Vol.23no.12007,pages71–76
doi:10.1093/bioinformatics/btl557 BIOINFORMATICS ORIGINAL PAPER
Genetics and population analysis
Odds ratio bad multifactor-dimensionality reduction method
for detecting gene–gene interactions
Yujin Chung1,Seung Yeoun Lee2,Robert C.Elston3and Taesung Park1,Ã
1Department of Statistics,Seoul National University,San56-1Shillim-Dong,Kwanak-Gu,Seoul151-747,Korea,
2Department of Applied Mathematics,Sejong University,98Gunja-Dong Kwangjin-Gu,Seoul143-747,Korea and 3Department of Epidemiology and Biostatistics,Ca Western Rerve University,10900Euclid Avenue Cleveland, OH44106-7281,USA
Received on June27,2006;revid on September11,2006;accepted on October27,2006
Advance Access publication November8,2006
Associate Editor:Keith A Crandall
ABSTRACT
Motivation:The identification and characterization of genes that increa the susceptibility to common complex multifactorial dias is a challenging task in genetic association studies.The multifactor dimensionality reduction(MDR)method has been propod and implemented by Ritchie et al.(2001)to identify the combinations of multilocus genotypes and discrete environmental factors that are associated with a particular dia.However,the original MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups in an ad hoc manner bad on a simple comparison of the ratios of the number of cas and controls. Hence,the MDR approach is prone to fal positive and negative errors when the ratio of the number of cas and controls in a combi-nation of genotypes is similar to that in the entire data,or when both the number of cas and controls is small.Hence,we propo the odds ratio bad multifactor dimensionality reduction(OR MDR)method that us the odds ratio as a new quantitative measure of dia risk. Results:While the original MDR method provides a simple binary measure of risk,the OR MDR method provides no
t only the odds ratio as a quantitative measure of risk but also the ordering of the multilocus combinations from the highest risk to lowest risk groups. Furthermore,the OR MDR method provides a confidence interval for the odds ratio for each multilocus combination,which is extremely informative in judging its importance as a risk factor.The propod OR MDR method is illustrated using the datat obtained from the CDC Chronic Fatigue Syndrome Rearch Group.
Availability:The program written in R is available.
kebiContact:tspark@snu.ac.kr
1INTRODUCTION
The general strategy for identifying Mendelian dia genes has largely been unsuccessful when applied to identifying susceptibility genes for common complex multifactorial dias,such as asthma (Altmuller et al.,2001).This is becau the Mendelian approach requires each susceptibility factor to have a large independent main effect on dia risk(Moore and William,2002).The effect of any single genetic variation for a common complex dia may be dependent on other genetic variations(gene–gene interaction) and environmental factors(gene–environment interaction).To address this issue,veral methods,such as logistic regression models,multilocus linkage diquilibri
um(LD)tests,and Hardy–Weinberg equilibrium tests have been applied.However, most of the methods require a large sample size to model high-order interactions(Moore and William,2002).Unfortunately, it is not easy to collect large sample size data.Moreover,when logistic regression is ud,multicollinearity may occur due to LD. For moderate sample size data,one method for detecting and characterizing interactions in common complex multifactorial dias is the multifactor dimensionality reduction(MDR)method (Ritchie et al.,2001).This method detects and characterizes the high-order gene–gene and gene–environment interactions in ca-control studies.Using this method,multilocus genotypes are classified into high-risk and low-risk groups,effectively reducing the genotype predictors from n dimensions to one dimension.The new,one-dimensional multilocus genotype variable is evaluated for its ability to classify and predict dia status through cross-validation(CV).The MDR method is model-free,in that it does not assume any particular genetic model.This is important for dias in which the mode of inheritance is unknown and possibly very complex.Moreover,the MDR method is non-parametric,in that it does not estimate any parameters(Ritchie et al.,2001). Although the MDR method provides many uful features,it has veral drawbacks.First,its method of determining high-risk or low-risk groups is ad hoc—in the n that it classifies cells, defined by combination of multilocus genotypes,into high-risk or low-risk groups bad on a simple comparison of the ratios of the number of cas and contro
ls.Hence,the MDR method is prone to fal positive and negative errors when the ratio of the number of cas and controls in a combination of genotypes is similar to that in the entire data,or when both the number of cas and controls in a combination of genotypes is small.
Second,the MDR binary classification does not provide any quantitative measure of dia risk for each combination of geno-types but only provides a binary measure(high or low)of dia risk.Further,the MDR method does not provide any information regarding how well the high-risk group is characterized.Third, the MDR method does not allow comparison of the dia risks between different combinations of genotypes.Thus,it is not pos-sible to identify which combination of genotypes in the high-risk group has the highest risk or which combination in the low-risk group has the lowest risk.In practical applications,however,it is
ÃTo whom correspondence should be addresd.
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important to know whether a certain combination of genotypes has a higher risk than other combinati
ons.
In this paper,we propo the odds ratio bad multifactor dimen-sionality reduction(OR MDR)method to overcome the above mentioned limitations of the MDR method.The OR MDR method us the odds ratio of each combination of genotypes as a quanti-tative measure of dia risk,so that we can order the combinations of genotypes from the highest to the lowest in terms of the odds ratios.Moreover,a confidence interval of the odds ratio can be obtained,either by using large sample theory or bootstrap samples for each combination of genetoypes.
The MDR method is briefly reviewed in Section2.1,and the new OR MDR method is propod in Section2.2.An example giving a comparison between the results of the MDR and the OR MDR methods is provided in Section3using a datat obtained from the CDC Chronic Fatigue Syndrome Rearch Group.The discussion andfinal conclusions are included in Section4.
2METHODS
2.1MDR method
The MDR method has been propod by Ritchie et al.(2001)and Moore and William(2002),and imple
mented by Hahn et al.(2003)and Ritchie et al. (2003).It compris the following two stages.Stage1involves choosing the best combination of multifactors.Stage2involves classifying the com-binations of genotypes into high-risk and low-risk groups.
Figure1describes the procedure ud to implement the MDR method. First,the data are divided into10subts for CV—nine are classified as training ts and one as an independent test t.Second,the value of n is designated depending upon the number of factors being considered.Then,a t of n genetic and/or environmental factors is lected.The n factors and their possible multifactor class are reprented in n-dimensional space. Next,the ratio of the number of cas to the number of controls within each multifactor class is calculated.Each multifactor class in n-dimensional space is labeled as‘high risk’if the ratio of the number of cas to that of the controls is equal to or exceeds a particular threshold;it is labeled as‘low risk’if that threshold is not exceeded.Thus the n-dimensional space is reduced to one dimension with two levels(low-risk and high-risk). Usually,the threshold is determined as the ratio of the number of cas to the number of controls in the training datat.The threshold is equal to one in a balanced datat.Among all the multifactor combinations,the MDR model with the lowest number of misclassified individuals is lected. In order to evaluate the predictive ability of the model,the prediction error for the lected combination of factors is estimated using the independent test data.until的用法
After repeating the above procedures for each of the10training and test t,a single model that minimizes the average prediction error is lected from the various n-multifactor combinations,and the CV consistency is calculated.CV consistency is a measure of the number of times a particular t of multifactors is identified during the CV (Moore et al.,2002b).
Moreover,the whole process is repeated for different values of n,and the best combination is lected from among each possible dimension of combinations by repeating the above procedure.The result is a t of best models;one for each dimension.That is,for each different value of n,we have a list of the best models.
Furthermore,the above procedures are performed10times using different random number eds to reduce the probability of obrving spurious results due to chance divisions of the data.The average prediction errors and CV consistencies are calculated,and the best combination with a minimum average of prediction errors is lected.From the lected
combinations,Fig.1.Summary of OR MDR method.
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the model with the combination of genotypes that maximizes the CV con-sistency and minimizes the prediction error is lected.If the CV consistency is maximal for one model and the prediction error is minimal for another model,then the model with the lowest number of multifactors is lected. Once the MDR method identifies the best combination of multifactors, Stage2of the MDR method is performed.This involves classifying the multilocus genotype levels as high-or low-risk.However,the MDR binary classification of multilocus genotypes into the high-risk and low-risk groups is bad on a simple comparison of the ratios of the number of cas and controls to that of each multilocus genotype combination.
2.2OR MDR method
We propo the OR MDR method to improve the ad hoc classification of the MDR method.Figure1illustrates the procedure to implement the OR MDR method.Stage1is the same as th
at of the MDR method explained in ction2.1.In Stage2,the odds ratio for each combination of genotypes is ud as a quantitative measure of dia risk.
To illustrate the OR MDR method,we assume that two single nucleotide polymorphisms(SNPs;SNP1and SNP2)each with three genotypes are lected as the best model in Stage1.The two SNPs and a binary variable distinguishing cas and controls yield a3·3·2contingency table for N subjects.The obrved cell frequencies are denoted by{n ijk},where the subscripts i and j reprent the two SNPs and k reprents the dia(ca) and normal(control)phenotypes.The odds of the dia for the given genotype combination(SNP1¼i,SNP2¼j)is
P½Dia j SNP1¼i‚SNP2¼j
P½Normal j SNP1¼i‚SNP2¼j
当幸福来敲门 电影 2008¼P½SNP1¼i‚SNP2¼j j Dia
·
P½Dia
:
Then,the odds for the genotypes(i,j), ij is given as follows: P½SNP1¼i‚SNP2¼j j Dia
¼P½Dia j SNP1¼i‚SNP2¼j
/
P½Dia
:
Note that the righthand side is the odds of the dia for the genotypes (i,j)divided by the odds of the dia for all the data disregarding the genotype information.Then, ij is estimated as follows
^ ij ¼
n ij1/nþþ1
ij2þþ2
‚
where nþþk¼P
i
P
j
n ijk for k¼1,2.Note that this estimator is different
from the ordinary odds ratio estimator,becau the marginal sum n++k contains n ijk.We propo using the odds ratio estimator^ ij as a quantitative measure of dia risk for a given genotype combination.If this odds ratio is equal to one,then the odds of the ca for the given genotype combination is equal to the odds of the ca for the entire he risk associated with the dia for the given genotype combination is the same as the overall risk estimated from all the ca and control samples.Thus,this genotype combination is not associated with the dia.On the other hand,the larger the odds ratio(>1),the stronger the positive association between the genotype combination and the dia.Similarly,the lower the odds ratio(<1),the stronger the negative(protective)association between the genotype combination and the dia.
We can u ij as a quantitative measure to reprent the dia risk for a given genotype combination.As in the MDR method,each multifactor combination in n-dimensional space is labeled as‘high-risk’if the odds ratio exceeds the threshold,or as‘low-risk’if that threshold is not exceeded. If the threshold chon is one,the binary classification of the OR MDR method is the same as that of the MDR method.
In addition,we can compare combinations of genotypes by using the odds ratios.For example,two genotype combinations(SNP1¼i,SNP2¼j)and (SNP1¼i0,SNP2¼j0)can be compared using the two odds ratios ij and i0j0.That is,if ij> i0j0,then(SNP1¼i,SNP2¼j)has a higher risk than(SNP1¼
i0,SNP2¼j0).Bad on the values of ,we can order the combination of
genotypes from the highest risk group to the lowest risk group.
The relative dia risk among the genotype combinations can also be
compared by choosing a baline genotype combination.The most common
genotype combination is usually lected as the baline combination.As an
example,suppo the genotype combination(SNP1¼1,SNP2¼1)has the
largest frequency.Then,it is lected as a baline combination.For the
genotype combination(SNP1¼i,SNP2¼j),the ratio ij/ 11provides the
relative dia risk.In fact,the ratio is the ordinary odds ratio and the can
be compared with each other.
The propod OR MDR method also provides information on the accu-
racy of the odds ratio estimators.Unlike the original MDR method,the
OR MDR method provides a measure of accuracy by deriving a cell-specific
confidence interval for ij.We consider two types of confidence intervals:
one is the usual asymptotic confidence interval for the ratio of two success probabilities derived from the two independent binomial distributions,andang
the other is a bootstrap confidence interval that can be ud when the sample
size is not large.For the best combination obtained in Stage1,the bootstrap
samples are generated by randomly lecting cas and controls with replacement for each genotype combination.This resampling procedure
is repeated approximately100000times.Then,the empirical distributions
of odds ratios for each combination of genotypes are constructed.The
empirical confidence interval for each combination of genotypes can be八年级上册英语课文翻译
obtained from the bootstrap distributions.Finally,we can u the con-
fidence intervals of the odds ratios to conclude whether a particular genotype combination is significantly more or less associated with the dia than
another genotype combination.
3EXAMPLE
The datat obtained from the CDC Chronic Fatigue Syndrome
Rearch Group includes gene expression,proteomic,SNP and
heldclinical data.In this paper,we focus only on the SNP data.Informa-
tion pertaining to the42SNPs in the datat is described in Table1;
more information is available on the website(www.camda.
duke.edu/camda06/datats/index.html).Our analysis is bad on
55subjects ever having had chronic fatigue syndrome(CFS)and54
non-fatigued controls.In this analysis,we ud the35CFS subjects
and36non-fatigue subjects who do not have any missing SNP
values.
We applied the MDR and the OR MDR methods to all possible combinations of the42SNPs up to the fourth order.Table2sum-
marizes the CV consistency and the prediction errors obtained from
Stage1of the OR MDR method,which is identical to the MDR
method.One of the two-SNP models has a maximum CV consis-
tency of6.6out of10,and one of the four-SNP models has a
minimum prediction error of0.35.Generally,the combination of
SNPs that maximizes the CV consistency and minimizes the pre-
diction error is lected.In our example,however,the CV consis-
tency was maximum for one model and the prediction error was
minimum for an other model.Thus,the model with the fewer SNPs
jeans是什么意思was he two-SNP model comprising rs6196(NR3C1)
and rs140701(SLC6A4).
In Table3,the results of Stage2of the OR MDR method and the
MDR method are compared.Thefirst column reprents genotypes
of the best combination of two SNPs,rs6196(NR3C1)and rs140701
(SLC6A4),and the cond column shows their frequencies in the
cas and controls.The third column shows the binary classification
of high-risk and low-risk groups for each combination of genotypes.
Three combinations of genotypes are classified as high-risk,five
as low-risk,and one empty cell is undetermined.
Odds ratio bad multifactor-dimensionality reduction method
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However,the MDR method does not provide any information beyond simple binary classification.The
three high-risk genotype groups may have different dia risks.Moreover,the MDR method is vulnerable to fal positive and negative errors when the ratio of the numbers of cas and controls in a combination of genotypes is similar to that of the entire data,or when the numbers of cas and controls are very small.For example,consider the genotype AA/CC.Its frequency ratio in the cas and controls is equal to one,which is similar to the ratio for the entire data. Although AA/CC is classified as high-risk,a small change in this frequency can change this classification from the high-risk group to the low-risk group.Thus,the classification of AA/CC is vulnerable to fal positive error.On the other hand,although AA/ TT is classified as high risk,this combination is quite robust to a small change in the frequencies of the cas and controls.Thus,AA/ TT appears to show much stronger evidence for its classification as high risk.Unfortunately,the MDR method does not distinguish between the two combinations.Moreover,the number of cas and controls in AG/CC is very small;hence,the MDR method classifies AG/CC as low-risk.However,AG/CC is also vulnerable to fal negative error becau a small change in its frequencies can cau a change in its classification from the low-risk group to the high-risk group.
In the OR MDR method,however,the odds ratio provides a more rigorous quantitative measure of dia risk.For each combination of genotypes,the fourth column in Table3indicates the odds ratios;
thefifth column,its rank and the sixth column,its95%asymptotic confidence interval;the venth column,the95%confidence inter-val from the bootstrap samples.Note that the genotypes AG/CC, AG/CT and AG/TT have0frequencies,which made it difficult (impossible in the ca of AG/TT)to estimate a confidence interval by either method.
Both asymptotic and bootstrap confidence intervals provided consistent results.There is reasonably good evidence bad on the95%confidence interval that AA/TT is a high risk combination, but the large confidence intervals clearly show that there is little evidence regarding the other combinations—whereas the MDR classifies veral of them as high risk.If the upper(lower)limit of the confidence interval for one of the other combinations were less(greater)than1,that would be good evidence for a truly low (high)risk combination.Only the confidence interval of the cell with the genotype AA/TT does not contain1.The odds of dia for this genotype are2.674times that of the overall odds,showing positive association between the genotype of AA/TT and CFS. Therefore,we conclude that the risk of CFS is positively associated with two genotypes—AA and TT.
The ranks of the odds ratios indicate which is the highest-risk and lowest-risk group.We can also compare two different combi-nations of genotypes.For example,when the genotype AA/CC is ud as a baline combination of genotypes,the odds of dia for AA/TT is2.599(¼2.674/1.029)times l
arger than the odds of dia for AA/CC.
Thefirst SNP rs6196is located in nuclear receptor subfamily3; group C,member1glucocorticoid receptor(NR3C1),which regu-lates glucocorticoid levels in the blood.NR3C1was shown to have a significant association with CFS;this supports the hypothesis that medically unexplained chronic fatigue is heterogeneous and pre-nts preliminary evidence of the genetic mechanisms underlying a few of the putative conditions(Smith et al.,2006).In particular, different class of subjects with unexplained fatigue were distin-guished by gene polymorphsims that were involved in either hypothalanmic-pituitary-adrenal(HPA)axis function or neurotrans-mitter systems,including proopiomelanocortin(POMC),NR3C1, monoamine oxida A(MAOA),monoamine oxida B(MAOB) and tryptophan hydroxyla2(TPH2).Recently,Geortzel et al. (2006)showed that28well-lected SNPs could predict with 76%accuracy whether a person has CFS,and that the top three important genes are TPH2,catechol-O-methyltransfera(COMT) and NR3C1.rs6196,in particular,is a special ca of misn mutations in which a change in one nucleotide results in the sub-stitution of one amino acid that results in a non-functional protein. The other SNP rs140701is located in solutes carrier family6, neurotransmitter transporter,rotonin,member4(SLC6A4).Neu-roendocrine axis asssment is one of the best and safest approaches for the asssment of specific neurotransmitte
r function.Bad on the neuroendocrine respons in fatiguing disorders,Chaudhuri and Behan(2004)derived a biological model of central fatigue.
We expect rs140701,which is the sixth intronic SNP in SLC6A4, to play an important role as a transcription regulator.By examining the evolutionary origin and mechanisms of the differential transcrip-tional regulation of SLC6A4,Soeby et al.(2005)addresd the possible impact of the cond intronic variable number of tandem repeats(VNTR)on behavior and dia,and found new putative binding sites for veral transcription factors in the VNTRs of the mammalian SLC6A4gene.Further,Soeby et al.showed that the
黄薇薇Table1.List of42SNPs
Gene SNPs
CRHR1rs110402,rs242924,rs173365,rs242940,rs7209436,
rs1396862
SLC6A4rs140701,hCV7911132,rs2066713
MAOA rs979605,rs1801291,rs979606
NR3C1rs860458,rs258750,rs2918419,rs6188,rs1866388,rs852977 rs6196
COMT rs6269,rs4633,rs933271,rs4646312,rs5993882,rs740603 rs165722
TPH2rs10784941,rs2171363,rs4760816,rs1872824,rs4760750 rs1386486,rs1487280
TH rs2070762,rs4074905
POMC rs12473543
MAOB rs2283729,rs3027452,rs1799836
CRHR2rs2267710,rs2284217,rs2267714
Table2.Selection of the best combination of SNPs by Stage1of the OR MDR method and the MDR method
The best combination in
each dimension
Prediction error CV consistency
rs6196,rs1407010.366505 6.6
rs740603,rs6196,rs1407010.3819942
rs1799836,rs2171363,rs140701,
rs1396862
0.3544444
The model with maximum CV consistency and minimum prediction error is indicated in bold type.
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intronic VNTR has been lectively targeted through mammalian evolution tofine tune the transcriptional regulation of SLC6A4 expression.
In summary,it has been shown that rs6196of NR3C1regulates the HPA axis and rs140701of SLC6A is a neurotransmitter trans-porter.Thus,we hypothesize that rs6196and rs140701are impor-tant CFS-
related polymorphisms.In CFS-susceptible individuals, environmental stressors induce changes in the neuroendocrine axis mainly through the HPA axis and the norepinephrine system.Our analysis reveals a possible interaction between rs6196in NR3C1 and rs140701in SLC6A that is expected to play an important role in the biological mechanism of CFS.
4DISCUSSION AND CONCLUSION
In this paper,we propod the OR MDR method that us the odds ratio as a quantitative measure of dia risk.Similar to the original MDR method,the OR MDR method is a non-parametric approach and assumes no particular genetic model.In addition,as in the ca of the MDR method,the OR MDR method us CV to lect optimal models.
However,the OR MDR method has veral advantages over the original MDR method that us a binary measure of dia risk. First,the OR MDR method is bad on the odds ratio for each combination of genotypes and reveals more information regarding the effect of a certain genotype combination on the dia risk, since the quantitative value of the odds ratio reprents the strength of the association between the genotypes and dia.Second,the OR MDR method provides a more solid statistical validation by providing a confidence interval for each combination of
genotypes. In particular,when the number of cas is similar to the number of controls,or when both the number of cas and controls is too small,the validity of the MDR approach in determining the high-risk and low-risk groups is questionable.On the other hand, the confidence interval from the OR MDR method provides much more information for the high-risk and low-risk classification.If the upper(lower)limit of the confidence interval for one or other of the combinations is less(greater)than1,that is an evidence for a truly low(high)risk combination.We expect the OR MDR method to play a more important role than the MDR method in the identification of gene–gene interactions in real data. However,similar to the MDR method,the OR MDR method has the limitation that comes with having empty cells becau it cannot classify an empty cell as high risk or low risk.Further, confidence intervals cannot then be estimated by either the asymptotic method or bootstrap method.To solve this problem, a method bad on the continuity correction needs to be developed. Such a method will be prented in a parate paper in the near future.
Finally,note that the odds ratio we have ud for the OR MDR method is different from the ordinary odds ratio.One of the main reasons why we u for the OR MDR method is that we want to include MDR as a special ca of OR MDR.That is,if OR MDR us a binary classification with a threshold value of1,then it is equivalent to MDR.
ACKNOWLEDGEMENTS
The authors would like to thank the associate editor and two anon-ymous referees who comments were extremely helpful.This work was supported by the National Rearch Laboratory Program of Korea Science and Engineering Foundation(M10500000126),the Brain Korea21Project of the Ministry of Education,a grant of the Korea Health21R&D Project,Ministry of Health&Welfare,R.O. K(03-PJ10-PG13-GD01-0002),and grants from the U.S.Public Health Service:resource grant RR03655from the National Center for Rearch Resources;rearch grant GM-28356from the National Institute of General Medical Sciences;and Cancer Center Support Grant P30CAD43703from the National Cancer Institute. Conflict of Interest:none declared.
REFERENCES
al.(2001)Genomwide scans of complex human dia:true linkage is hard tofind.Am.J.Hum.Genet.,69,936–950.
Table3.Comparison between the results of Stage2of the MDR and OR MDR methods SNPs a
SNPs a Cell frequency b High/Low-risk c Odds ratio Rank d95%Asymptotic e CI95%Bootstrap f CI AA/CC10:10High 1.0292(0.489,2.162)(0.441,2.400)
二年级下册数学应用题100道AG/CC0:1Low07..
GG/CC5:8Low0.6435(0.233,1.775)(0.187,1.646)
AA/CT3:3High 1.0292(0.223,4.756)(0.205,5.143)
AG/CT0:1Low07..
GG/CT1:4Low0.2576(0.030,2.189)(0.000,1.543)
AA/TT13:5High 2.6741(1.065,6.714)(1.018,8.229)
delisAG/TT0:0.
GG/TT3:4Low0.7714(0.186,3.201)(0.171,6.171)
a The genotype before the solidus is rs6196(NR3C1gene)and that after the the solidus is rs140701(SLC6A4gene).
b The first number indicates the number of cas and the cond the number of controls in each cell.
c The threshol
d is th
e ratio o
f the total number of cas and controls,0.9722.
d Order of odds ratio.Th
e high risk genotype has the largest odds ratio value.
e Asymptotic confidence interval.
f Confidence interval bad on the100000bootstrap samples.
Odds ratio bad multifactor-dimensionality reduction method
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