In clustering problems, to model the intrinsic structure of unlabeled data, the latent variable models are frequently used. These model-based clustering methods often provide a clustering rule minimizing the total false assignment error. However, in many clustering applications, it is desirable to treat false assignment errors for a certain cluster differently. In this paper, we introduce the false assignment rate for clustering and estimate it by using the extended likelihood approach. We propose VRclust, a novel clustering rule that controls various errors differently across clusters. Real data examples illustrate the usage of estimation of false assignment rate and a simulation study shows that error controls are consistent as the sample size increases.
WiwieCBaumbachJRøttgerR.Comparing the performance of biomedical clustering methods.Nat Meth2015;
12: 1033–1038.
3.
HastieTTibshiraniRFriedmanJ.The elements of statistical learning.
New York, NY:
Springer-Verlag, 2001.
4.
FraleyCRafteryAE.Model-based clustering, discriminant analysis, and density estimation. J Am Stat Assoc2002;
97: 611–631.
5.
Elkan C. The foundations of cost-sensitive learning. In: Proceedings of the seventeenth international joint conference of artificial intelligence, Seattle, Washington, USA, 4--10 August 2001, pp.973--978.
6.
GenoveseCRWassermanL.Operating characteristics and extensions of the FDR procedure. J Royal Stat Soc Ser B2002;
64: 499–518.
7.
LeeYBjørnstadJF.Extended likelihood approach to large-scale multiple testing. J Royal Stat Soc Ser B2013;
75: 553–575.
8.
SchwarzGE.Estimating the dimension of a model. Annals Stat1978;
6: 461–464.
9.
LoYMendellNRubinD.Testing the number of components in a normal mixture. Biometrika2001;
88: 767–778.
10.
McLachlanGPeelD.Finite mixture models.
New York, NY:
Wiley, 2000.
11.
NylundKLAsparouhovTMuthénBO.Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Struct Equation Model: Multidiscipl J2007;
14: 535–569.
12.
LeeYNelderJA.Hierarchical generalized linear models (with discussion). J Royal Stat Soc Ser B1996;
58: 619–678.
13.
BjørnstadJF. On the generalization of the likelihood function and likelihood principle. J Am Stat Assoc 19996; 91: 791–806.
14.
BanfieldJDRafteryAE.Model-based Gaussian and non-Gaussian clustering. Biometrics1993;
49: 803–821.
15.
EfronB.Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. J Am Stat Assoc2004;
99: 96–104.
16.
SunWCaiTT.Oracle and adaptive compounded clustering rules for false discovery rate control. J Am Stat Assoc2007;
102: 901–912.
17.
MuralidharanO.An empirical Bayes mixture method for effect size and false discovery rate estimation. Ann Appl Stat2010;
4: 422–438.
18.
DempsterAPLairdNMRubinDB.Maximum likelihood from incomplete data via the EM algorithmJ Royal Stat Soc Ser B1977;
39: 1–38.
19.
LinzerDALewisJB.poLCA: An R package for polytomous variable latent class analysis. J Stat Software2011;
42: 1--29.
20.
ScruccaLFopMMurphyTB, et al.mclust 5: Clustering, classification and density estimation using Gaussian finite mixture models. R J2016;
8: 289–317.
21.
BenjaminiYHochbergY.Controlling the false discovery rate: A practical and powerful approach to multiple testing. J Royal Stat Soc Ser B1995;
57: 289–300.
22.
KrzanowskiWJHandDJ.ROC curves for continuous data.
London:
Chapman and Hall, 2009.
23.
ScottCNowakRD.A Neyman-Pearson approach to statistical learning. IEEE Trans Inform Theory2005;
51: 3806–3819.
24.
LeeDLeeY.Extended likelihood approach to multiple testing with directional error control under a hidden Markov random field model. J Multivariate Analys2016;
151: 1–13.
25.
WallaceJELemaireJBGhaliWA.Physician wellness: a missing quality indicator. Lancet2009;
374: 1714–1721.
26.
SchernhammerE.Taking their own lives – high rate of physician suicide.New Engl J Med2005;
352: 2473–2476.
27.
Eckleberry-HuntJLickDBouraJ, et al.An exploratory study of resident burnout and wellness.Acad Med2009;
84: 269–277.
28.
Eckleberry-HuntJVan DykeALickD, et al.Changing the conversation from burnout to wellness: physician well-being in residency training programs.J Graduate Med Educ2009;
1: 225–230.
29.
LefebvreDC.Perspective: resident physician wellness: a new hope.Acad Med2012;
87: 598–602.
30.
ThomasNK.Resident burnout.J Am Med Assoc2004;
292: 2880–2889.
31.
ShanafeltTDBradleyKAWipfJE, et al.Burnout and self-reported patient care in an internal medicine residency programe. Ann Intern Med2002;
135: 358–367.
32.
EySMoffitMKinzieJM, et al.“If you build it, they will come”: attitudes of medical residents and fellows about seeking services in a resident wellness program. J Graduate Med Educ2013;
5: 486–492.
33.
ChoiDCedfeldtAFloresC, et al.Resident wellness: institutional trends over 10 years since 2003.Adv Med Educ Practice2017;
26: 513–523.
34.
CedfeldtABowerEFloresC, et al.Promoting resident wellness: evaluation of a time-off policy to increase residents’ utilization of health care services.Acad Med2015;
90: 678–683.
35.
GordonGHGirardDEHickamDH.Comparison of mood changes and satisfaction among first-year medical residents in three programs.J Med Educ1987;
62: 428–430.
36.
WestCPHuschkaMMNovotnyPJ, et al.Association of perceived medical errors with resident distress and empathy: a prospective longitudinal study.JAMA2006;
296: 1071–1078.
37.
PrinsJTGazendam-DonofrioSMTubbenBJ, et al.Burnout in medical residents. Med Educ2007;
41: 788–800.
38.
SchwartzAJ.College student suicide in the United States: 1990–1991 through 2003–2004.J Am College Health2006;
54: 341–352.
39.
BrownGKTen HaveTHenriquesGR, et al.Cognitive therapy for the prevention of suicide attempts. JAMA2005;
294: 563–570.
40.
LambertMJ.Bergin and Garfield’s handbook of psychotherapy and behavior change.
Hoboken, NJ:
John Wiley and Sons, 2004.
41.
GilbertCFosterA.Childhood blindness in the context of VISION 2020 – the right to sight. Bull World Health Organiz2001;
79: 227–232.
42.
ReynoldsJDDobsonVQuinnGE, et al.Evidence-based screening criteria for retinopathy of prematurity: natural history data from the cryo-rop and light-rop studies.Archives Ophthalmol2002;
120: 1470–1476.
43.
ChiangMFJiangLGelmanR, et al.Interexpert agreement of plus disease diagnosis in retinopathy of prematurity.Archives Ophthalmol2007;
125: 875–880.
44.
WallaceDKQuinnGEFreedmanSF, et al.Agreement among pediatric ophthalmologists in diagnosing plus and pre-plus disease in retinopathy of prematurity.J Am Assoc Pediatric Ophthalmol Strabismus2008;
12: 352–356.
45.
Ataer-CansizogluEBolon-CanedoVCampbellJP, et al.Computer-based image analysis for plus disease diagnosis in retinopathy of prematurity: performance of the “i-ROP” system and image features associated with expert diagnosis.Transl Vision Sci Technol2015;
4: 5.
