Statistics in Biosciences

, Volume 7, Issue 2, pp 167–186 | Cite as

Random Effects Model for Multiple Pathway Analysis with Applications to Type II Diabetes Microarray Data

  • Herbert PangEmail author
  • Inyoung Kim
  • Hongyu Zhao
Original Paper


Close to three percent of the world’s population suffer from diabetes. Despite the range of treatment options available for diabetes patients, not all patients benefit from them. Investigating how different pathways correlate with phenotype of interest may help unravel novel drug targets and discover a possible cure. Many pathway-based methods have been developed to incorporate biological knowledge into the study of microarray data. Most of these methods can only analyze individual pathways but cannot deal with two or more pathways in a model based framework. This represents a serious limitation because, like genes, individual pathways do not work in isolation, and joint modeling may enable researchers to uncover patterns not seen in individual pathway-based analysis. In this paper, we propose a random effects model to analyze two or more pathways. We also derive score test statistics for significance of pathway effects. We apply our method to a microarray study of Type II diabetes. Our method may eludicate how pathways crosstalk with each other and facilitate the investigation of pathway crosstalks. Further hypothesis on the biological mechanisms underlying the disease and traits of interest may be generated and tested based on this method.


Diabetes Gene expression analysis Microarray Pathway tests Random pathway effects Score test 



This research was partially supported by National Institutes of Health (NIH) grant GM59507, CA142538, CA154295, a pilot grant from the Yale Pepper Center, the National Science Foundation (NSF) grant DMS 1106738, and start-up funds from Duke University School of Medicine. We would also like to thank ‘Yale University Biomedical High Performance Computing Center’ NIH grant RR19895, which funded the instrumentation.

Supplementary material

12561_2014_9109_MOESM1_ESM.pdf (399 kb)
Supplementary material 1 (pdf 398 KB)


  1. 1.
    American Diabetes Association (2013) Economic costs of diabetes in the U.S. in 2012. Diabetes Care 36: 1033–1046Google Scholar
  2. 2.
    Algul H, Tando Y, Beil M, Weber C, Von Weyhern C, Schneider G, Adler G, Schmid R (2002) Different modes of NF-kappaB/Rel activation in pancreatic lobules. J Physiol Gastrointest Liver Physiol 283:G270–281CrossRefGoogle Scholar
  3. 3.
    Baldi C, Cho S, Ellis R (2009) Mutations in two independent pathways are sufficient to create hermaphroditic nematodes. Science 326:1002–1005CrossRefGoogle Scholar
  4. 4.
    Beinborn M, Worrall C, McBride E, Kopin A (2005) A human glucagon-like peptide-1 receptor polymorphism results in reduced agonist responsiveness. Regul Pept 130:1–6CrossRefGoogle Scholar
  5. 5.
    Buse J, Hirst K (2003) The HEALTHY study: introduction. Int J Obes 33(Suppl 4):S1–2Google Scholar
  6. 6.
    Canty T, Boyle E Jr, Farr A, Morgan E, Verrier E, Pohlman T (1999) Oxidative stress induces NF-kappaB nuclear translocation without degradation of IkappaBalpha. Circulation 100: II361–364Google Scholar
  7. 7.
    Centers for Disease Control and Prevention (2011) National diabetes fact sheet: general information and national estimates on diabetes in the United States, 2011. U.S. Department of Health and Human Services 2011, AtlantaGoogle Scholar
  8. 8.
    Chakrabarti S, Varghese S, Vitseva O, Tanriverdi K, Freedman J (2005) D40 ligand influences platelet release of reactive oxygen intermediates. Arterioscler Thromb Vasc Biol 25:2428–2434CrossRefGoogle Scholar
  9. 9.
    Chen C, Chai H, Wang X, Jiang J, Jamaluddin M, Liao D, Zhang Y, Wang H, Bharadwaj U, Zhang S, Li M, Lin P, Yao Q (2008) Soluble CD40 ligand induces endothelial dysfunction in human and porcine coronary artery endothelial cells. Blood 112:3205–3216CrossRefGoogle Scholar
  10. 10.
    Chung K (1974) A course in probability theory, 2nd edn. Academic Press, New YorkzbMATHGoogle Scholar
  11. 11.
    Croom K, McCormack P (2009) Liraglutide: a review of its use in type 2 diabetes mellitus. Drugs 69:1985–2004CrossRefGoogle Scholar
  12. 12.
    Dettling M (2004) BagBoosting for tumor classification with gene expression data. Bioinformatics 20:3583–3593CrossRefGoogle Scholar
  13. 13.
    Duckworth W, Abraira C, Moritz T, Reda D, Emanuele N, Reaven P, Zieve F, Marks J, Davis S, Hayward R, Warren S, Goldman S, McCarren M, Vitek M, Henderson W, Huang G (2009) VADT Investigators. Glucose control and vascular complications in veterans with type 2 diabetes. N Engl J Med 360:129–139CrossRefGoogle Scholar
  14. 14.
    Gerstein H, Miller M, Byington R, Goff D Jr, Bigger J, Buse J, Cushman W, Genuth S, Ismail-Beigi F, Grimm R Jr, Probstfield J, Simons-Morton D, Friedewald W (2008) Effects of intensive glucose lowering in type 2 diabetes. Action to Control Cardiovascular Risk in Diabetes Study Group. N Engl J Med 358:2545–2559CrossRefGoogle Scholar
  15. 15.
    Goeman J, van de Geer S, de Kort F, van Houwelingen H (2004) A global test for groups of genes: testing association with a clinical outcome. Bioinformatics 20:93–99CrossRefGoogle Scholar
  16. 16.
    Goeman J, Oosting J, Cleton-Jansen A, Anninga J, van Houwelingen H (2005) Testing association of a pathway with survival using gene expression data. Bioinformatics 21:1950–1957CrossRefGoogle Scholar
  17. 17.
    Henderson C, Kempthorne O, Searle S, von Krosigk C (1959) The estimation of environmental and genetic trends from records subject to culling. Biometrics 15:192–218CrossRefzbMATHGoogle Scholar
  18. 18.
    Kanehisa M, Goto S, Kawashima S, Okuno Y, Hattori M (2004) The KEGG resource for deciphering the genome. Nucleic Acids Res 32:D277–280CrossRefGoogle Scholar
  19. 19.
    Ke Z, Calingasan N, DeGiorgio L, Volpe B, Gibson G (2005) CD40–CD40L interactions promote neuronal death in a model of neurodegeneration due to mild impairment of oxidative metabolism. Neurochem Int 47:204–215CrossRefGoogle Scholar
  20. 20.
    Kim I, Pang H, Zhao H (2012) Semiparametric methods for evaluating pathway effects on clinical outcomes using gene expression data. Stat Med 10:1633–1651MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kingwell B, Formosa M, Muhlmann M, Bradley S, McConell G (2002) Nitric oxide synthase inhibition reduces glucose uptake during exercise in individuals with Type 2 diabetes more than in control subjects. Diabetes 51:2572–2580CrossRefGoogle Scholar
  22. 22.
    Lin X (1997) Variance component testing in generalised linear models with random effects. Biometrika 84:309–326MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Lin J, Wu H, Tarr P, Zhang C, Wu Z, Boss O, Michael L, Puigserver P, Isotani E, Olson E, Lowell B, Bassel-Duby R, Spiegelman B (2002) Transcriptional co-activator PGC-1 alpha drives the formation of slow-twitch muscle fibres. Nature 418:797–801CrossRefGoogle Scholar
  24. 24.
    Liu D, Lin X, Ghosh D (2007) Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63:1079–1088MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Malhotra R, Liu Z, Vincenz C, Brosius F 3rd (2001) Hypoxia induces apoptosis via two independent pathways in Jurkat cells: differential regulation by glucose. Am J Physiol Cell Physiol 281:C1596–1603Google Scholar
  26. 26.
    Mandrup-Poulsen T (2003) Apoptotic signal transduction pathways in diabetes. Biochem Pharmacol 66:1433–1440CrossRefGoogle Scholar
  27. 27.
    Mansmann U, Meister R (2003) Testing differential gene expression in functional groups. Goeman’s global test versus an ANCOVA approach. Methods Inf Med 44:449–453Google Scholar
  28. 28.
    Mootha V, Lindgren C, Eriksson K, Subramanian A, Sihag S, Lehar J, Puigserver P, Carlsson E, Ridderstrle M, Laurila E, Houstis N, Daly M, Patterson N, Mesirov J, Golub T, Tamayo P, Spiegelman B, Lander E, Hirschhorn J, Altshuler D, Groop L (2003) PGC-1alpha-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes. Nat Genetics 34:267–273CrossRefGoogle Scholar
  29. 29.
    Pande V, Sharma R, Inoue J, Otsuka M, Ramos M (2003) A molecular modeling study of inhibitors of nuclear factor kappa-B (p50)-DNA binding. J Comput Aided Mol Des 17:825–836CrossRefGoogle Scholar
  30. 30.
    Pang H, Lin A, Holford M, Enerson BE, Lu B, Lawton MP, Floyd E, Zhao H (2006) Pathway analysis using random forests classification and regression. Bioinformatics 22:2028–2036CrossRefGoogle Scholar
  31. 31.
    Pang H, Zhao H (2008) Building pathway clusters from random forests classification using class votes. BMC Bioinform 9:87CrossRefGoogle Scholar
  32. 32.
    Pang H, Datta D, Zhao H (2010) Pathway analysis using random forests with bivariate node-split for survival outcomes. Bioinformatics 26:250–258CrossRefGoogle Scholar
  33. 33.
    Pang H, Hauser M, Minvielle S (2011) Pathway-based identification of SNPs predictive of survival. Eur J Hum Genet 19:704–709Google Scholar
  34. 34.
    Pang H, George SL, Hui K, Tong T (2012) Gene selection using iterative feature elimination random forests for survival outcomes. IEEE/ACM Trans Comput Biol Bioinform 9:1422–1431Google Scholar
  35. 35.
    Raz I, Hanefeld M, Xu L, Caria C, Williams-Herman D, Khatami H, Sitagliptin Study 023 Group (2006) Efficacy and safety of the dipeptidyl peptidase-4 inhibitor sitagliptin as monotherapy in patients with type 2 diabetes mellitus. Diabetologia 49:2564–2571Google Scholar
  36. 36.
    Robinson G (1991) That BLUP is a good thing: the estimation of random effects. Stat Sci 6:15–32CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Ryan G, Jobe L, Martin R (2010) Pramlintide in the treatment of type 1 and type 2 diabetes mellitus. Clin Ther 27:1500–1512CrossRefGoogle Scholar
  38. 38.
    Shackelford D, Shaw R (2009) The LKB1-AMPK pathway: metabolism and growth control in tumor suppression. Nat Rev Cancer 9:563–575CrossRefGoogle Scholar
  39. 39.
    Shaik Z, Fifer E, Nowak G (2010) Akt activation improves oxidative phosphorylation in renal proximal tubular cells following nephrotoxicant injury. Am J Physiol Renal Physiol 294:F423–432CrossRefGoogle Scholar
  40. 40.
    Stelzl U, Worm U, Lalowski M, Haenig C, Brembeck F, Goehler H, Stroedicke M, Zenkner M, Schoenherr A, Koeppen S, Timm J, Mintzlaff S, Abraham C, Bock N, Kietzmann S, Goedde A, Toksz E, Droege A, Krobitsch S, Korn B, Birchmeier W, Lehrach H, Wanker E (2005) A human protein–protein interaction network: a resource for annotating the proteome. Cell 122:957–968CrossRefGoogle Scholar
  41. 41.
    Wang X, Shaw S, Amiri F, Eaton D, Marrero M (2002) Inhibition of the JAK/STAT signaling pathway prevents the high glucose-induced increase in TGF-b and fibronectin synthesis in mesangial cells. Diabetes 51:3505–3509CrossRefGoogle Scholar
  42. 42.
    Wei Z, Li H (2007) Nonparametric pathway-based regression models for analysis of genomic data. Biostatistics 8:265–284CrossRefzbMATHGoogle Scholar
  43. 43.
    Wild S, Roglic G, Green A, Sicree R, King H (2004) Global prevalence of diabetes: estimates for the year 2000 and projections for 2030. Diabetes Care 27:1047–1053CrossRefGoogle Scholar
  44. 44.
    Yang J, Yeh H, Lin K, Wang P (2009) Insulin stimulates Akt translocation to mitochondria: implications on dysregulation of mitochondrial oxidative phosphorylation in diabetic myocardium. J Mol Cell Cardiol 46:919–926CrossRefGoogle Scholar
  45. 45.
    Zeitler P, Epstein L, Grey M, Hirst K, Kaufman F, Tamborlane W, Wilfley D (2007) Treatment options for type 2 diabetes in adolescents and youth: a study of the comparative efficacy of metformin alone or in combination with rosiglitazone or lifestyle intervention in adolescents with type 2 diabetes. Pediatr Diabetes 8:74–87CrossRefGoogle Scholar
  46. 46.
    Zhang D, Lin X (2003) Hypothesis testing in semiparametric additive mixed models. Biostatistics 4:57–74CrossRefzbMATHGoogle Scholar
  47. 47.
    Zhang L, Lon S, Subramani S (2006) Two independent pathways traffic the intraperoxisomal peroxin PpPex8p into peroxisomes. Mol Biol Cell 17:690–699CrossRefGoogle Scholar

Copyright information

© International Chinese Statistical Association 2014

Authors and Affiliations

  1. 1.Department of Biostatistics and BioinformaticsDuke University School of MedicineDurhamUSA
  2. 2.School of Public HealthLi Ka Shing Faculty of MedicineHong KongChina
  3. 3.Department of StatisticsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  4. 4.Department of Biostatistics, Yale School of Public Health, and Department of GeneticsYale University School of MedicineNew HavenUSA

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