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1

Humes, Larry. "Response to Hochberg." American Journal of Audiology 2, no. 2 (July 1993): 77. http://dx.doi.org/10.1044/1059-0889.0202.77.

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2

LaBossiere, Michael C. "Reply to Hochberg." Australasian Journal of Philosophy 74, no. 1 (March 1996): 162–70. http://dx.doi.org/10.1080/00048409612347141.

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3

Tamhane, A. C., and L. Liu. "On weighted Hochberg procedures." Biometrika 95, no. 2 (February 4, 2008): 279–94. http://dx.doi.org/10.1093/biomet/asn018.

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4

Raphael, Lawrence J. "Irving Hochberg • 1934–1999." Journal of the Acoustical Society of America 109, no. 5 (May 2001): 1759. http://dx.doi.org/10.1121/1.1369380.

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5

Ferreira, J. A., and A. H. Zwinderman. "On the Benjamini–Hochberg method." Annals of Statistics 34, no. 4 (August 2006): 1827–49. http://dx.doi.org/10.1214/009053606000000425.

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6

Arnheim, Rudolf. "A reply to Hochberg and Perkins." New Ideas in Psychology 4, no. 3 (January 1986): 301–2. http://dx.doi.org/10.1016/0732-118x(86)90039-5.

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7

Baddeley, Roland. "Review: In the Mind's Eye: Julian Hochberg on the Perception of Pictures, Films, and the World by J Hochberg." Perception 37, no. 1 (January 2008): 165–66. http://dx.doi.org/10.1068/p3701rvw.

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8

Ferreira, J. A., and S. O. Nyangoma. "A multivariate version of the Benjamini–Hochberg method." Journal of Multivariate Analysis 99, no. 9 (October 2008): 2108–24. http://dx.doi.org/10.1016/j.jmva.2008.02.013.

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9

Palejev, Dean, and Mladen Savov. "On the Convergence of the Benjamini–Hochberg Procedure." Mathematics 9, no. 17 (September 3, 2021): 2154. http://dx.doi.org/10.3390/math9172154.

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The Benjamini–Hochberg procedure is one of the most used scientific methods up to date. It is widely used in the field of genetics and other areas where the problem of multiple comparison arises frequently. In this paper we show that under fairly general assumptions for the distribution of the test statistic under the alternative hypothesis, when increasing the number of tests, the power of the Benjamini–Hochberg procedure has an exponential type of asymptotic convergence to a previously shown limit of the power. We give a theoretical lower bound for the probability that for a fixed number of tests the power is within a given interval around its limit together with a software routine that calculates these values. This result is important when planning costly experiments and estimating the achieved power after performing them.
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10

Levin, B. "On the Holm, Simes, and Hochberg multiple test procedures." American Journal of Public Health 86, no. 5 (May 1996): 628–29. http://dx.doi.org/10.2105/ajph.86.5.628.

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11

Li, Ang, and Rina Foygel Barber. "Multiple testing with the structure-adaptive Benjamini-Hochberg algorithm." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 81, no. 1 (November 2, 2018): 45–74. http://dx.doi.org/10.1111/rssb.12298.

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12

Chen, Xiongzhi, and Sanat K. Sarkar. "On Benjamini–Hochberg procedure applied to mid p-values." Journal of Statistical Planning and Inference 205 (March 2020): 34–45. http://dx.doi.org/10.1016/j.jspi.2019.06.001.

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13

Retzer, Elena. "¿Por qué? 101 Questions about Spanish by Judy Hochberg." Hispania 101, no. 2 (2018): 332–33. http://dx.doi.org/10.1353/hpn.2018.0138.

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14

Spurrier, John D. "Multiple Comparison Procedures (Yosef Hochberg and Ajit C. Tamhane)." SIAM Review 31, no. 2 (June 1989): 349–50. http://dx.doi.org/10.1137/1031084.

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15

Rom, Dror M. "An improved Hochberg procedure for multiple tests of significance." British Journal of Mathematical and Statistical Psychology 66, no. 1 (February 20, 2012): 189–96. http://dx.doi.org/10.1111/j.2044-8317.2012.02042.x.

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16

Feener, Donald H. "Parasitoid Population Biology. Michael E. Hochberg , Anthony R. Ives." Quarterly Review of Biology 76, no. 4 (December 2001): 504–5. http://dx.doi.org/10.1086/420602.

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17

Abbas, Ahmed, Xin-Bing Kong, Zhi Liu, Bing-Yi Jing, and Xin Gao. "Automatic Peak Selection by a Benjamini-Hochberg-Based Algorithm." PLoS ONE 8, no. 1 (January 7, 2013): e53112. http://dx.doi.org/10.1371/journal.pone.0053112.

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18

Levin, Alexander D. "Improvement of pressure chamber protocols - Response to Hochberg (2019)." Agricultural Water Management 227 (January 2020): 105837. http://dx.doi.org/10.1016/j.agwat.2019.105837.

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19

Thissen, David, Lynne Steinberg, and Daniel Kuang. "Quick and Easy Implementation of the Benjamini-Hochberg Procedure for Controlling the False Positive Rate in Multiple Comparisons." Journal of Educational and Behavioral Statistics 27, no. 1 (March 2002): 77–83. http://dx.doi.org/10.3102/10769986027001077.

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Williams, Jones, and Tukey (1999) showed that a sequential approach to controlling the false discovery rate in multiple comparisons, due to Benjamini and Hochberg (1995), yields much greater power than the widely used Bonferroni technique that limits the familywise Type I error rate. The Benjamini-Hochberg (B-H) procedure has since been adopted for use in reporting results from the National Assessment of Educational Progress (NAEP), as well as in other research applications. This short note illustrates that the B-H procedure is extremely simple to implement using widely available spreadsheet software. Given its easy implementation, it is feasible to include the B-H procedure in introductory instruction in inferential statistics, augmenting or replacing the Bonferroni technique.
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20

Ghosh, Debashis. "Wavelet-based Benjamini-Hochberg procedures for multiple testing under dependence." Mathematical Biosciences and Engineering 17, no. 1 (2020): 56–72. http://dx.doi.org/10.3934/mbe.2020003.

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21

MacBride, Fraser. "How Hochberg Helped Us Take the Ontological Turn: An Introduction." Dialectica 68, no. 2 (June 2014): 163–69. http://dx.doi.org/10.1111/1746-8361.12064.

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22

Adlard, Edward R. "Michael Hochberg: An Editor’s Guide to Writing and Publishing Science." Chromatographia 82, no. 12 (September 25, 2019): 1847. http://dx.doi.org/10.1007/s10337-019-03810-0.

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23

Vonèche, J. Jacques. "The trouble with Arnheim and Hochberg: A response to Arnheim." New Ideas in Psychology 4, no. 3 (January 1986): 303–4. http://dx.doi.org/10.1016/0732-118x(86)90040-1.

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24

Thomas, William. "Multiple comparison procedures, by Yosef Hochberg and Ajit C. Tamhane." Chemometrics and Intelligent Laboratory Systems 5, no. 3 (March 1989): 189–90. http://dx.doi.org/10.1016/0169-7439(89)80040-1.

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25

Huque, Mohammad F. "Validity of the Hochberg procedure revisited for clinical trial applications." Statistics in Medicine 35, no. 1 (August 16, 2015): 5–20. http://dx.doi.org/10.1002/sim.6617.

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26

Ouerdiane, Habib. "Solutions of evolution equations associated to infinite-dimensional Laplacian." International Journal of Quantum Information 14, no. 04 (June 2016): 1640018. http://dx.doi.org/10.1142/s0219749916400189.

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We study an evolution equation associated with the integer power of the Gross Laplacian [Formula: see text] and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with [Formula: see text], as well as by Barhoumi–Kuo–Ouerdiane for the case [Formula: see text] (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).
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27

Benjamini, Yoav, and Yosef Hochberg. "On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics." Journal of Educational and Behavioral Statistics 25, no. 1 (March 2000): 60–83. http://dx.doi.org/10.3102/10769986025001060.

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A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.
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28

Chung, Pei-Jung, Johann F. Bohme, Christoph F. Mecklenbrauker, and Alfred O. Hero. "Detection of the Number of Signals Using the Benjamini-Hochberg Procedure." IEEE Transactions on Signal Processing 55, no. 6 (June 2007): 2497–508. http://dx.doi.org/10.1109/tsp.2007.893749.

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29

Westfall, P. H. "The Benjamini-Hochberg method with infinitely many contrasts in linear models." Biometrika 95, no. 3 (September 1, 2008): 709–19. http://dx.doi.org/10.1093/biomet/asn033.

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30

Simons, Peter. "Relations and Idealism: On Some Arguments of Hochberg against Trope Nominalism." Dialectica 68, no. 2 (June 2014): 305–15. http://dx.doi.org/10.1111/1746-8361.12063.

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31

de Mesnard, Louis. "On Hochberg et al.’s “The tragedy of the reviewer commons”." Scientometrics 84, no. 3 (December 31, 2009): 903–17. http://dx.doi.org/10.1007/s11192-009-0141-8.

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32

Ge, Yongchao, and Xiaochun Li. "Control of the False Discovery Proportion for Independently Tested Null Hypotheses." Journal of Probability and Statistics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/320425.

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Consider the multiple testing problem of testingmnull hypothesesH1,…,Hm, among whichm0hypotheses are truly null. Given theP-values for each hypothesis, the question of interest is how to combine theP-values to find out which hypotheses are false nulls and possibly to make a statistical inference onm0. Benjamini and Hochberg proposed a classical procedure that can control the false discovery rate (FDR). The FDR control is a little bit unsatisfactory in that it only concerns the expectation of the false discovery proportion (FDP). The control of the actual random variable FDP has recently drawn much attention. For any level1−α, this paper proposes a procedure to construct an upper prediction bound (UPB) for the FDP for a fixed rejection region. When1−α=50%, our procedure is very close to the classical Benjamini and Hochberg procedure. Simultaneous UPBs for all rejection regions' FDPs and the upper confidence bound for the unknownm0are presented consequently. This new proposed procedure works for finite samples and hence avoids the slow convergence problem of the asymptotic theory.
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33

von der Mohlen, MA, SJ van Deventer, M. Levi, B. van den Ende, NI Wedel, BJ Nelson, N. Friedmann, and JW ten Cate. "Inhibition of endotoxin-induced activation of the coagulation and fibrinolytic pathways using a recombinant endotoxin-binding protein (rBPI23)." Blood 85, no. 12 (June 15, 1995): 3437–43. http://dx.doi.org/10.1182/blood.v85.12.3437.bloodjournal85123437.

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A recombinant endotoxin-neutralizing protein, rBPI23, was shown to partially prevent endotoxin-induced activation of the fibrinolytic and coagulation systems in experimental endotoxemia in humans. In a placebo-controlled, blinded crossover study, eight volunteers were challenged twice with an intravenous bolus injection of endotoxin (40 EU/kg of body weight) and concurrently received either rBPI23 (1 mg/kg) or placebo (human serum albumin, 0.2 mg/kg). rBPI23 treatment significantly lowered the endotoxin-induced fibrinolytic response, ie, reduced the release of tissue-type plasminogen activator, urokinase-type plasminogen activator, plasminogen activator inhibitor antigen, and complex formation of plasmin alpha 2-antiplasmin (P = .0078 for each). Plasminogen activator inhibitor activity was also reduced, but not significantly according to the Hochberg method (P = .0304). The endotoxin-induced activation of the procoagulant state as reflected by increase in F1 + 2 fragments and TAT complexes was blunted by rBPI23 infusion (P = .0391 [not significant according to the Hochberg method] and .0078, respectively). These results indicate that rBPI23 is capable of reducing both the activation of the fibrinolytic and the coagulation systems after low-dose endotoxin infusion in humans.
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34

Smith, Robin. "Logic, Ontology, and Language: Essays on Truth and Reality. By Herbert Hochberg." Modern Schoolman 65, no. 4 (1988): 279–82. http://dx.doi.org/10.5840/schoolman198865449.

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35

Mertz, D. W. "Herbert Hochberg. Introducing Analytic Philosophy: Its Sense and Its Nonsense, 1879-2002." Modern Schoolman 81, no. 4 (2004): 313–15. http://dx.doi.org/10.5840/schoolman200481422.

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36

Cai, Qingyun, and Hock Peng Chan. "A Double Application of the Benjamini-Hochberg Procedure for Testing Batched Hypotheses." Methodology and Computing in Applied Probability 19, no. 2 (March 5, 2016): 429–43. http://dx.doi.org/10.1007/s11009-016-9491-x.

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37

McLaughlin, Matthew J., and Kristin L. Sainani. "Bonferroni, Holm, and Hochberg Corrections: Fun Names, Serious Changes to P Values." PM&R 6, no. 6 (April 22, 2014): 544–46. http://dx.doi.org/10.1016/j.pmrj.2014.04.006.

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38

Guo, Wenge, and M. Bhaskara Rao. "On optimality of the Benjamini–Hochberg procedure for the false discovery rate." Statistics & Probability Letters 78, no. 14 (October 2008): 2024–30. http://dx.doi.org/10.1016/j.spl.2008.01.069.

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39

Xi, Dong, and Frank Bretz. "Symmetric graphs for equally weighted tests, with application to the Hochberg procedure." Statistics in Medicine 38, no. 27 (October 27, 2019): 5268–82. http://dx.doi.org/10.1002/sim.8375.

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40

Boselie, Frans, and Emanuel Leeuwenberg. "A Test of the Minimum Principle Requires a Perceptual Coding System." Perception 15, no. 3 (June 1986): 331–54. http://dx.doi.org/10.1068/p150331.

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The minimum principle states that a perceiver will see the simplest possible interpretation of a pattern. Some theorists of human perception take this principle as a core explanatory concept. Others, especially Rock and Hochberg, hold the view that a perceptual minimum principle is untenable. Rock presents a great number of demonstrations which, in his opinion, rule out the minimum principle. Hochberg states that ‘impossible’ figures especially present a difficulty for this principle. It is argued here that, in order to test the minimum principle, a method is needed to describe interpretations of patterns in such a way that they can be ordered according to simplicity. To achieve this, Leeuwenberg's coding system was used. The analyses reported here of the patterns which Rock produces as evidence against the principle show that, contrary to Rock's claim, the way these patterns are preferentially perceived provides strong support for the minimum principle. Next, it is demonstrated that interpreting certain patterns as ‘impossible’ figures is not incompatible with the principle. Finally, it is argued that a test of the minimum principle is necessarily conflated with two other hypotheses, one concerning the metric of simplicity and one concerning the task conception of the experimental subjects.
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41

Etheridge, Alison M. "Limiting behaviour of two-level measure-branching." Advances in Applied Probability 25, no. 04 (December 1993): 773–82. http://dx.doi.org/10.1017/s000186780002574x.

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A measure-valued diffusion approximation to a two-level branching structure was introduced in Dawson and Hochberg (1991) where it was shown that conditioned on non-extinction at time t, and appropriately rescaled, the process converges as t → ∞to a non-trivial limiting distribution. Here we discuss a different approach to conditioning on non-extinction (popular in one-level branching) and relate the two limiting distributions.
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42

Etheridge, Alison M. "Limiting behaviour of two-level measure-branching." Advances in Applied Probability 25, no. 4 (December 1993): 773–82. http://dx.doi.org/10.2307/1427791.

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A measure-valued diffusion approximation to a two-level branching structure was introduced in Dawson and Hochberg (1991) where it was shown that conditioned on non-extinction at time t, and appropriately rescaled, the process converges as t → ∞to a non-trivial limiting distribution. Here we discuss a different approach to conditioning on non-extinction (popular in one-level branching) and relate the two limiting distributions.
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43

Kwong, Koon Shing, Burt Holland, and Siu Hung Cheung. "A modified Benjamini–Hochberg multiple comparisons procedure for controlling the false discovery rate." Journal of Statistical Planning and Inference 104, no. 2 (June 2002): 351–62. http://dx.doi.org/10.1016/s0378-3758(01)00252-x.

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44

Gou, J., A. C. Tamhane, D. Xi, and D. Rom. "A class of improved hybrid Hochberg-Hommel type step-up multiple test procedures." Biometrika 101, no. 4 (October 24, 2014): 899–911. http://dx.doi.org/10.1093/biomet/asu032.

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45

Guilbaud, Olivier. "Simultaneous confidence regions for closed tests, including Holm-, Hochberg-, and Hommel-related procedures." Biometrical Journal 54, no. 3 (May 2012): 317–42. http://dx.doi.org/10.1002/bimj.201100123.

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46

Gou, Jiangtao, and Ajit C. Tamhane. "A Flexible Choice of Critical Constants for the Improved Hybrid Hochberg-Hommel Procedure." Sankhya B 80, no. 1 (June 6, 2017): 85–97. http://dx.doi.org/10.1007/s13571-017-0135-0.

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47

McFalls, Laurence, Jeffrey J. Anderson, and Vanessa Beck. "Book Reviews." German Politics and Society 18, no. 3 (September 1, 2000): 157–70. http://dx.doi.org/10.3167/104503000782486570.

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Jennifer A. Yoder, From East Germans to Germans? The New Postcommunist Elitesn(Durham: Duke University Press, 1999)Review by Laurence McFallsHölscher, Jens and Anja Hochberg, eds., East Germany’s Economic Development Since Unification: Domestic and Global Aspects (New York: St. Martin’s Press, 1998)Review by Jeffrey J. AndersonBrigitte Young, Triumph of the Fatherland. German Unification and the Marginalization of Women (Ann Arbor: University of Michigan Press, 1999) Review by Vanessa Beck
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48

Tyurin, Anton, Daria Shapovalova, Halida Gantseva, Valentin Pavlov, and Rita Khusainova. "Association between miRNA Target Sites and Incidence of Primary Osteoarthritis in Women from Volga-Ural Region of Russia: A Case-Control Study." Diagnostics 11, no. 7 (July 6, 2021): 1222. http://dx.doi.org/10.3390/diagnostics11071222.

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Over the past decades, numerous studies on the genetic markers of osteoarthritis (OA) have been conducted. MiRNA targets sites are a promising new area of research. In this study, we analyzed the polymorphic variants in 3′ UTR regions of COL1A1, COL11A1, ADAMTS5, MMP1, MMP13, SOX9, GDF5, FGF2, FGFR1, and FGFRL1 genes to examine the association between miRNA target site alteration and the incidence of OA in women from the Volga-Ural region of Russia using competitive allele-specific PCR. The T allele of the rs9659030 was associated with generalized OA (OR = 2.0), whereas the C allele of the rs229069 was associated with total OA (OR = 1.43). The T allele of the rs13317 was associated with the total OA (OR = 1.67). After Benjamini-Hochberg correction, only rs13317 remained statistically significant. According to ethnic heterogeneity, associations between the T allele (rs1061237) with OA in women of Russian descent (OR = 1.77), the G allele (rs6854081) in women of Tatar descent (OR = 4.78), the C allele (rs229069) and the T allele (rs73611720) in women of mixed descent and other ethnic groups (OR = 2.25 and OR = 3.02, respectively) were identified. All associations remained statistically significant after Benjamini-Hochberg correction. Together, this study identified miRNA target sites as a genetic marker for the development of OA in various ethnic groups.
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49

Sabatti, Chiara, Susan Service, and Nelson Freimer. "False Discovery Rate in Linkage and Association Genome Screens for Complex Disorders." Genetics 164, no. 2 (June 1, 2003): 829–33. http://dx.doi.org/10.1093/genetics/164.2.829.

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Abstract We explore the implications of the false discovery rate (FDR) controlling procedure in disease gene mapping. With the aid of simulations, we show how, under models commonly used, the simple step-down procedure introduced by Benjamini and Hochberg controls the FDR for the dependent tests on which linkage and association genome screens are based. This adaptive multiple comparison procedure may offer an important tool for mapping susceptibility genes for complex diseases.
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50

Beck, Matthias, and Thomas Zaslavsky. "A Shorter, Simpler, Stronger Proof of the Meshalkin–Hochberg–Hirsch Bounds on Componentwise Antichains." Journal of Combinatorial Theory, Series A 100, no. 1 (October 2002): 196–99. http://dx.doi.org/10.1006/jcta.2002.3295.

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