odm: Outlier Dectection for Multi-replicated data

Description Usage Arguments Value References See Also Examples

Description

This function provides some routines for detecting outlying observations (peptides) for multi-replicated high-throughput data, especially in LC/MS experiments.

Usage

1
2
3
4
odm(x, k = 3, 
  quantreg = c("linear", "nonlin", "constant", "nonpar"), 
  method = c("proj", "diff", "pair", "grubbs", "dixon", 
  "iqr",  "siqr", "Zscore"), ...)

Arguments

x

data vectors or matrices. These can be given as named arguments. If the number of predictors is 2, x1 describes one n-by-1 vector for data and x2 describes the other n-by-1 vector for data (n= number of peptides, proteins, or genes)

k

non-negative tuning parameter for the outlier detection algorithm. For IQR-based algorithms such as 'iqr', 'siqr', 'proj', 'diff', and 'pair', it works in the formula of Q1-k*IQR and Q3+k*IQR, where IQR=Q3-Q1. For 'Zscore', it works for the 'k' in |Z| > k. A default value is 3.

quantreg

type of quantile regression models used for the outlier detection method. You can use one of the 'constant', 'linear', 'nonlin', and 'nonpar' which mean the constant, linear, non-linear, and non-parametric quantile regression in order. For more details, see the quantreg package.

method

type of outlier detection methods. You can select one of the 'Zscore', 'iqr', 'dixon', 'grubbs', 'pair', 'diff', and 'proj' algorithms as follows.
Zscore: Z-score based criterion (Cho and Eo, 2015)
iqr: Interquartile range (IQR) criterion (Cho and Eo, 2015)
siqr: Semi-interquartile range (IQR) criterion (Cho and Eo, 2015)
dixon: Dixon's test (Dixon, 1950; 1951)
grubbs: Grubbs test (Grubbs, 1950; 1969)
pair: Pariwise OutlierD algorithm (Cho et al., 2008; Eo et al., 2012)
proj: Projection-based OutlierD algortihm (Eo et al., 2012)
diff: Difference-based OutlierD algorithm (Eo and Cho, 2015)

...

minor tuning parameters used in odm.control(). See odm.control.

Value

call:

evaluated function call

raw.data:

raw dataset used in the model fitting

res:

result matrix of the model fitting. It consists of used data set with some transformation and outlying statistic.

x.pair:

Object of class "list"

k:

threshold parameter for constructing outlier detection methods

outlier:

matrix including the status of each outlying peptide and sample

n.outliers:

the number of outlying parameters (peptides) to be detected by the model fitting.

quantreg:

type of quantile regression used for the model fitting

method:

type of outlier detection method used for the model fitting

contrl.para:

a list of minor parameters

References

Eo, S-H and Cho, H (2015) OutlierDM: More robust outlier detection algorithms for multi-replicated high-throughput data.

Cho, H and Eo, S-H. (2015) Outlier detection for mass-spectrometry data.

Eo, S-H, Pak D, Choi J, Cho H (2012) Outlier detection using projection quantile regression for mass spectrometry data with low replication. BMC Res Notes.

Cho H, Lee JW, Kim Y-J, et al. (2008) OutlierD: an R package for outlier detection using quantile regression on mass spectrometry data. Bioinformatics 24:882–884.

Grubbs FE (1969) Procedures for detecting outlying observations in samples. Technometrics 11:1–21.

Dixon WJ (1951) Ratios involving extreme values. Ann Math Statistics 22:68–78.

Dixon WJ (1950) Analysis of extreme values. Ann Math Statistics 21:488–506.

Grubbs FE (1950) Sample criteria for testing outlying observations. Ann Math Statistics 21:27–58.

See Also

OutlierDM-package to provide the general information about the OutlierDC package
OutlierDM-class to provide the information about the "OutlierDM" class
odm.control to control tuning parameters

Examples

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
  ## Not run: 
    ##############################################################
    #
    #   Outlier Detection for Mass Spectrometry Data
    #   Section 3. Illustration
    #   by HyungJun Cho and Soo-Heang Eo,
    #   Dept of Statistics, Korea University, Seoul, Korea
    #
    ##############################################################

    #####
    # Load a package OutlierDM

    # If an OutlierDM package is not installed on your system, type
    #install.package('OutlierDM', dependency = TRUE)
    library(OutlierDM)

    #####
    # Sec 3.1 When the number of replicates is large enough
    ## Load toy dataset
    data(toy)
    head(toy)
    pairs(log2(toy), pch = 20, cex = .7)

    #####
    # Fit 1. Z-score based criterion
    fit1 = odm(x = toy, method = "Zscore", k = 3)
    fit1
    summary(fit1)
    head(input(fit1))
    head(output(fit1))
    print(outliers(fit1), digits = 3)
    plot(fit1)
    rect(1, -4, 10, 4, col = heat.colors(20,alpha = 0.3), border = heat.colors(20,alpha = 0.5))
    oneplot(object = fit1, i = 4)
    title("Outlier Detection by the Z-score criterion")

    # Add a peptide name on a dot-plot
    #oneplot(fit1, 191,1)
    #title("Outlier Detection by the Z-score criterion")

    #####
    # Fit 2. Grubbs test criteria
    fit2 = odm(x = toy, method ="grubbs", alpha = 0.01)
    fit2
    summary(fit2)
    head(output(fit2))
    print(outliers(fit2), digits = 3)
    oneplot(object = fit2, i = 1)
    title("Outlier Detection by the Grubbs criterion")

    # Add text
    #oneplot(fit2, 191,1)
    #title("Outlier Detection by the Grubbs criterion")

    #####
    # Fit 3. IQR criteria
    fit3 = odm(x = toy, method = "iqr", k = 3)
    fit3
    summary(fit3)
    print(outliers(fit3), digits = 3)
    plot(fit3)
    rect(1, -4, 10, 40, col = heat.colors(20,alpha = 0.3), border = heat.colors(20,alpha = 0.5))
    oneplot(fit3, 1)
    title("Outlier Detection by the IQR criterion")

    # Add a peptide name on a dot-plot
    #oneplot(fit3, 1, 1)
    #title("Outlier Detection by the IQR criterion")

    #####
    # Fit 4. SIQR criteria
    fit4 = odm(x = toy, method = "siqr", k = 3)
    fit4
    summary(fit4)
    print(outliers(fit4), digits = 3)
    plot(fit4)
    rect(1, -4, 10, 4, col = heat.colors(20,alpha = 0.3), border = heat.colors(20,alpha = 0.5))
    oneplot(fit4, 1)
    title("Outlier Detection by the SIQR criterion")

    #####################
    ## Real data example
    #####################
    data(lcms3)
    head(lcms3)
    pairs(log2(lcms3), pch = 20, cex = .7)

    #####
    # Fit 5. OutlierD
    fit5 = odm(lcms3[,1:2], method = "pair", k = 3)
    fit5
    summary(fit5)
    head(output(fit5))
    print(outliers(fit5), digits = 3)
    plot(fit5)
    title("Outlier Detection by the OutlierD algorithm")

    #####
    # Fit 6. OutlierDM 
    fit6 = odm(lcms3, method = "proj", k = 3, center = TRUE)
    fit6
    summary(fit6)
    print(outliers(fit6), digits = 3)
    plot(fit6)
    title("Outlier Detection by the OutlierDM algorithm")
    oneplot(fit6, 18)
    #oneplot(fit6, 18, 1)
    title("The dotplot for the 18th samples of the lcms3 data")
    ### End of the illustration

    
    #####
    # Other OutlierDM algorithms
    data(lcms3)
    
    ## Load 
    ## Fit projection approaches
    fit.proj.const <- odm(lcms3, quantreg="constant")
    fit.proj.linear <- odm(lcms3, quantreg="linear")
    fit.proj.nonlin <- odm(lcms3, quantreg="nonlin")
    fit.proj.nonpara <- odm(lcms3, quantreg="nonpar", lbda = 1)
    
    par(mfrow = c(2,2))
    plot(fit.proj.const, main = "Constant")
    plot(fit.proj.linear, main = "Linear")
    plot(fit.proj.nonlin, main = "NonLinear")
    plot(fit.proj.nonpara, main = "Nonparametric")

  
## End(Not run)

Example output

Package OutlierDM (1.1.1) loaded.
              Y1          Y2          Y3          Y4         Y5          Y6
[1,]    26783800    25999425    12261435    15899444 2917266265    41721220
[2,] 23590082416 26217449538 24966545767 25356948796  563871754 27198324106
[3,]   104073761   145261911   160333545   190778246  122346655   157835864
[4,]  1264867022  1136510555   949419238  1908955569  995395157  1944121226
[5,]   854562021   836104879  1494102552   757282589  551074573 31969323311
[6,]   463327911   573439414   463991305   563645631  630575491   596544140
              Y7          Y8          Y9         Y10         Y11         Y12
[1,]    28995062    19159370    23991286    14909836    22517745    28098385
[2,] 25123907000 30762477540 21573786718 32314611785 27542098540 18686856711
[3,]   141236692   161154539   110055848   119390039   183411946    88799743
[4,]  1374127749  1609172868  1240469934  1551775778   959126814  1441518203
[5,]   711510830   889235783  1114078381   807480809   730038584  1103440211
[6,]   685898577   488392855   898960080   647209727   625225322   492196078
             Y13         Y14         Y15
[1,]    18769087    31522265    13833118
[2,] 24379205665 23654728747 28706961292
[3,]   129488807   303499529     1564839
[4,]  1406965363 29832199806  1648536466
[5,]  1057219333   977140013   702802584
[6,]   651534620   578519247     4264738
Please wait... 

Call:
odm(x = toy, k = 3, method = "Zscore")

Outlier Detection for Multi-replicative High-throughput Data

 Method: Z-score criterion ( Zscore ) 
 k:  3 for |Z| > k 
 Number of Observations:  200 
 Number of Outliers:  10 
 Transformation:  log2 

 Head of the Output Results 
  Outlier    Z_Y1   Z_Y2    Z_Y3   Z_Y4   Z_Y5  Z_Y6    Z_Y7    Z_Y8     Z_Y9
1    TRUE -0.0954 -0.118 -0.6928 -0.494  3.491 0.244 -0.0347 -0.3515 -0.17956
2    TRUE  0.1778  0.284  0.2349  0.251 -3.581 0.321  0.2412  0.4451  0.08786
3    TRUE -0.0213  0.255  0.3374  0.482  0.113 0.324  0.2322  0.3417  0.02509
4    TRUE -0.3293 -0.458 -0.6748  0.166 -0.618 0.188 -0.2296 -0.0394 -0.35280
5    TRUE -0.2716 -0.294  0.3100 -0.397 -0.728 3.499 -0.4624 -0.2302  0.00445
6    TRUE  0.0702  0.236  0.0713  0.223  0.310 0.267  0.3758  0.1112  0.58657
    Z_Y10  Z_Y11    Z_Y12   Z_Y13   Z_Y14   Z_Y15   SD LB UB
1 -0.5433 -0.228 -0.05872 -0.3673  0.0292 -0.6006 1.89 -3  3
2  0.4946  0.334 -0.05677  0.2109  0.1806  0.3755 1.43 -3  3
3  0.0927  0.449 -0.15305  0.1601  0.8671 -3.5054 1.74 -3  3
4 -0.0832 -0.663 -0.17193 -0.2011  3.4766 -0.0103 1.20 -3  3
5 -0.3306 -0.436 -0.00554 -0.0501 -0.1321 -0.4752 1.39 -3  3
6  0.3306  0.304  0.11728  0.3358  0.2432 -3.5822 1.85 -3  3
To see the full information for the result, use a command, 'output(your_object_name)'. 

Call:
odm(x = toy, k = 3, method = "Zscore")

Outlier Detection for Multi-replicative High-throughput Data

 Method: Z-score criterion ( Zscore ) 
 k:  3 for |Z| > k 
 Number of Observations:  200 
 Number of Outliers:  10 
 Transformation:  log2 

 Head of the Input Data 
        Y1       Y2       Y3       Y4       Y5       Y6       Y7       Y8
1 2.68e+07 2.60e+07 1.23e+07 1.59e+07 2.92e+09 4.17e+07 2.90e+07 1.92e+07
2 2.36e+10 2.62e+10 2.50e+10 2.54e+10 5.64e+08 2.72e+10 2.51e+10 3.08e+10
3 1.04e+08 1.45e+08 1.60e+08 1.91e+08 1.22e+08 1.58e+08 1.41e+08 1.61e+08
4 1.26e+09 1.14e+09 9.49e+08 1.91e+09 9.95e+08 1.94e+09 1.37e+09 1.61e+09
5 8.55e+08 8.36e+08 1.49e+09 7.57e+08 5.51e+08 3.20e+10 7.12e+08 8.89e+08
6 4.63e+08 5.73e+08 4.64e+08 5.64e+08 6.31e+08 5.97e+08 6.86e+08 4.88e+08
        Y9      Y10      Y11      Y12      Y13      Y14      Y15
1 2.40e+07 1.49e+07 2.25e+07 2.81e+07 1.88e+07 3.15e+07 1.38e+07
2 2.16e+10 3.23e+10 2.75e+10 1.87e+10 2.44e+10 2.37e+10 2.87e+10
3 1.10e+08 1.19e+08 1.83e+08 8.88e+07 1.29e+08 3.03e+08 1.56e+06
4 1.24e+09 1.55e+09 9.59e+08 1.44e+09 1.41e+09 2.98e+10 1.65e+09
5 1.11e+09 8.07e+08 7.30e+08 1.10e+09 1.06e+09 9.77e+08 7.03e+08
6 8.99e+08 6.47e+08 6.25e+08 4.92e+08 6.52e+08 5.79e+08 4.26e+06
To see the full information of the input dataset, use a command, 'input(your_object_name)'. 

 Head of the Output Results 
  Outlier    Z_Y1   Z_Y2    Z_Y3   Z_Y4   Z_Y5  Z_Y6    Z_Y7    Z_Y8     Z_Y9
1    TRUE -0.0954 -0.118 -0.6928 -0.494  3.491 0.244 -0.0347 -0.3515 -0.17956
2    TRUE  0.1778  0.284  0.2349  0.251 -3.581 0.321  0.2412  0.4451  0.08786
3    TRUE -0.0213  0.255  0.3374  0.482  0.113 0.324  0.2322  0.3417  0.02509
4    TRUE -0.3293 -0.458 -0.6748  0.166 -0.618 0.188 -0.2296 -0.0394 -0.35280
5    TRUE -0.2716 -0.294  0.3100 -0.397 -0.728 3.499 -0.4624 -0.2302  0.00445
6    TRUE  0.0702  0.236  0.0713  0.223  0.310 0.267  0.3758  0.1112  0.58657
    Z_Y10  Z_Y11    Z_Y12   Z_Y13   Z_Y14   Z_Y15   SD LB UB
1 -0.5433 -0.228 -0.05872 -0.3673  0.0292 -0.6006 1.89 -3  3
2  0.4946  0.334 -0.05677  0.2109  0.1806  0.3755 1.43 -3  3
3  0.0927  0.449 -0.15305  0.1601  0.8671 -3.5054 1.74 -3  3
4 -0.0832 -0.663 -0.17193 -0.2011  3.4766 -0.0103 1.20 -3  3
5 -0.3306 -0.436 -0.00554 -0.0501 -0.1321 -0.4752 1.39 -3  3
6  0.3306  0.304  0.11728  0.3358  0.2432 -3.5822 1.85 -3  3
To see the full information for the result, use a command, 'output(your_object_name)'. 

 Head of the Peptide Numbers detected to be an Outlier
 [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10"
To see the full information for the candidate outliers, use a command, 'outliers(your_object_name)'. 
           Y1          Y2          Y3          Y4         Y5          Y6
1    26783800    25999425    12261435    15899444 2917266265    41721220
2 23590082416 26217449538 24966545767 25356948796  563871754 27198324106
3   104073761   145261911   160333545   190778246  122346655   157835864
4  1264867022  1136510555   949419238  1908955569  995395157  1944121226
5   854562021   836104879  1494102552   757282589  551074573 31969323311
6   463327911   573439414   463991305   563645631  630575491   596544140
           Y7          Y8          Y9         Y10         Y11         Y12
1    28995062    19159370    23991286    14909836    22517745    28098385
2 25123907000 30762477540 21573786718 32314611785 27542098540 18686856711
3   141236692   161154539   110055848   119390039   183411946    88799743
4  1374127749  1609172868  1240469934  1551775778   959126814  1441518203
5   711510830   889235783  1114078381   807480809   730038584  1103440211
6   685898577   488392855   898960080   647209727   625225322   492196078
          Y13         Y14         Y15
1    18769087    31522265    13833118
2 24379205665 23654728747 28706961292
3   129488807   303499529     1564839
4  1406965363 29832199806  1648536466
5  1057219333   977140013   702802584
6   651534620   578519247     4264738
  Outlier       Y1       Y2       Y3       Y4       Y5       Y6       Y7
1    TRUE 24.67486 24.63198 23.54762 23.92247 31.44197 25.31428 24.78930
2    TRUE 34.45746 34.60981 34.53928 34.56166 29.07079 34.66280 34.54834
3    TRUE 26.63303 27.11408 27.25650 27.50732 26.86640 27.23385 27.07354
4    TRUE 30.23634 30.08196 29.82247 30.83014 29.89069 30.85647 30.35587
5    TRUE 29.67061 29.63911 30.47663 29.49626 29.03767 34.89597 29.40631
6    TRUE 28.78746 29.09507 28.78952 29.07021 29.23209 29.15205 29.35342
        Y8       Y9      Y10      Y11      Y12      Y13      Y14      Y15
1 24.19155 24.51601 23.82976 24.42456 24.74398 24.16186 24.90987 23.72162
2 34.84045 34.32856 34.91147 34.68092 34.12130 34.50493 34.46141 34.74068
3 27.26387 26.71366 26.83111 27.45051 26.40405 26.94825 28.17712 20.57758
4 30.58367 30.20824 30.53127 29.83715 30.42494 30.38994 34.79615 30.61854
5 29.72799 30.05320 29.58885 29.44340 30.03936 29.97763 29.86399 29.38854
6 28.86347 29.74368 29.26966 29.21980 28.87466 29.27927 29.10779 22.02403
         Z_Y1       Z_Y2        Z_Y3       Z_Y4       Z_Y5      Z_Y6       Z_Y7
1 -0.09536193 -0.1180897 -0.69281657 -0.4941398  3.4913351 0.2435431 -0.0347031
2  0.17781271  0.2841269  0.23490724  0.2505284 -3.5812350 0.3211058  0.2412329
3 -0.02130445  0.2554765  0.33742035  0.4817344  0.1129682 0.3243875  0.2321502
4 -0.32934778 -0.4581996 -0.67479138  0.1662774 -0.6178468 0.1882581 -0.2295793
5 -0.27163296 -0.2943647  0.31000233 -0.3974485 -0.7283684 3.4990495 -0.4623547
6  0.07019154  0.2363051  0.07130623  0.2228842  0.3103027 0.2670795  0.3758210
         Z_Y8         Z_Y9       Z_Y10      Z_Y11        Z_Y12       Z_Y13
1 -0.35152563 -0.179555502 -0.54327887 -0.2280248 -0.058723561 -0.36726276
2  0.44508032  0.087860070  0.49463759  0.3337512 -0.056771661  0.21093976
3  0.34165996  0.025087160  0.09266224  0.4490483 -0.153051687  0.16006371
4 -0.03943888 -0.352801128 -0.08317492 -0.6625415 -0.171926255 -0.20114157
5 -0.23022628  0.004451239 -0.33062996 -0.4355922 -0.005537515 -0.05008534
6  0.11123749  0.586569339  0.33058802  0.3036643  0.117280868  0.33577680
        Z_Y14       Z_Y15       SD LB UB
1  0.02919807 -0.60059406 1.886725 -3  3
2  0.18056790  0.37545581 1.432988 -3  3
3  0.86711471 -3.50541721 1.738017 -3  3
4  3.47659061 -0.01033688 1.198078 -3  3
5 -0.13208754 -0.47517499 1.385786 -3  3
6  0.24317622 -3.58218329 1.851790 -3  3
   Outlier    Y1   Y2   Y3   Y4    Y5   Y6    Y7   Y8   Y9   Y10  Y11   Y12
1     TRUE 24.67 24.6 23.5 23.9 31.44 25.3 24.79 24.2 24.5 23.83 24.4 24.74
2     TRUE 34.46 34.6 34.5 34.6 29.07 34.7 34.55 34.8 34.3 34.91 34.7 34.12
3     TRUE 26.63 27.1 27.3 27.5 26.87 27.2 27.07 27.3 26.7 26.83 27.5 26.40
4     TRUE 30.24 30.1 29.8 30.8 29.89 30.9 30.36 30.6 30.2 30.53 29.8 30.42
5     TRUE 29.67 29.6 30.5 29.5 29.04 34.9 29.41 29.7 30.1 29.59 29.4 30.04
6     TRUE 28.79 29.1 28.8 29.1 29.23 29.2 29.35 28.9 29.7 29.27 29.2 28.87
7     TRUE 30.95 31.0 25.6 31.3 31.46 30.9 31.60 31.6 31.6 31.97 31.7 31.27
8     TRUE  9.25 11.1 10.6 30.5  6.32 13.2  6.16  5.3 15.7  7.14 12.8  1.27
9     TRUE 34.78 35.3 29.8 35.3 35.13 34.8 35.08 34.9 35.0 34.86 35.0 34.45
10    TRUE 23.85 23.3 24.2 24.7 24.27 24.4 24.54 22.9 23.7 24.56 14.6 22.84
     Y13  Y14   Y15    Z_Y1    Z_Y2    Z_Y3   Z_Y4   Z_Y5    Z_Y6    Z_Y7
1  24.16 24.9 23.72 -0.0954 -0.1181 -0.6928 -0.494  3.491  0.2435 -0.0347
2  34.50 34.5 34.74  0.1778  0.2841  0.2349  0.251 -3.581  0.3211  0.2412
3  26.95 28.2 20.58 -0.0213  0.2555  0.3374  0.482  0.113  0.3244  0.2322
4  30.39 34.8 30.62 -0.3293 -0.4582 -0.6748  0.166 -0.618  0.1883 -0.2296
5  29.98 29.9 29.39 -0.2716 -0.2944  0.3100 -0.397 -0.728  3.4990 -0.4624
6  29.28 29.1 22.02  0.0702  0.2363  0.0713  0.223  0.310  0.2671  0.3758
7  31.25 31.7 31.58 -0.0557 -0.0454 -3.5420  0.191  0.277 -0.0617  0.3666
8   8.64  8.5  9.47 -0.1724  0.1042  0.0302  3.048 -0.617  0.4194 -0.6416
9  34.97 34.8 34.76  0.1331  0.5088 -3.5666  0.544  0.395  0.1560  0.3552
10 24.75 24.9 23.60  0.1766 -0.0354  0.2982  0.519  0.343  0.3792  0.4463
      Z_Y8     Z_Y9   Z_Y10  Z_Y11    Z_Y12   Z_Y13   Z_Y14   Z_Y15   SD LB UB
1  -0.3515 -0.17956 -0.5433 -0.228 -0.05872 -0.3673  0.0292 -0.6006 1.89 -3  3
2   0.4451  0.08786  0.4946  0.334 -0.05677  0.2109  0.1806  0.3755 1.43 -3  3
3   0.3417  0.02509  0.0927  0.449 -0.15305  0.1601  0.8671 -3.5054 1.74 -3  3
4  -0.0394 -0.35280 -0.0832 -0.663 -0.17193 -0.2011  3.4766 -0.0103 1.20 -3  3
5  -0.2302  0.00445 -0.3306 -0.436 -0.00554 -0.0501 -0.1321 -0.4752 1.39 -3  3
6   0.1112  0.58657  0.3306  0.304  0.11728  0.3358  0.2432 -3.5822 1.85 -3  3
7   0.3382  0.39092  0.6139  0.440  0.15551  0.1410  0.4337  0.3573 1.53 -3  3
8  -0.7720  0.80280 -0.4930  0.365 -1.38238 -0.2656 -0.2863 -0.1388 6.59 -3  3
9   0.2449  0.31062  0.1934  0.273 -0.11471  0.2725  0.1750  0.1199 1.34 -3  3
10 -0.2023  0.12034  0.4547 -3.490 -0.22569  0.5324  0.6063  0.0777 2.53 -3  3
       Z_Y1        Z_Y2        Z_Y3        Z_Y4        Z_Y5        Z_Y6 
-0.32934778 -0.45819964 -0.67479138  0.16627737 -0.61784679  0.18825811 
       Z_Y7        Z_Y8        Z_Y9       Z_Y10       Z_Y11       Z_Y12 
-0.22957934 -0.03943888 -0.35280113 -0.08317492 -0.66254152 -0.17192626 
      Z_Y13       Z_Y14       Z_Y15 
-0.20114157  3.47659061 -0.01033688 
Please wait... 

Call:
odm(x = toy, method = "grubbs", alpha = 0.01)

Outlier Detection for Multi-replicative High-throughput Data

 Method: Grubbs test ( grubbs ) 
 Number of Observations:  200 
 Number of Outliers:  12 
 Transformation:  log2 

 Head of the Output Results 
  Outlier G1 G2 G3 G4     G5    G6 G7 G8    G9 G10 G11 G12 G13   G14    G15
1    TRUE  .  .  .  .  3.491     .  .  .     .   .   .   .   .     .      .
2    TRUE  .  .  .  . -3.581     .  .  .     .   .   .   .   .     .      .
3    TRUE  .  .  .  .      .     .  .  .     .   .   .   .   . 2.434 -3.505
4    TRUE  .  .  .  .      .     .  .  .     .   .   .   .   . 3.477      .
5    TRUE  .  .  .  .      . 3.499  .  .     .   .   .   .   .     .      .
6    TRUE  .  .  .  .      .     .  .  . 2.378   .   .   .   .     . -3.582
To see the full information for the result, use a command, 'output(your_object_name)'. 

Call:
odm(x = toy, method = "grubbs", alpha = 0.01)

Outlier Detection for Multi-replicative High-throughput Data

 Method: Grubbs test ( grubbs ) 
 Number of Observations:  200 
 Number of Outliers:  12 
 Transformation:  log2 

 Head of the Input Data 
        Y1       Y2       Y3       Y4       Y5       Y6       Y7       Y8
1 2.68e+07 2.60e+07 1.23e+07 1.59e+07 2.92e+09 4.17e+07 2.90e+07 1.92e+07
2 2.36e+10 2.62e+10 2.50e+10 2.54e+10 5.64e+08 2.72e+10 2.51e+10 3.08e+10
3 1.04e+08 1.45e+08 1.60e+08 1.91e+08 1.22e+08 1.58e+08 1.41e+08 1.61e+08
4 1.26e+09 1.14e+09 9.49e+08 1.91e+09 9.95e+08 1.94e+09 1.37e+09 1.61e+09
5 8.55e+08 8.36e+08 1.49e+09 7.57e+08 5.51e+08 3.20e+10 7.12e+08 8.89e+08
6 4.63e+08 5.73e+08 4.64e+08 5.64e+08 6.31e+08 5.97e+08 6.86e+08 4.88e+08
        Y9      Y10      Y11      Y12      Y13      Y14      Y15
1 2.40e+07 1.49e+07 2.25e+07 2.81e+07 1.88e+07 3.15e+07 1.38e+07
2 2.16e+10 3.23e+10 2.75e+10 1.87e+10 2.44e+10 2.37e+10 2.87e+10
3 1.10e+08 1.19e+08 1.83e+08 8.88e+07 1.29e+08 3.03e+08 1.56e+06
4 1.24e+09 1.55e+09 9.59e+08 1.44e+09 1.41e+09 2.98e+10 1.65e+09
5 1.11e+09 8.07e+08 7.30e+08 1.10e+09 1.06e+09 9.77e+08 7.03e+08
6 8.99e+08 6.47e+08 6.25e+08 4.92e+08 6.52e+08 5.79e+08 4.26e+06
To see the full information of the input dataset, use a command, 'input(your_object_name)'. 

 Head of the Output Results 
  Outlier G1 G2 G3 G4                G5               G6 G7 G8               G9
1    TRUE  .  .  .  .  3.49133507967136                .  .  .                .
2    TRUE  .  .  .  . -3.58123496282741                .  .  .                .
3    TRUE  .  .  .  .                 .                .  .  .                .
4    TRUE  .  .  .  .                 .                .  .  .                .
5    TRUE  .  .  .  .                 . 3.49904951444859  .  .                .
6    TRUE  .  .  .  .                 .                .  .  . 2.37810886505246
  G10 G11 G12 G13              G14               G15
1   .   .   .   .                .                 .
2   .   .   .   .                .                 .
3   .   .   .   .  2.4344103286513 -3.50541721005009
4   .   .   .   . 3.47659061386896                 .
5   .   .   .   .                .                 .
6   .   .   .   .                . -3.58218328957321
To see the full information for the result, use a command, 'output(your_object_name)'. 

 Head of the Peptide Numbers detected to be an Outlier
 [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10"
To see the full information for the candidate outliers, use a command, 'outliers(your_object_name)'. 
  Outlier       Y1       Y2       Y3       Y4       Y5       Y6       Y7
1    TRUE 24.67486 24.63198 23.54762 23.92247 31.44197 25.31428 24.78930
2    TRUE 34.45746 34.60981 34.53928 34.56166 29.07079 34.66280 34.54834
3    TRUE 26.63303 27.11408 27.25650 27.50732 26.86640 27.23385 27.07354
4    TRUE 30.23634 30.08196 29.82247 30.83014 29.89069 30.85647 30.35587
5    TRUE 29.67061 29.63911 30.47663 29.49626 29.03767 34.89597 29.40631
6    TRUE 28.78746 29.09507 28.78952 29.07021 29.23209 29.15205 29.35342
        Y8       Y9      Y10      Y11      Y12      Y13      Y14      Y15 G1 G2
1 24.19155 24.51601 23.82976 24.42456 24.74398 24.16186 24.90987 23.72162 NA NA
2 34.84045 34.32856 34.91147 34.68092 34.12130 34.50493 34.46141 34.74068 NA NA
3 27.26387 26.71366 26.83111 27.45051 26.40405 26.94825 28.17712 20.57758 NA NA
4 30.58367 30.20824 30.53127 29.83715 30.42494 30.38994 34.79615 30.61854 NA NA
5 29.72799 30.05320 29.58885 29.44340 30.03936 29.97763 29.86399 29.38854 NA NA
6 28.86347 29.74368 29.26966 29.21980 28.87466 29.27927 29.10779 22.02403 NA NA
  G3 G4        G5      G6 G7 G8       G9 G10 G11 G12 G13      G14       G15
1 NA NA  3.491335      NA NA NA       NA  NA  NA  NA  NA       NA        NA
2 NA NA -3.581235      NA NA NA       NA  NA  NA  NA  NA       NA        NA
3 NA NA        NA      NA NA NA       NA  NA  NA  NA  NA 2.434410 -3.505417
4 NA NA        NA      NA NA NA       NA  NA  NA  NA  NA 3.476591        NA
5 NA NA        NA 3.49905 NA NA       NA  NA  NA  NA  NA       NA        NA
6 NA NA        NA      NA NA NA 2.378109  NA  NA  NA  NA       NA -3.582183
    Outlier    Y1   Y2   Y3   Y4    Y5   Y6    Y7   Y8   Y9   Y10  Y11   Y12
1      TRUE 24.67 24.6 23.5 23.9 31.44 25.3 24.79 24.2 24.5 23.83 24.4 24.74
2      TRUE 34.46 34.6 34.5 34.6 29.07 34.7 34.55 34.8 34.3 34.91 34.7 34.12
3      TRUE 26.63 27.1 27.3 27.5 26.87 27.2 27.07 27.3 26.7 26.83 27.5 26.40
4      TRUE 30.24 30.1 29.8 30.8 29.89 30.9 30.36 30.6 30.2 30.53 29.8 30.42
5      TRUE 29.67 29.6 30.5 29.5 29.04 34.9 29.41 29.7 30.1 29.59 29.4 30.04
6      TRUE 28.79 29.1 28.8 29.1 29.23 29.2 29.35 28.9 29.7 29.27 29.2 28.87
7      TRUE 30.95 31.0 25.6 31.3 31.46 30.9 31.60 31.6 31.6 31.97 31.7 31.27
8      TRUE  9.25 11.1 10.6 30.5  6.32 13.2  6.16  5.3 15.7  7.14 12.8  1.27
9      TRUE 34.78 35.3 29.8 35.3 35.13 34.8 35.08 34.9 35.0 34.86 35.0 34.45
10     TRUE 23.85 23.3 24.2 24.7 24.27 24.4 24.54 22.9 23.7 24.56 14.6 22.84
41     TRUE 22.00 23.2 22.1 22.0 20.96 21.8 22.56 19.0 22.0 20.95 22.3 21.40
186    TRUE 13.81 12.9 13.1 13.1 12.38 13.9 13.78 14.2 12.7 14.01 14.0 16.56
      Y13  Y14   Y15 G1 G2    G3   G4    G5  G6 G7    G8   G9 G10   G11  G12
1   24.16 24.9 23.72 NA NA    NA   NA  3.49  NA NA    NA   NA  NA    NA   NA
2   34.50 34.5 34.74 NA NA    NA   NA -3.58  NA NA    NA   NA  NA    NA   NA
3   26.95 28.2 20.58 NA NA    NA   NA    NA  NA NA    NA   NA  NA    NA   NA
4   30.39 34.8 30.62 NA NA    NA   NA    NA  NA NA    NA   NA  NA    NA   NA
5   29.98 29.9 29.39 NA NA    NA   NA    NA 3.5 NA    NA   NA  NA    NA   NA
6   29.28 29.1 22.02 NA NA    NA   NA    NA  NA NA    NA 2.38  NA    NA   NA
7   31.25 31.7 31.58 NA NA -3.54   NA    NA  NA NA    NA   NA  NA    NA   NA
8    8.64  8.5  9.47 NA NA    NA 3.05    NA  NA NA    NA   NA  NA    NA   NA
9   34.97 34.8 34.76 NA NA -3.57   NA    NA  NA NA    NA   NA  NA    NA   NA
10  24.75 24.9 23.60 NA NA    NA   NA    NA  NA NA    NA   NA  NA -3.49   NA
41  21.56 22.3 22.03 NA NA    NA   NA    NA  NA NA -2.88   NA  NA    NA   NA
186 12.65 12.9 13.45 NA NA    NA   NA    NA  NA NA    NA   NA  NA    NA 2.96
    G13  G14   G15
1    NA   NA    NA
2    NA   NA    NA
3    NA 2.43 -3.51
4    NA 3.48    NA
5    NA   NA    NA
6    NA   NA -3.58
7    NA   NA    NA
8    NA   NA    NA
9    NA   NA    NA
10   NA   NA    NA
41   NA   NA    NA
186  NA   NA    NA
      Y1       Y2       Y3       Y4       Y5       Y6       Y7       Y8 
24.67486 24.63198 23.54762 23.92247 31.44197 25.31428 24.78930 24.19155 
      Y9      Y10      Y11      Y12      Y13      Y14      Y15 
24.51601 23.82976 24.42456 24.74398 24.16186 24.90987 23.72162 
Please wait... 

Call:
odm(x = toy, k = 3, method = "iqr")

Outlier Detection for Multi-replicative High-throughput Data

 Method: Interquartile range (IQR) criterion ( iqr ) 
 k:  3 for k * IQR
 Number of Observations:  200 
 Number of Outliers:  15 
 Transformation:  log2 

 Head of the Output Results 
  Outlier   Y1   Y2   Y3   Y4   Y5   Y6   Y7   Y8   Y9  Y10  Y11  Y12  Y13  Y14
1    TRUE 24.7 24.6 23.5 23.9 31.4 25.3 24.8 24.2 24.5 23.8 24.4 24.7 24.2 24.9
2    TRUE 34.5 34.6 34.5 34.6 29.1 34.7 34.5 34.8 34.3 34.9 34.7 34.1 34.5 34.5
3    TRUE 26.6 27.1 27.3 27.5 26.9 27.2 27.1 27.3 26.7 26.8 27.5 26.4 26.9 28.2
4    TRUE 30.2 30.1 29.8 30.8 29.9 30.9 30.4 30.6 30.2 30.5 29.8 30.4 30.4 34.8
5    TRUE 29.7 29.6 30.5 29.5 29.0 34.9 29.4 29.7 30.1 29.6 29.4 30.0 30.0 29.9
6    TRUE 28.8 29.1 28.8 29.1 29.2 29.2 29.4 28.9 29.7 29.3 29.2 28.9 29.3 29.1
   Y15   Q1   Q2   Q3   LB   UB
1 23.7 24.0 24.5 24.8 21.9 26.9
2 34.7 34.5 34.5 34.7 33.8 35.3
3 20.6 26.8 27.1 27.3 25.3 28.7
4 30.6 30.1 30.4 30.6 28.8 32.0
5 29.4 29.5 29.7 30.0 27.9 31.6
6 22.0 28.9 29.1 29.3 27.7 30.4
To see the full information for the result, use a command, 'output(your_object_name)'. 

Call:
odm(x = toy, k = 3, method = "iqr")

Outlier Detection for Multi-replicative High-throughput Data

 Method: Interquartile range (IQR) criterion ( iqr ) 
 k:  3 for k * IQR
 Number of Observations:  200 
 Number of Outliers:  15 
 Transformation:  log2 

 Head of the Input Data 
        Y1       Y2       Y3       Y4       Y5       Y6       Y7       Y8
1 2.68e+07 2.60e+07 1.23e+07 1.59e+07 2.92e+09 4.17e+07 2.90e+07 1.92e+07
2 2.36e+10 2.62e+10 2.50e+10 2.54e+10 5.64e+08 2.72e+10 2.51e+10 3.08e+10
3 1.04e+08 1.45e+08 1.60e+08 1.91e+08 1.22e+08 1.58e+08 1.41e+08 1.61e+08
4 1.26e+09 1.14e+09 9.49e+08 1.91e+09 9.95e+08 1.94e+09 1.37e+09 1.61e+09
5 8.55e+08 8.36e+08 1.49e+09 7.57e+08 5.51e+08 3.20e+10 7.12e+08 8.89e+08
6 4.63e+08 5.73e+08 4.64e+08 5.64e+08 6.31e+08 5.97e+08 6.86e+08 4.88e+08
        Y9      Y10      Y11      Y12      Y13      Y14      Y15
1 2.40e+07 1.49e+07 2.25e+07 2.81e+07 1.88e+07 3.15e+07 1.38e+07
2 2.16e+10 3.23e+10 2.75e+10 1.87e+10 2.44e+10 2.37e+10 2.87e+10
3 1.10e+08 1.19e+08 1.83e+08 8.88e+07 1.29e+08 3.03e+08 1.56e+06
4 1.24e+09 1.55e+09 9.59e+08 1.44e+09 1.41e+09 2.98e+10 1.65e+09
5 1.11e+09 8.07e+08 7.30e+08 1.10e+09 1.06e+09 9.77e+08 7.03e+08
6 8.99e+08 6.47e+08 6.25e+08 4.92e+08 6.52e+08 5.79e+08 4.26e+06
To see the full information of the input dataset, use a command, 'input(your_object_name)'. 

 Head of the Output Results 
  Outlier   Y1   Y2   Y3   Y4   Y5   Y6   Y7   Y8   Y9  Y10  Y11  Y12  Y13  Y14
1    TRUE 24.7 24.6 23.5 23.9 31.4 25.3 24.8 24.2 24.5 23.8 24.4 24.7 24.2 24.9
2    TRUE 34.5 34.6 34.5 34.6 29.1 34.7 34.5 34.8 34.3 34.9 34.7 34.1 34.5 34.5
3    TRUE 26.6 27.1 27.3 27.5 26.9 27.2 27.1 27.3 26.7 26.8 27.5 26.4 26.9 28.2
4    TRUE 30.2 30.1 29.8 30.8 29.9 30.9 30.4 30.6 30.2 30.5 29.8 30.4 30.4 34.8
5    TRUE 29.7 29.6 30.5 29.5 29.0 34.9 29.4 29.7 30.1 29.6 29.4 30.0 30.0 29.9
6    TRUE 28.8 29.1 28.8 29.1 29.2 29.2 29.4 28.9 29.7 29.3 29.2 28.9 29.3 29.1
   Y15   Q1   Q2   Q3   LB   UB
1 23.7 24.0 24.5 24.8 21.9 26.9
2 34.7 34.5 34.5 34.7 33.8 35.3
3 20.6 26.8 27.1 27.3 25.3 28.7
4 30.6 30.1 30.4 30.6 28.8 32.0
5 29.4 29.5 29.7 30.0 27.9 31.6
6 22.0 28.9 29.1 29.3 27.7 30.4
To see the full information for the result, use a command, 'output(your_object_name)'. 

 Head of the Peptide Numbers detected to be an Outlier
 [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10"
To see the full information for the candidate outliers, use a command, 'outliers(your_object_name)'. 
    Outlier    Y1    Y2    Y3    Y4    Y5     Y6    Y7    Y8    Y9   Y10  Y11
1      TRUE 24.67 24.63 23.55 23.92 31.44 25.314 24.79 24.19 24.52 23.83 24.4
2      TRUE 34.46 34.61 34.54 34.56 29.07 34.663 34.55 34.84 34.33 34.91 34.7
3      TRUE 26.63 27.11 27.26 27.51 26.87 27.234 27.07 27.26 26.71 26.83 27.5
4      TRUE 30.24 30.08 29.82 30.83 29.89 30.856 30.36 30.58 30.21 30.53 29.8
5      TRUE 29.67 29.64 30.48 29.50 29.04 34.896 29.41 29.73 30.05 29.59 29.4
6      TRUE 28.79 29.10 28.79 29.07 29.23 29.152 29.35 28.86 29.74 29.27 29.2
7      TRUE 30.95 30.97 25.62 31.33 31.46 30.941 31.60 31.55 31.63 31.97 31.7
8      TRUE  9.25 11.07 10.59 30.48  6.32 13.151  6.16  5.30 15.68  7.14 12.8
9      TRUE 34.78 35.28 29.83 35.33 35.13 34.812 35.08 34.93 35.02 34.86 35.0
10     TRUE 23.85 23.32 24.16 24.72 24.27 24.367 24.54 22.90 23.71 24.56 14.6
12     TRUE 11.56 15.49 14.75 16.13 12.22 16.280 14.70 14.86 13.10 15.10 14.7
41     TRUE 22.00 23.18 22.09 22.00 20.96 21.847 22.56 19.01 22.04 20.95 22.3
68     TRUE  5.97  6.35  3.75  6.98  5.21  0.839 10.62  5.75  5.86  6.46 10.9
86     TRUE 10.63 10.93  8.20 17.06 11.93 11.930 11.20 10.57 18.94  8.64 12.0
111    TRUE 31.83 31.95 31.77 31.84 31.84 32.083 31.85 31.26 32.05 32.30 31.8
      Y12   Y13   Y14   Y15    Q1    Q2    Q3    LB   UB
1   24.74 24.16 24.91 23.72 24.04 24.52 24.77 21.87 26.9
2   34.12 34.50 34.46 34.74 34.46 34.55 34.67 33.82 35.3
3   26.40 26.95 28.18 20.58 26.77 27.07 27.26 25.31 28.7
4   30.42 30.39 34.80 30.62 30.15 30.39 30.60 28.78 32.0
5   30.04 29.98 29.86 29.39 29.47 29.67 30.01 27.85 31.6
6   28.87 29.28 29.11 22.02 28.87 29.11 29.25 27.72 30.4
7   31.27 31.25 31.70 31.58 31.11 31.46 31.61 29.59 33.1
8    1.27  8.64  8.50  9.47  6.73  9.25 11.93 -8.89 27.5
9   34.45 34.97 34.84 34.76 34.80 34.93 35.05 34.04 35.8
10  22.84 24.75 24.94 23.60 23.46 24.16 24.55 20.20 27.8
12  15.25 15.32 14.93 16.77 14.69 14.93 15.41 12.55 17.6
41  21.40 21.56 22.32 22.03 21.48 22.00 22.20 19.32 24.4
68   5.85  7.10  7.79  7.29  5.80  6.35  7.19  1.63 11.4
86  12.90 12.21 15.05 10.37 10.60 11.93 12.55  4.73 18.4
111 31.62 31.85 31.36 31.94 31.79 31.84 31.94 31.31 32.4
      Y1       Y2       Y3       Y4       Y5       Y6       Y7       Y8 
24.67486 24.63198 23.54762 23.92247 31.44197 25.31428 24.78930 24.19155 
      Y9      Y10      Y11      Y12      Y13      Y14      Y15 
24.51601 23.82976 24.42456 24.74398 24.16186 24.90987 23.72162 
Please wait... 

Call:
odm(x = toy, k = 3, method = "siqr")

Outlier Detection for Multi-replicative High-throughput Data

 Method: Semiinterquartile range (SIQR) criterion ( siqr ) 
 k:  3 for 2k * SIQR 
 Number of Observations:  200 
 Number of Outliers:  28 
 Transformation:  log2 

 Head of the Output Results 
  Outlier   Y1   Y2   Y3   Y4   Y5   Y6   Y7   Y8   Y9  Y10  Y11  Y12  Y13  Y14
1    TRUE 24.7 24.6 23.5 23.9 31.4 25.3 24.8 24.2 24.5 23.8 24.4 24.7 24.2 24.9
2    TRUE 34.5 34.6 34.5 34.6 29.1 34.7 34.5 34.8 34.3 34.9 34.7 34.1 34.5 34.5
3    TRUE 26.6 27.1 27.3 27.5 26.9 27.2 27.1 27.3 26.7 26.8 27.5 26.4 26.9 28.2
4    TRUE 30.2 30.1