{{cite journal |author=Zhang XHD, Ferrer M, Espeseth AS, Marine SD, Stec EM, Crackower MA, Holder DJ, Heyse JF, Strulovici B | |
| |title=The use of strictly standardized mean difference for hit selection in primary RNA interference high-throughput screening experiments
| |
| |journal=Journal of Biomolecular Screening |volume=12 |issue= 4|pages=645–55
| |
| |year=2007 |month= |pmid= |doi=10.1177/1087057107300646 |url=}}</ref>
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| <ref name=Quon2009>{{cite journal |author=Quon K, Kassner PD
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| |title=RNA interference screening for the discovery of oncology targets
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| |journal=Expert Opinion on Therapeutic Targets |volume=13 |issue= 9|pages=1027–35
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| |year=2009 |month= |pmid= 19650760|doi=10.1517/14728220903179338 |url=}}</ref>
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| <ref name=ZhangJBS2010>{{cite journal |author=Zhang XHD
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| |title= An effective method controlling false discoveries and false non-discoveries in genome-scale RNAi screens
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| |journal=Journal of Biomolecular Screening |volume=15 |issue= 9|pages= 1116–22
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| |year=2010 |month= |pmid= 20855561|doi= 10.1177/1087057110381783 |url=}}</ref>
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| <ref name=ZhangetalJBS2010>{{cite journal |author=Zhang XHD, Lacson R, Yang R, Marine SD, McCampbell, Toolan DM, Hare TR, Kajdas J, Berger JP, Holder DJ, Heyse JF, Ferrer M
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| |title= The use of SSMD-based false discovery and false non-discovery rates in genome-scale RNAi screens
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| |journal=Journal of Biomolecular Screening |volume=15 |issue= 9|pages= 1123–31
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| |year=2010 |month= |pmid= 20852024|doi=10.1177/1087057110381919 |url=}}</ref>
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| <ref name=ZhangetalJBS2009>{{cite journal |author=Zhang XHD, Marine SD, Ferrer M
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| |title= Error rates and power in genome-scale RNAi screens
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| |journal=Journal of Biomolecular Screening |volume=14 |issue= 3|pages= 230–38
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| |year=2009 |month= |pmid= |doi=10.1177/1087057109331475 |url=}}</ref>
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| <ref name=BirminghamNaturemethods2009>{{cite journal |author=Birmingham A, Selfors LM, Forster T, Wrobel D, Kennedy CJ, Shanks E, Santoyo-Lopez J, Dunican DJ, Long A, Kelleher D, Smith Q, Beijersbergen RL, Ghazal P, Shamu CE
| |
| |title= Statistical methods for analysis of high-throughput RNA interference screens
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| |journal=Nature Methods |volume=6 |issue= 8|pages=569–75
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| |year=2009 |month= |pmid= 19644458|doi=10.1038/nmeth.1351 |url= |pmc=2789971}}</ref>
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| <ref name=Klinghoffer2010>{{cite journal | |
| |author=Klinghoffer RA, Frazier J, Annis J, Berndt JD, Roberts BS, Arthur WT, Lacson R, Zhang XHD, Ferrer M, Moon RT, Cleary MA
| |
| |title= A lentivirus-mediated genetic screen identifies dihydrofolate reductase (DHFR) as a modulator of beta-catenin/GSK3 signaling
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| |journal=PLoS ONE |volume=4 |issue= 9|pages= e6892
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| |year=2010 |month= |pmid= 19727391|doi=10.1371/journal.pone.0006892 |url=
| |
| |editor1-last=Bereswill
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| |editor1-first=Stefan
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| |pmc=2731218}}</ref>
| |
| <ref name=Malo2010>{{cite journal |author=Malo N, Hanley JA, Carlile G, Liu J, Pelletier J, Thomas D, Nadon R
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| |title=Experimental design and statistical methods for improved hit detection in high-throughput screening
| |
| |journal=Journal of Biomolecular Screening |volume=15 |issue= 8|pages=990–1000
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| |year=2010 |month= |pmid= 20817887|doi=10.1177/1087057110377497 |url=}}</ref>
| |
| <ref name=ZhangBook2011>{{cite book
| |
| |author= Zhang XHD
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| |year=2011
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| |title= Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research
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| |publisher =Cambridge University Press
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| |url=
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| |isbn=978-0-521-73444-8}}</ref>
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| <ref name=Zhou2008>{{cite journal |author=Zhou HL, Xu M, Huang Q, Gates AT, Zhang XD, Castle JC, Stec E, Ferrer M, Strulovici B, Hazuda DJ, Espeseth AS
| |
| |title= Genome-scale RNAi screen for host factors required for HIV replication
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| |journal=Cell Host & Microbe |volume=4 |issue= 5|pages=495–504
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| |year=2008 |month= |pmid= |doi=10.1016/j.chom.2008.10.004 |url=}}</ref>
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| ==Concept==
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| ===Statistical parameter===
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| As a statistical parameter, SSMD (denoted as <math>\beta</math>) is defined as the ratio of [[mean]] to [[standard deviation]] of the difference of two random values respectively from two groups. Assume that one group with random values has [[mean]] <math>\mu_1</math> and [[variance]] <math>\sigma_1^2</math> and another group has [[mean]] <math>\mu_2</math> and [[variance]] <math>\sigma_2^2</math>. The [[covariance]] between the two groups is <math>\sigma_{12}.</math> Then, the SSMD for the comparison of these two groups is defined as<ref name="ZhangGenomics2007"/>
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| :<math>\beta = \frac{\mu_1 - \mu_2}{\sqrt{\sigma_1^2 + \sigma_2^2 - 2\sigma_{12} }}.</math>
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| If the two groups are independent,
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| :<math>\beta = \frac{\mu_1 - \mu_2}{\sqrt{\sigma_1^2 + \sigma_2^2 }}.</math>
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| If the two independent groups have equal [[variance]]s <math>\sigma^2</math>,
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| :<math>\beta = \frac{\mu_1 - \mu_2}{\sqrt{2}\sigma}.</math>
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| In the situation where the two groups are correlated, a commonly used strategy to avoid the calculation of <math>\sigma_{12}</math> is first to obtain paired observations from the two groups and then to estimate SSMD based on the paired observations. Based on a paired difference <math>D</math> with population [[mean]] <math>\mu_D</math> and <math>\sigma_D^2</math>, SSMD is
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| :<math>\beta = \frac{\mu_D}{\sigma_D}.</math>
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| ===Statistical estimation===
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| In the situation where the two groups are independent, Zhang XHD
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| <ref name="ZhangGenomics2007"/>
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| derived the maximum-likelihood estimate (MLE) and method-of-moment (MM) estimate of SSMD. Assume that groups 1 and 2 have sample [[mean]] <math>\bar{X}_1, \bar{X}_2</math>, and sample [[variance]]s <math>s_1^2, s_2^2</math>. The MM estimate of SSMD is then<ref name="ZhangGenomics2007"/>
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| :<math>\hat{\beta} = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{s_1^2+s_2^2}}.</math>
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| When the two groups have normal distributions with equal [[variance]],
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| the uniformly minimal variance unbiased estimate
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| (UMVUE) of SSMD is,<ref name="ZhangJBS2008"/>
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| :<math>\hat{\beta} = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{2} {K} ((n_1-1) s_1^2 + (n_2-1) s_2^2)}},</math>
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| where <math>n_1, n_2</math> are the sample sizes in the two groups and
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| <math>K \approx n_1 + n_2 - 3.48 </math>.<ref name="ZhangSBR2010"/>
| |
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| In the situation where the two groups are correlated, based on a paired difference with a sample size <math>n</math>, sample [[mean]] <math>\bar{D}</math> and sample [[variance]] <math>s_D^2</math>, the MM estimate of SSMD is
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| :<math>\hat{\beta} = \frac{\bar{D}}{s_D}. </math>
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| The UMVUE estimate of SSMD is
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| <ref name=ZhangBMCrn2008>{{cite journal |author=Zhang XHD
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| |title= Genome-wide screens for effective siRNAs through assessing the size of siRNA effects
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| |journal=BMC Research Notes |volume=1|pages=33
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| |year=2010 |month= |pmid= 18710486|doi=10.1186/1756-0500-1-33 |url= |pmc=2526086}}</ref>
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| :<math>\hat{\beta} = \frac{\Gamma(\frac{n-1}{2})}{\Gamma(\frac{n-2}{2})} \sqrt{\frac{2}{n-1}} \frac{\bar{D}}{s_D}. </math>
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| SSMD looks similar to t-statistic and Cohen's d, but they are different with one another as illustrated in.<ref name="ZhangSBR2010"/>
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| ==Application in high-throughput screening assays==
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| SSMD is the ratio of [[mean]] to the [[standard deviation]] of the difference between two groups. When the data is preprocessed using log-transformation as we normally do in HTS experiments, SSMD is the [[mean]] of log fold change divided by the [[standard deviation]] of log fold change with respect to a negative reference. In other words, SSMD is the average fold change (on the log scale) penalized by the variability of fold change (on the log scale)
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| <ref name=ZhangJBS2011>{{cite journal |author=Zhang XHD
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| |title=Illustration of SSMD, z Score, SSMD*, z* Score, and t Statistic for Hit Selection in RNAi High-Throughput Screens
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| |journal=Journal of Biomolecular Screening |volume= 16|issue= 7|pages= 775–85
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| |year=2011 |month= |pmid= 21515799|doi=10.1177/1087057111405851 |url=}}</ref>
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| . For quality control, one index for the quality of an HTS assay is the magnitude of difference between a positive control and a negative reference in an [[assay]] plate. For hit selection, the size of effects of a [[Chemical compound|compound]] (i.e., a [[small molecule]] or an [[siRNA]]) is represented by the magnitude of difference between the [[Chemical compound|compound]] and a negative reference. SSMD directly measures the magnitude of difference between two groups. Therefore, SSMD can be used for both quality control and hit selection in HTS experiments.
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| ===Quality control===
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| The number of wells for the positive and negative controls in a plate in the 384-well or 1536-well platform is normally designed to be reasonably large
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| .<ref name=ZhangBioinformatics2009>{{cite journal |author=Zhang XHD, Heyse JF
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| |title= Determination of sample size in genome-scale RNAi screens
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| |journal= Bioinformatics |volume=25 |issue= 7|pages=841–44
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| |year=2009 |month= |pmid= |doi=10.1093/bioinformatics/btp082 |url=}}</ref>
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| Assume that the positive and negative controls in a plate have sample [[mean]] <math>\bar{X}_P, \bar{X}_N</math>, sample [[variance]]s <math>s_P^2, s_N^2</math>, and sample sizes <math>n_P, n_N</math>. Usually, the assumption that the controls have equal variance in a plate holds. In such a case, The SSMD for assessing quality in that plate is estimated as
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| <ref name="ZhangJBS2008"/>
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| :<math>\hat{\beta} = \frac{\bar{X}_P - \bar{X}_N}{\sqrt{\frac{2} {K} ((n_P-1) s_P^2 + (n_N-1) s_N^2)}},</math>
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| where <math>K \approx n_P + n_N - 3.48 </math>.
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| When the assumption of equal variance does not hold, the SSMD for assessing quality in that plate is estimated as
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| <ref name="ZhangGenomics2007"/>
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| :<math>\hat{\beta} = \frac{\bar{X}_P - \bar{X}_N}{\sqrt{s_P^2+s_N^2}}.</math>
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| If there are clearly [[outlier]]s in the controls, the SSMD can be estimated as
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| <ref name="ZhangJBS2011"/>
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| :<math>\hat{\beta} = \frac{\tilde{X}_P - \tilde{X}_N}{1.4826 \sqrt{\tilde{s}_P^2 + \tilde{s}_N^2}},</math>
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| where <math>\tilde{X}_P, \tilde{X}_N, \tilde{s}_P, \tilde{s}_N</math> are the [[median]]s and [[median absolute deviation]]s in the positive and negative controls, respectively.
| |
| | |
| The [[Z-factor]] based QC criterion is popularly used in HTS assays. However, it has been demonstrated that this QC criterion is most suitable for an [[assay]] with very or extremely strong positive controls.<ref name="ZhangJBS2008"/> In an [[RNAi]] HTS assay, a strong or moderate positive control is usually more instructive than a very or extremely strong positive control because the effectiveness of this control is more similar to the hits of interest. In addition, the positive controls in the two HTS experiments theoretically have different sizes of effects. Consequently, the QC thresholds for the moderate control should be different from those for the strong control in these two experiments. Furthermore, it is common that two or more positive controls are adopted in a single experiment.<ref name="ZhangetalJBS2008"/> Applying the same [[Z-factor]]-based QC criteria to both controls leads to inconsistent results as illustrated in the literatures.<ref name="ZhangJBS2008"/><ref name="ZhangetalJBS2008"/>
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| The SSMD-based QC criteria listed in the following table<ref name="ZhangBook2011"/> take into account the effect size of a positive control in an HTS assay where the positive control (such as an inhibition control) theoretically has values less than the negative reference.
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| | |
| {| class="wikitable"
| |
| |-
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| ! Quality Type !! A: Moderate Control !! B: Strong Control !! C: Very Strong Control !! D: Extremely Strong Control
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| |-
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| |Excellent || <math>\beta \le -2</math> || <math>\beta \le -3</math> || <math>\beta \le -5</math> || <math>\beta \le -7</math>
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| |-
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| |Good || <math>-2 < \beta \le -1</math> || <math>-3 < \beta \le -2</math> || <math>-5 < \beta \le -3</math> || <math>-7 < \beta \le -5</math>
| |
| |-
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| |Inferior || <math>-1 < \beta \le -0.5</math> || <math>-2 < \beta \le -1</math> || <math>-3 < \beta \le -2</math> || <math>-5 < \beta \le -3</math>
| |
| |-
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| |Poor || <math> \beta > -0.5</math> || <math>\beta > -1</math> || <math>\beta > -2 </math> || <math>\beta > -3</math>
| |
| |}
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| In application, if the effect size of a positive control is known biologically, adopt the corresponding criterion based on this table. Otherwise, the following strategy should help to determine which QC criterion should be applied: (i) in many small molecule HTS assay with one positive control, usually criterion D (and occasionally criterion C) should be adopted because this control usually has very or extremely strong effects; (ii) for RNAi HTS assays in which cell viability is the measured response, criterion D should be adopted for the controls without cells (namely, the wells with no cells added) or background controls; (iii) in a viral [[assay]] in which the amount of viruses in host cells is the interest, criterion C is usually used, and criterion D is occasionally used for the positive control consisting of siRNA from the virus.<ref name="ZhangBook2011"/>
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| | |
| Similar SSMD-based QC criteria can be constructed for an HTS assay where the positive control (such as an activation control) theoretically has values greater than the negative reference. More details about how to apply SSMD-based QC criteria in HTS experiments can be found in a book.<ref name="ZhangBook2011"/>
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| ===Hit selection===
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| In an HTS assay, one primary goal is to select [[Chemical compound|compound]]s with a desired size of inhibition or activation effect. The size of the compound effect is represented by the magnitude of difference between a test [[Chemical compound|compound]] and a negative reference group with no specific inhibition/activation effects. A [[Chemical compound|compound]] with a desired size of effects in an HTS screen is called a hit. The process of selecting hits is called hit selection. There are two main strategies of selecting hits with large effects.<ref name="ZhangBook2011"/> One is to use certain metric(s) to rank and/or classify the [[Chemical compound|compound]]s by their effects and then to select the largest number of potent [[Chemical compound|compound]]s that is practical for validation [[assay]]s.<ref name="BirminghamNaturemethods2009"/>
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| <ref name="Malo2010"/><ref name="ZhangBMCrn2008"/> | |
| The other strategy is to test whether a [[Chemical compound|compound]] has effects strong enough to reach a pre-set level. In this strategy, false-negative rates (FNRs) and/or false-positive rates (FPRs) must be controlled.<ref name="ZhangJBS2010"/> | |
| <ref name="ZhangetalJBS2010"/>
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| <ref name="ZhangetalJBS2009"/><ref name=MaloNaturebiotech2006>{{cite journal |author=Malo N, Hanley JA, Cerquozzi S, Pelletier J, Nadon R
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| |title= Statistical practice in high-throughput screening data analysis
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| |journal=Nature Biotechnology |volume=24 |issue= 2|pages=167–75
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| |year=2006 |month= |pmid= 16465162|doi=10.1038/nbt1186 |url=}}</ref>
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| <ref name=ZhangNAR2009>{{cite journal |author= Zhang XHD, Kuan PF, Ferrer M, Shu X, Liu YC, Gates AT, Kunapuli P, Stec EM, Xu M, Marine SD, Holder DJ, Stulovici B, Heyse JF, Espeseth AS
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| |title= Hit selection with false discovery rate control in genome-scale RNAi screens
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| |journal= Nucleic Acids Research |volume=36 |issue= 14|pages= 4667–79
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| |year=2009 |month= |pmid= 18628291|doi=10.1093/nar/gkn435 |url= |pmc= 2504311}}</ref>
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| SSMD can not only rank the size of effects but also classify effects as shown in the following table based on the population value (<math>\beta </math>) of SSMD.<ref name="ZhangBook2011"/>
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| <ref name=ZhangPharmacogenomics2009>{{cite journal |author=Zhang XHD
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| |title= A method for effectively comparing gene effects in multiple conditions in RNAi and expression-profiling research
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| |journal=Pharmacogenomics |volume=10 |issue= 3|pages=345–58
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| |year=2009 |month= |pmid= 20397965|doi=10.2217/14622416.10.3.345 |url=}}</ref>
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| {| class="wikitable"
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| |-
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| ! Effect subtype !! Thresholds for negative SSMD !! Thresholds for positive SSMD
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| |-
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| |Extremely strong || <math>\beta \le -5</math> || <math>\beta \ge 5</math>
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| |-
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| |Very strong || <math>-5 < \beta \le -3</math> || <math> 5 > \beta \ge 3</math>
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| |-
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| |Strong || <math>-3 < \beta \le -2</math> || <math> 3 > \beta \ge 2</math>
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| |-
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| |Fairly strong || <math>-2 < \beta \le -1.645</math> || <math> 2 > \beta \ge 1.645</math>
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| |-
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| |Moderate || <math>-1.645 < \beta \le -1.28</math> || <math>1.645 > \beta \ge 1.28</math>
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| |-
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| |Fairly moderate || <math>-1.28 < \beta \le -1</math> || <math>1.28 > \beta \ge 1</math>
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| |-
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| |Fairly weak || <math>-1 < \beta \le -0.75</math> || <math> 1 > \beta \ge 0.75</math>
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| |-
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| |Weak || <math>-0.75 < \beta < -0.5</math> || <math> 0.75 > \beta > 0.5</math>
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| |-
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| |Very weak || <math>-0.5 \le \beta < -0.25</math> || <math>0.5 \ge \beta > 0.25</math>
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| |-
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| |Extremely weak || <math>-0.25 \le \beta < 0</math> || <math>0.25 \ge \beta > 0</math>
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| |-
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| |No effect || <math> \beta = 0</math>
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| |}
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| The estimation of SSMD for screens without replicates differs from that for screens with replicates.<ref name="ZhangBook2011"/><ref name="ZhangJBS2011"/>
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| In a primary screen without replicates, assuming the measured value (usually on the log scale) in a well for a tested [[Chemical compound|compound]] is <math> X_i </math> and the negative reference in that plate has sample size <math> n_N</math>, sample [[mean]] <math> \bar{X}_N </math>, [[median]] <math> \tilde{X}_N </math>, [[standard deviation]] <math> s_N </math> and [[median absolute deviation]] <math> \tilde{s}_N </math>, the SSMD for this [[Chemical compound|compound]] is estimated as
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| <ref name="ZhangBook2011"/><ref name="ZhangJBS2011"/>
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| :<math>\text{SSMD}= \frac{X_i - \bar{X}_N}{s_N \sqrt{2(n_N-1)/K}},</math>
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| where <math> K \approx n_N-2.48</math>.
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| When there are outliers in an [[assay]] which is usually common in HTS experiments, a robust version of SSMD <ref name="ZhangJBS2011"/> can be obtained using
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| :<math>\text{SSMD*}= \frac{X_i - \tilde{X}_N}{1.4826\tilde{s}_N \sqrt{2(n_N-1)/K}}</math>
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| In a confirmatory or primary screen with replicates, for the i-th test [[Chemical compound|compound]] with <math>n</math> replicates, we calculate the paired difference between the measured value (usually on the log scale) of the [[Chemical compound|compound]] and the [[median]] value of a negative control in a plate, then obtain the [[mean]] <math>\bar{d}_i </math> and [[variance]] <math>s_i^2 </math> of the paired difference across replicates. The SSMD for this [[Chemical compound|compound]] is estimated as
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| <ref name="ZhangBook2011"/>
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| :<math>\text{SSMD}= \frac{\Gamma(\frac{n-1}{2})}{\Gamma(\frac{n-2}{2})} \sqrt{\frac{2}{n-1}} \frac{\bar{d}_i}{s_i} </math>
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| In many cases, scientists may use both SSMD and average fold change for hit selection in HTS experiments. The dual-flashlight plot
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| <ref name=ZhangPharmacogenomics2010>{{cite journal |author=Zhang XHD
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| |title= Assessing the size of gene or RNAi effects in multifactor high-throughput experiments
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| |journal=Pharmacogenomics |volume=11 |issue= 2|pages=199–213
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| |year=2010 |month= |pmid= 20136359|doi=10.2217/PGS.09.136 |url=}}</ref>
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| can display both average fold change and SSMD for all test [[Chemical compound|compound]]s in an [[assay]] and help to integrate both of them to select hits in HTS experiments
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| <ref name=ZhaoHBC2010>{{cite journal |author=Zhao WQ, Santini F, Breese R, Ross D, Zhang XD, Stone DJ, Ferrer M, Townsend M, Wolfe AL, Seager MA, Kinney GG, Shughrue PJ, Ray WJ
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| |title= Inhibition of calcineurin-mediated endocytosis and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors prevents amyloid beta oligomer-induced synaptic disruption
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| |journal=Journal of Biological Chemistry |volume=10 |issue= 10|pages=7619–32
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| |year=2010 |month= |pmid= |doi=10.1074/jbc.M109.057182 |url=}}</ref>
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| . The use of SSMD for hit selection in HTS experiments is illustrated step-by-step in
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| <ref name="ZhangJBS2011"/>
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| ==See also==
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| * [[Effect size]]
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| * [[high-throughput screening]]
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| * [[Z-factor]]
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| * [[Hit selection]]
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| * [[SMCV]]
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| * [[c+-probability|c<sup>+</sup>-probability]]
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| * [[Contrast variable]]
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| * [[Dual-flashlight plot]]
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| ==Further reading==
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| * Zhang XHD (2011) [http://www.cambridge.org/9780521734448 "Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research, Cambridge University Press"]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:SSMD}}
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| [[Category:Effect size]]
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| [[Category:Data analysis]]
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