README.md
In rsait/ORdensity: ORdensity: User-friendly R package to identify Differentially Expressed genes
ORdensity
In this repository is located the R package ORdensity that implements the statistical method presented in the paper Identification of differentially expressed genes by means of outlier detection by Irigoien and Arenas, BMC Bioinformatics 2018 ([1]).
Introduction
An important issue in microarray data is to select, from thousands of genes, a small number of informative differentially expressed (DE) genes that may be key elements for a disease. If each gene is analyzed individually, there is a big number of hypotheses to test and a multiple comparison correction method must be used. Consequently, the resulting cut-off value may be too small. Moreover, an important issue is the selection’s replicability of the DE genes. The package ORdensity is designed to obtain a reproducible selection of DE genes by the method presented in [1], which is not a gene-by-gene approach. The core function 'findDEgenes' provides three measures related to the concepts of outlier and density of false positives in a neighbourhood, which allow identify the DE genes with high classification accuracy. The first measure is an index called OR and previously introduced in [2, 3]; the other two measures called FP and dFP were introduced in [1]. Additional functions provided in this package like 'preclusteredData' and 'plot' facilitate exploring and understanding the results. As, working with large datasets, long execution times and great computational efforts are required, parallelization strategies were used to perform the analysis in a short time.
References
[1] Irigoien I, Arenas C. Identification of differentially expressed genes by means of outlier detection. 19(1): 317:1–317:20 (2018)
[2] Arenas C, Toma C, Cormand B, Irigoien I. Identifying extreme observations, outliers and noise in clinical and genetic data. Current Bioinformatics 2017;12(2):101–17.
[3] Arenas C, Irigoien I, Mestres F, Toma C, Cormand B. Extreme observations in biomedical data. In: Ainsbury EA, Calle ML, Cardis E, et al., editors. Extended Abstracts Fall 2015. Trends in Mathematics vol 7. Birkhäuser, Cham: Springer; 2017. p. 3–8.
Installation
To install the package from this repository, just run the following code
library('devtools')
install_github('rsait/ORdensity')
This package requires the cluster library to be installed; otherwise it will automatically install and load it. Likewise, the foreach library is used for parallelization.
To start working with the package, just load it in the R enviroment with the following command
library('ORdensity')
Example
There is an example dataframe called simexpr shipped with the package. This data is the result of a simulation of 100 differentially expressed genes in a pool of 1000 genes. It contains 1000 observations of 62 variables. Each row correspond to a gene and contains 62 values: DEgen, gap and the values for the gene expression in 30 positive cases and in 30 negative cases. The DEgen field value is 1 for differentially expressed genes and 0 for those which are not.
First, let us extract the samples from each experimental condition from the simexpr database.
x <- simexpr[, 3:32]
y <- simexpr[, 33:62]
EXC.1 <- as.matrix(x)
EXC.2 <- as.matrix(y)
To create an S4 object to perform the analysis, follow this command
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2)
By default, no parallelizing is enabled. To enable it, just run instead
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, parallel = TRUE)
The number of processes launched is equal to the number of processors detected in the machine. That number can be changed with the nprocs parameter
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, parallel = TRUE, nprocs = 3)
It is also possible to enable or disable replicability, and to pass the seed to the pseudorandom number generator. The default values are
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, replicable = TRUE, seed = 0)
with the function using the given seed to set the random generator. If replicable = FALSE, no seed is used.
A summary of the object can be generated with the summary function.
> summary(myORdensity)
The ORdensity method has found that the optimal clustering of the data consists of 2 clusters, computed from a maximum of 10 when the ORdensity object was created
$Cluster1
$Cluster1$numberOfGenes
[1] 83
$Cluster1$CharacteristicsCluster
OR FP dFP
mean 63.58152 0.6361446 2.090888
sd 40.60755 1.0377718 3.577757
$Cluster1$genes
[1] "Gene1" "Gene10" "Gene100" "Gene11" "Gene12" "Gene13" "Gene14"
[8] "Gene15" "Gene16" "Gene17" "Gene2" "Gene20" "Gene21" "Gene22"
[15] "Gene23" "Gene24" "Gene25" "Gene26" "Gene27" "Gene28" "Gene29"
[22] "Gene3" "Gene30" "Gene32" "Gene34" "Gene35" "Gene36" "Gene37"
[29] "Gene39" "Gene4" "Gene40" "Gene42" "Gene47" "Gene48" "Gene49"
[36] "Gene5" "Gene50" "Gene52" "Gene53" "Gene54" "Gene55" "Gene56"
[43] "Gene57" "Gene58" "Gene59" "Gene6" "Gene60" "Gene61" "Gene62"
[50] "Gene63" "Gene64" "Gene65" "Gene66" "Gene67" "Gene68" "Gene69"
[57] "Gene7" "Gene70" "Gene71" "Gene72" "Gene73" "Gene76" "Gene79"
[64] "Gene8" "Gene80" "Gene81" "Gene82" "Gene83" "Gene84" "Gene86"
[71] "Gene87" "Gene88" "Gene89" "Gene9" "Gene90" "Gene91" "Gene92"
[78] "Gene93" "Gene95" "Gene96" "Gene97" "Gene98" "Gene99"
$Cluster2
$Cluster2$numberOfGenes
[1] 24
$Cluster2$CharacteristicsCluster
OR FP dFP
mean 11.114243 7.504167 42.69873
sd 3.318156 1.964794 20.47935
$Cluster2$genes
[1] "Gene104" "Gene18" "Gene19" "Gene277" "Gene31" "Gene33" "Gene38"
[8] "Gene399" "Gene41" "Gene43" "Gene44" "Gene45" "Gene46" "Gene51"
[15] "Gene598" "Gene618" "Gene651" "Gene670" "Gene74" "Gene75" "Gene78"
[22] "Gene85" "Gene94" "Gene946"
The summary tells us the estimated optimal clustering of the data, and the number of genes in each cluster, along with their names. The clusters are ordered in decreasig order according to the value of the mean of the OR statistic. We see that the mean is higher in the first cluster (61.8986) than in the second one (10.510895), which means that the first cluster is more likely composed of true differentially expressed genes, and the second one to be composed of false positives. With more clusters, the last ones are likely false negatives.
If the researcher just wants to extract the differentially expressed genes detected by the ORdensity method, a call to findDEgenes will return a list with the clusters found, along with the values of the OR statistic corresponding to each gene, and an indicator showing if the gene fulfil the strong and/or relaxed selection requirements. Following [1], two types of differentially expressed gene selection can be made:
- ORdensity strong selection: take as differentially expressed genes those with a largeOR value and with FP and dFP equal to 0.
- ORdensity relaxed selection: take as differentially expressed genes those with a largeOR value and with small FP and dFP values. As a reference to look for small values the expected number of false positive neighbours is computed.
The motivation of the clustering is to distinguish those false positives that score high in OR and low in meanFP and density, but are similar to other known false positives obtained by boostrapping. The procedure is detailed in [1] and it uses the PAM cluster procedure.
After running this code
result <- findDEgenes(myORdensity)
the method indicated that the optimal clustering consists of just two clusters,
The ORdensity method has found that the optimal clustering of the data consists of 2 clusters
we could then look the results
> result
$neighbours
[1] 10
$expectedFalsePositiveNeighbours
[1] 8.237232
$clusters
$clusters[[1]]
id OR FP dFP Strong Relaxed
62 Gene62 175.04322 0.0 0.0000000 S R
50 Gene50 172.28779 0.0 0.0000000 S R
61 Gene61 155.53626 0.0 0.0000000 S R
70 Gene70 152.54705 0.0 0.0000000 S R
2 Gene2 149.65335 0.0 0.0000000 S R
68 Gene68 148.87294 0.0 0.0000000 S R
52 Gene52 134.87709 0.0 0.0000000 S R
34 Gene34 77.32266 0.0 0.0000000 S R
71 Gene71 74.37630 0.0 0.0000000 S R
53 Gene53 69.74061 0.0 0.0000000 S R
28 Gene28 62.75227 0.0 0.0000000 S R
80 Gene81 54.30241 0.0 0.0000000 S R
40 Gene40 104.99403 0.1 0.1991604 - R
81 Gene82 93.45266 0.1 0.2892853 - R
15 Gene15 93.16310 0.1 0.2956274 - R
64 Gene64 92.59491 0.1 0.2513645 - R
73 Gene73 91.67733 0.1 0.2812384 - R
67 Gene67 88.44531 0.1 0.3110092 - R
29 Gene29 88.43950 0.1 0.3097112 - R
6 Gene6 84.47275 0.1 0.3047120 - R
23 Gene23 76.09034 0.1 0.2390754 - R
90 Gene91 52.91573 0.1 0.3281189 - R
21 Gene21 50.88095 0.1 0.3199397 - R
96 Gene97 48.44279 0.1 0.2908925 - R
42 Gene42 44.77756 0.1 0.5999895 - R
1 Gene1 40.13427 0.1 0.3922824 - R
82 Gene83 39.63938 0.1 0.4893582 - R
14 Gene14 38.54946 0.1 0.4340459 - R
78 Gene79 35.04591 0.1 0.3481011 - R
32 Gene32 144.80790 0.2 0.1803355 - R
7 Gene7 143.42201 0.2 0.1889123 - R
10 Gene10 130.61843 0.2 0.2217622 - R
36 Gene36 120.82917 0.2 0.2507271 - R
92 Gene93 103.66296 0.2 0.3341376 - R
65 Gene65 98.36178 0.2 0.3128623 - R
24 Gene24 92.20146 0.2 0.3046823 - R
17 Gene17 84.10083 0.2 0.3811577 - R
11 Gene11 68.71638 0.2 0.4969852 - R
88 Gene89 64.38506 0.2 0.4804907 - R
54 Gene54 59.93344 0.2 0.5642517 - R
26 Gene26 58.38549 0.2 0.6215621 - R
25 Gene25 51.70272 0.2 0.7066071 - R
3 Gene3 46.00194 0.2 0.8028123 - R
91 Gene92 45.90385 0.2 0.4838004 - R
58 Gene58 45.50605 0.2 0.7348415 - R
16 Gene16 43.84997 0.2 0.9786969 - R
89 Gene90 42.72040 0.2 0.8680919 - R
9 Gene9 42.01739 0.2 0.9558635 - R
48 Gene48 41.82011 0.2 1.0728645 - R
22 Gene22 40.45328 0.2 0.8163934 - R
76 Gene76 38.54992 0.2 0.8814084 - R
87 Gene88 35.14700 0.2 0.8821751 - R
79 Gene80 34.41224 0.2 0.6539720 - R
56 Gene56 34.25862 0.2 0.6983485 - R
37 Gene37 64.09250 0.3 0.7072218 - R
98 Gene99 48.72145 0.3 0.8812622 - R
86 Gene87 44.27434 0.3 1.1906371 - R
4 Gene4 38.79233 0.3 1.0669108 - R
83 Gene84 31.73809 0.3 0.9771723 - R
5 Gene5 73.18440 0.4 0.8496894 - R
8 Gene8 35.75173 0.4 1.1839906 - R
85 Gene86 31.39571 0.4 1.1725224 - R
72 Gene72 54.06801 0.5 1.1406095 - R
39 Gene39 44.21818 0.5 1.6425369 - R
99 Gene100 30.78572 0.5 1.9949584 - R
63 Gene63 65.35801 0.6 1.4317514 - R
35 Gene35 34.61744 0.6 2.0142300 - R
13 Gene13 33.95962 0.7 2.2632251 - R
20 Gene20 29.47171 0.8 2.3888816 - R
47 Gene47 38.60668 1.0 2.7468553 - R
66 Gene66 24.24462 1.8 5.6432982 - R
60 Gene60 23.04710 2.2 7.7529417 - R
94 Gene95 19.42965 2.3 8.4947719 - R
59 Gene59 18.74276 2.4 9.8450535 - R
27 Gene27 24.79341 3.0 8.4300048 - R
55 Gene55 26.19269 3.1 9.9946725 - R
12 Gene12 20.62520 3.1 10.0703651 - R
97 Gene98 18.32814 3.1 12.8366699 - R
49 Gene49 23.11792 3.3 10.2350192 - R
30 Gene30 18.37483 3.3 7.4443107 - R
69 Gene69 22.76688 3.5 11.4504084 - R
57 Gene57 18.91166 3.5 12.7353833 - R
95 Gene96 16.85913 3.6 14.4007254 - R
$clusters[[2]]
id OR FP dFP Strong Relaxed
46 Gene46 14.632071 4.3 15.79809 - R
31 Gene31 17.597946 4.9 19.29094 - R
45 Gene45 14.734285 4.9 20.34821 - R
74 Gene74 17.892081 5.2 16.30316 - R
84 Gene85 13.488933 5.2 21.94855 - R
43 Gene43 14.577235 5.8 26.09057 - R
33 Gene33 11.898146 5.9 22.86455 - R
77 Gene78 10.339745 5.9 37.95774 - R
75 Gene75 14.767943 6.5 30.38618 - R
18 Gene18 9.955954 6.7 39.78764 - R
19 Gene19 11.400038 6.8 32.18989 - R
51 Gene51 11.009624 7.1 42.79650 - R
93 Gene94 8.452682 8.0 58.82594 - R
102 Gene399 7.992158 8.1 63.43035 - R
100 Gene104 9.543673 8.3 55.43697 - -
44 Gene44 9.085678 8.6 60.68339 - -
38 Gene38 8.201157 8.7 75.19811 - -
41 Gene41 14.155428 9.3 32.65473 - -
103 Gene598 7.385797 9.9 45.75472 - -
101 Gene277 8.133859 10.0 35.83662 - -
104 Gene618 8.115440 10.0 83.18225 - -
107 Gene946 8.108665 10.0 55.55365 - -
105 Gene651 7.659571 10.0 50.64723 - -
106 Gene670 7.613712 10.0 81.80362 - -
As a rule of thumb, differentially expressed genes are expected to present high values of OR and low values of meanFP and density. We could also analyze each gene individually inside each cluster. The motivation of the clustering is to distinguish those false positives that score high in OR and low in meanFP and density, but are similar to other known false positives obtained by boostrapping. The procedure is detailed in the paper referenced above.
If the researcher is interested in a more thorough analysis, other functions are at their service.
The data before being clustered can be obtained with the following function
> preclusteredData(myORdensity)
Columns "Strong" and "Relaxed" show the genes identified as DE genes
They denote the strong selection (FP=0) with S and the relaxed selection (FP < expectedFalsePositives) with F
id OR FP dFP Strong Relaxed
62 Gene62 175.043223 0.0 0.0000000 S R
50 Gene50 172.287790 0.0 0.0000000 S R
61 Gene61 155.536259 0.0 0.0000000 S R
70 Gene70 152.547051 0.0 0.0000000 S R
2 Gene2 149.653354 0.0 0.0000000 S R
68 Gene68 148.872937 0.0 0.0000000 S R
52 Gene52 134.877088 0.0 0.0000000 S R
34 Gene34 77.322660 0.0 0.0000000 S R
71 Gene71 74.376304 0.0 0.0000000 S R
53 Gene53 69.740607 0.0 0.0000000 S R
28 Gene28 62.752272 0.0 0.0000000 S R
80 Gene81 54.302410 0.0 0.0000000 S R
40 Gene40 104.994030 0.1 0.1991604 - R
81 Gene82 93.452659 0.1 0.2892853 - R
15 Gene15 93.163103 0.1 0.2956274 - R
64 Gene64 92.594912 0.1 0.2513645 - R
73 Gene73 91.677326 0.1 0.2812384 - R
67 Gene67 88.445307 0.1 0.3110092 - R
29 Gene29 88.439498 0.1 0.3097112 - R
6 Gene6 84.472748 0.1 0.3047120 - R
23 Gene23 76.090339 0.1 0.2390754 - R
90 Gene91 52.915735 0.1 0.3281189 - R
21 Gene21 50.880954 0.1 0.3199397 - R
96 Gene97 48.442793 0.1 0.2908925 - R
42 Gene42 44.777559 0.1 0.5999895 - R
1 Gene1 40.134270 0.1 0.3922824 - R
82 Gene83 39.639383 0.1 0.4893582 - R
14 Gene14 38.549461 0.1 0.4340459 - R
78 Gene79 35.045910 0.1 0.3481011 - R
32 Gene32 144.807897 0.2 0.1803355 - R
7 Gene7 143.422005 0.2 0.1889123 - R
10 Gene10 130.618427 0.2 0.2217622 - R
36 Gene36 120.829166 0.2 0.2507271 - R
92 Gene93 103.662961 0.2 0.3341376 - R
65 Gene65 98.361779 0.2 0.3128623 - R
24 Gene24 92.201463 0.2 0.3046823 - R
17 Gene17 84.100832 0.2 0.3811577 - R
11 Gene11 68.716381 0.2 0.4969852 - R
88 Gene89 64.385061 0.2 0.4804907 - R
54 Gene54 59.933443 0.2 0.5642517 - R
26 Gene26 58.385493 0.2 0.6215621 - R
25 Gene25 51.702722 0.2 0.7066071 - R
3 Gene3 46.001939 0.2 0.8028123 - R
91 Gene92 45.903855 0.2 0.4838004 - R
58 Gene58 45.506047 0.2 0.7348415 - R
16 Gene16 43.849973 0.2 0.9786969 - R
89 Gene90 42.720397 0.2 0.8680919 - R
9 Gene9 42.017388 0.2 0.9558635 - R
48 Gene48 41.820112 0.2 1.0728645 - R
22 Gene22 40.453281 0.2 0.8163934 - R
76 Gene76 38.549919 0.2 0.8814084 - R
87 Gene88 35.147004 0.2 0.8821751 - R
79 Gene80 34.412237 0.2 0.6539720 - R
56 Gene56 34.258620 0.2 0.6983485 - R
37 Gene37 64.092504 0.3 0.7072218 - R
98 Gene99 48.721447 0.3 0.8812622 - R
86 Gene87 44.274336 0.3 1.1906371 - R
4 Gene4 38.792334 0.3 1.0669108 - R
83 Gene84 31.738086 0.3 0.9771723 - R
5 Gene5 73.184401 0.4 0.8496894 - R
8 Gene8 35.751730 0.4 1.1839906 - R
85 Gene86 31.395715 0.4 1.1725224 - R
72 Gene72 54.068005 0.5 1.1406095 - R
39 Gene39 44.218182 0.5 1.6425369 - R
99 Gene100 30.785716 0.5 1.9949584 - R
63 Gene63 65.358008 0.6 1.4317514 - R
35 Gene35 34.617445 0.6 2.0142300 - R
13 Gene13 33.959616 0.7 2.2632251 - R
20 Gene20 29.471714 0.8 2.3888816 - R
47 Gene47 38.606681 1.0 2.7468553 - R
66 Gene66 24.244624 1.8 5.6432982 - R
60 Gene60 23.047096 2.2 7.7529417 - R
94 Gene95 19.429654 2.3 8.4947719 - R
59 Gene59 18.742760 2.4 9.8450535 - R
27 Gene27 24.793410 3.0 8.4300048 - R
55 Gene55 26.192692 3.1 9.9946725 - R
12 Gene12 20.625201 3.1 10.0703651 - R
97 Gene98 18.328136 3.1 12.8366699 - R
49 Gene49 23.117921 3.3 10.2350192 - R
30 Gene30 18.374832 3.3 7.4443107 - R
69 Gene69 22.766881 3.5 11.4504084 - R
57 Gene57 18.911661 3.5 12.7353833 - R
95 Gene96 16.859134 3.6 14.4007254 - R
46 Gene46 14.632071 4.3 15.7980896 - R
31 Gene31 17.597946 4.9 19.2909380 - R
45 Gene45 14.734285 4.9 20.3482096 - R
74 Gene74 17.892081 5.2 16.3031581 - R
84 Gene85 13.488933 5.2 21.9485478 - R
43 Gene43 14.577235 5.8 26.0905728 - R
33 Gene33 11.898146 5.9 22.8645499 - R
77 Gene78 10.339745 5.9 37.9577425 - R
75 Gene75 14.767943 6.5 30.3861762 - R
18 Gene18 9.955954 6.7 39.7876362 - R
19 Gene19 11.400038 6.8 32.1898937 - R
51 Gene51 11.009624 7.1 42.7965016 - R
93 Gene94 8.452682 8.0 58.8259400 - R
102 Gene399 7.992158 8.1 63.4303484 - R
100 Gene104 9.543673 8.3 55.4369711 - -
44 Gene44 9.085678 8.6 60.6833925 - -
38 Gene38 8.201157 8.7 75.1981087 - -
41 Gene41 14.155428 9.3 32.6547299 - -
103 Gene598 7.385797 9.9 45.7547190 - -
101 Gene277 8.133859 10.0 35.8366225 - -
104 Gene618 8.115440 10.0 83.1822532 - -
107 Gene946 8.108665 10.0 55.5536499 - -
105 Gene651 7.659571 10.0 50.6472306 - -
106 Gene670 7.613712 10.0 81.8036205 - -
A plot with a representation of the potential genes based on OR (vertical axis), FP (horizontal axis) and dFP (size of the circle is inversely proportional to its value) can also be obtained. Genes that fulfil the relaxed criterion are drawn with triangles. The resulting plot is similar to Fig.3b in [1].
plot(myORdensity)
By default, the number of clusters computed by the ORdensity method is used. Other values for the number of clusters can be specified.
plot(myORdensity, k = 5)
The plot of k values against the silhouette measure is also provided.
silhouetteAnalysis(myORdensity)
rsait/ORdensity documentation built on Nov. 5, 2019, 4:16 a.m.
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ORdensity
In this repository is located the R package ORdensity that implements the statistical method presented in the paper Identification of differentially expressed genes by means of outlier detection by Irigoien and Arenas, BMC Bioinformatics 2018 ([1]).
Introduction
An important issue in microarray data is to select, from thousands of genes, a small number of informative differentially expressed (DE) genes that may be key elements for a disease. If each gene is analyzed individually, there is a big number of hypotheses to test and a multiple comparison correction method must be used. Consequently, the resulting cut-off value may be too small. Moreover, an important issue is the selection’s replicability of the DE genes. The package ORdensity is designed to obtain a reproducible selection of DE genes by the method presented in [1], which is not a gene-by-gene approach. The core function 'findDEgenes' provides three measures related to the concepts of outlier and density of false positives in a neighbourhood, which allow identify the DE genes with high classification accuracy. The first measure is an index called OR and previously introduced in [2, 3]; the other two measures called FP and dFP were introduced in [1]. Additional functions provided in this package like 'preclusteredData' and 'plot' facilitate exploring and understanding the results. As, working with large datasets, long execution times and great computational efforts are required, parallelization strategies were used to perform the analysis in a short time.
References
[1] Irigoien I, Arenas C. Identification of differentially expressed genes by means of outlier detection. 19(1): 317:1–317:20 (2018)
[2] Arenas C, Toma C, Cormand B, Irigoien I. Identifying extreme observations, outliers and noise in clinical and genetic data. Current Bioinformatics 2017;12(2):101–17.
[3] Arenas C, Irigoien I, Mestres F, Toma C, Cormand B. Extreme observations in biomedical data. In: Ainsbury EA, Calle ML, Cardis E, et al., editors. Extended Abstracts Fall 2015. Trends in Mathematics vol 7. Birkhäuser, Cham: Springer; 2017. p. 3–8.
Installation
To install the package from this repository, just run the following code
library('devtools')
install_github('rsait/ORdensity')
This package requires the cluster library to be installed; otherwise it will automatically install and load it. Likewise, the foreach library is used for parallelization.
To start working with the package, just load it in the R enviroment with the following command
library('ORdensity')
Example
There is an example dataframe called simexpr shipped with the package. This data is the result of a simulation of 100 differentially expressed genes in a pool of 1000 genes. It contains 1000 observations of 62 variables. Each row correspond to a gene and contains 62 values: DEgen, gap and the values for the gene expression in 30 positive cases and in 30 negative cases. The DEgen field value is 1 for differentially expressed genes and 0 for those which are not.
First, let us extract the samples from each experimental condition from the simexpr database.
x <- simexpr[, 3:32]
y <- simexpr[, 33:62]
EXC.1 <- as.matrix(x)
EXC.2 <- as.matrix(y)
To create an S4 object to perform the analysis, follow this command
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2)
By default, no parallelizing is enabled. To enable it, just run instead
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, parallel = TRUE)
The number of processes launched is equal to the number of processors detected in the machine. That number can be changed with the nprocs parameter
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, parallel = TRUE, nprocs = 3)
It is also possible to enable or disable replicability, and to pass the seed to the pseudorandom number generator. The default values are
myORdensity <- new("ORdensity", Exp_cond_1 = EXC.1, Exp_cond_2 = EXC.2, replicable = TRUE, seed = 0)
with the function using the given seed to set the random generator. If replicable = FALSE, no seed is used.
A summary of the object can be generated with the summary function.
> summary(myORdensity)
The ORdensity method has found that the optimal clustering of the data consists of 2 clusters, computed from a maximum of 10 when the ORdensity object was created
$Cluster1
$Cluster1$numberOfGenes
[1] 83
$Cluster1$CharacteristicsCluster
OR FP dFP
mean 63.58152 0.6361446 2.090888
sd 40.60755 1.0377718 3.577757
$Cluster1$genes
[1] "Gene1" "Gene10" "Gene100" "Gene11" "Gene12" "Gene13" "Gene14"
[8] "Gene15" "Gene16" "Gene17" "Gene2" "Gene20" "Gene21" "Gene22"
[15] "Gene23" "Gene24" "Gene25" "Gene26" "Gene27" "Gene28" "Gene29"
[22] "Gene3" "Gene30" "Gene32" "Gene34" "Gene35" "Gene36" "Gene37"
[29] "Gene39" "Gene4" "Gene40" "Gene42" "Gene47" "Gene48" "Gene49"
[36] "Gene5" "Gene50" "Gene52" "Gene53" "Gene54" "Gene55" "Gene56"
[43] "Gene57" "Gene58" "Gene59" "Gene6" "Gene60" "Gene61" "Gene62"
[50] "Gene63" "Gene64" "Gene65" "Gene66" "Gene67" "Gene68" "Gene69"
[57] "Gene7" "Gene70" "Gene71" "Gene72" "Gene73" "Gene76" "Gene79"
[64] "Gene8" "Gene80" "Gene81" "Gene82" "Gene83" "Gene84" "Gene86"
[71] "Gene87" "Gene88" "Gene89" "Gene9" "Gene90" "Gene91" "Gene92"
[78] "Gene93" "Gene95" "Gene96" "Gene97" "Gene98" "Gene99"
$Cluster2
$Cluster2$numberOfGenes
[1] 24
$Cluster2$CharacteristicsCluster
OR FP dFP
mean 11.114243 7.504167 42.69873
sd 3.318156 1.964794 20.47935
$Cluster2$genes
[1] "Gene104" "Gene18" "Gene19" "Gene277" "Gene31" "Gene33" "Gene38"
[8] "Gene399" "Gene41" "Gene43" "Gene44" "Gene45" "Gene46" "Gene51"
[15] "Gene598" "Gene618" "Gene651" "Gene670" "Gene74" "Gene75" "Gene78"
[22] "Gene85" "Gene94" "Gene946"
The summary tells us the estimated optimal clustering of the data, and the number of genes in each cluster, along with their names. The clusters are ordered in decreasig order according to the value of the mean of the OR statistic. We see that the mean is higher in the first cluster (61.8986) than in the second one (10.510895), which means that the first cluster is more likely composed of true differentially expressed genes, and the second one to be composed of false positives. With more clusters, the last ones are likely false negatives.
If the researcher just wants to extract the differentially expressed genes detected by the ORdensity method, a call to findDEgenes will return a list with the clusters found, along with the values of the OR statistic corresponding to each gene, and an indicator showing if the gene fulfil the strong and/or relaxed selection requirements. Following [1], two types of differentially expressed gene selection can be made:
- ORdensity strong selection: take as differentially expressed genes those with a largeOR value and with FP and dFP equal to 0.
- ORdensity relaxed selection: take as differentially expressed genes those with a largeOR value and with small FP and dFP values. As a reference to look for small values the expected number of false positive neighbours is computed.
The motivation of the clustering is to distinguish those false positives that score high in OR and low in meanFP and density, but are similar to other known false positives obtained by boostrapping. The procedure is detailed in [1] and it uses the PAM cluster procedure.
After running this code
result <- findDEgenes(myORdensity)
the method indicated that the optimal clustering consists of just two clusters,
The ORdensity method has found that the optimal clustering of the data consists of 2 clusters
we could then look the results
> result
$neighbours
[1] 10
$expectedFalsePositiveNeighbours
[1] 8.237232
$clusters
$clusters[[1]]
id OR FP dFP Strong Relaxed
62 Gene62 175.04322 0.0 0.0000000 S R
50 Gene50 172.28779 0.0 0.0000000 S R
61 Gene61 155.53626 0.0 0.0000000 S R
70 Gene70 152.54705 0.0 0.0000000 S R
2 Gene2 149.65335 0.0 0.0000000 S R
68 Gene68 148.87294 0.0 0.0000000 S R
52 Gene52 134.87709 0.0 0.0000000 S R
34 Gene34 77.32266 0.0 0.0000000 S R
71 Gene71 74.37630 0.0 0.0000000 S R
53 Gene53 69.74061 0.0 0.0000000 S R
28 Gene28 62.75227 0.0 0.0000000 S R
80 Gene81 54.30241 0.0 0.0000000 S R
40 Gene40 104.99403 0.1 0.1991604 - R
81 Gene82 93.45266 0.1 0.2892853 - R
15 Gene15 93.16310 0.1 0.2956274 - R
64 Gene64 92.59491 0.1 0.2513645 - R
73 Gene73 91.67733 0.1 0.2812384 - R
67 Gene67 88.44531 0.1 0.3110092 - R
29 Gene29 88.43950 0.1 0.3097112 - R
6 Gene6 84.47275 0.1 0.3047120 - R
23 Gene23 76.09034 0.1 0.2390754 - R
90 Gene91 52.91573 0.1 0.3281189 - R
21 Gene21 50.88095 0.1 0.3199397 - R
96 Gene97 48.44279 0.1 0.2908925 - R
42 Gene42 44.77756 0.1 0.5999895 - R
1 Gene1 40.13427 0.1 0.3922824 - R
82 Gene83 39.63938 0.1 0.4893582 - R
14 Gene14 38.54946 0.1 0.4340459 - R
78 Gene79 35.04591 0.1 0.3481011 - R
32 Gene32 144.80790 0.2 0.1803355 - R
7 Gene7 143.42201 0.2 0.1889123 - R
10 Gene10 130.61843 0.2 0.2217622 - R
36 Gene36 120.82917 0.2 0.2507271 - R
92 Gene93 103.66296 0.2 0.3341376 - R
65 Gene65 98.36178 0.2 0.3128623 - R
24 Gene24 92.20146 0.2 0.3046823 - R
17 Gene17 84.10083 0.2 0.3811577 - R
11 Gene11 68.71638 0.2 0.4969852 - R
88 Gene89 64.38506 0.2 0.4804907 - R
54 Gene54 59.93344 0.2 0.5642517 - R
26 Gene26 58.38549 0.2 0.6215621 - R
25 Gene25 51.70272 0.2 0.7066071 - R
3 Gene3 46.00194 0.2 0.8028123 - R
91 Gene92 45.90385 0.2 0.4838004 - R
58 Gene58 45.50605 0.2 0.7348415 - R
16 Gene16 43.84997 0.2 0.9786969 - R
89 Gene90 42.72040 0.2 0.8680919 - R
9 Gene9 42.01739 0.2 0.9558635 - R
48 Gene48 41.82011 0.2 1.0728645 - R
22 Gene22 40.45328 0.2 0.8163934 - R
76 Gene76 38.54992 0.2 0.8814084 - R
87 Gene88 35.14700 0.2 0.8821751 - R
79 Gene80 34.41224 0.2 0.6539720 - R
56 Gene56 34.25862 0.2 0.6983485 - R
37 Gene37 64.09250 0.3 0.7072218 - R
98 Gene99 48.72145 0.3 0.8812622 - R
86 Gene87 44.27434 0.3 1.1906371 - R
4 Gene4 38.79233 0.3 1.0669108 - R
83 Gene84 31.73809 0.3 0.9771723 - R
5 Gene5 73.18440 0.4 0.8496894 - R
8 Gene8 35.75173 0.4 1.1839906 - R
85 Gene86 31.39571 0.4 1.1725224 - R
72 Gene72 54.06801 0.5 1.1406095 - R
39 Gene39 44.21818 0.5 1.6425369 - R
99 Gene100 30.78572 0.5 1.9949584 - R
63 Gene63 65.35801 0.6 1.4317514 - R
35 Gene35 34.61744 0.6 2.0142300 - R
13 Gene13 33.95962 0.7 2.2632251 - R
20 Gene20 29.47171 0.8 2.3888816 - R
47 Gene47 38.60668 1.0 2.7468553 - R
66 Gene66 24.24462 1.8 5.6432982 - R
60 Gene60 23.04710 2.2 7.7529417 - R
94 Gene95 19.42965 2.3 8.4947719 - R
59 Gene59 18.74276 2.4 9.8450535 - R
27 Gene27 24.79341 3.0 8.4300048 - R
55 Gene55 26.19269 3.1 9.9946725 - R
12 Gene12 20.62520 3.1 10.0703651 - R
97 Gene98 18.32814 3.1 12.8366699 - R
49 Gene49 23.11792 3.3 10.2350192 - R
30 Gene30 18.37483 3.3 7.4443107 - R
69 Gene69 22.76688 3.5 11.4504084 - R
57 Gene57 18.91166 3.5 12.7353833 - R
95 Gene96 16.85913 3.6 14.4007254 - R
$clusters[[2]]
id OR FP dFP Strong Relaxed
46 Gene46 14.632071 4.3 15.79809 - R
31 Gene31 17.597946 4.9 19.29094 - R
45 Gene45 14.734285 4.9 20.34821 - R
74 Gene74 17.892081 5.2 16.30316 - R
84 Gene85 13.488933 5.2 21.94855 - R
43 Gene43 14.577235 5.8 26.09057 - R
33 Gene33 11.898146 5.9 22.86455 - R
77 Gene78 10.339745 5.9 37.95774 - R
75 Gene75 14.767943 6.5 30.38618 - R
18 Gene18 9.955954 6.7 39.78764 - R
19 Gene19 11.400038 6.8 32.18989 - R
51 Gene51 11.009624 7.1 42.79650 - R
93 Gene94 8.452682 8.0 58.82594 - R
102 Gene399 7.992158 8.1 63.43035 - R
100 Gene104 9.543673 8.3 55.43697 - -
44 Gene44 9.085678 8.6 60.68339 - -
38 Gene38 8.201157 8.7 75.19811 - -
41 Gene41 14.155428 9.3 32.65473 - -
103 Gene598 7.385797 9.9 45.75472 - -
101 Gene277 8.133859 10.0 35.83662 - -
104 Gene618 8.115440 10.0 83.18225 - -
107 Gene946 8.108665 10.0 55.55365 - -
105 Gene651 7.659571 10.0 50.64723 - -
106 Gene670 7.613712 10.0 81.80362 - -
As a rule of thumb, differentially expressed genes are expected to present high values of OR and low values of meanFP and density. We could also analyze each gene individually inside each cluster. The motivation of the clustering is to distinguish those false positives that score high in OR and low in meanFP and density, but are similar to other known false positives obtained by boostrapping. The procedure is detailed in the paper referenced above.
If the researcher is interested in a more thorough analysis, other functions are at their service.
The data before being clustered can be obtained with the following function
> preclusteredData(myORdensity)
Columns "Strong" and "Relaxed" show the genes identified as DE genes
They denote the strong selection (FP=0) with S and the relaxed selection (FP < expectedFalsePositives) with F
id OR FP dFP Strong Relaxed
62 Gene62 175.043223 0.0 0.0000000 S R
50 Gene50 172.287790 0.0 0.0000000 S R
61 Gene61 155.536259 0.0 0.0000000 S R
70 Gene70 152.547051 0.0 0.0000000 S R
2 Gene2 149.653354 0.0 0.0000000 S R
68 Gene68 148.872937 0.0 0.0000000 S R
52 Gene52 134.877088 0.0 0.0000000 S R
34 Gene34 77.322660 0.0 0.0000000 S R
71 Gene71 74.376304 0.0 0.0000000 S R
53 Gene53 69.740607 0.0 0.0000000 S R
28 Gene28 62.752272 0.0 0.0000000 S R
80 Gene81 54.302410 0.0 0.0000000 S R
40 Gene40 104.994030 0.1 0.1991604 - R
81 Gene82 93.452659 0.1 0.2892853 - R
15 Gene15 93.163103 0.1 0.2956274 - R
64 Gene64 92.594912 0.1 0.2513645 - R
73 Gene73 91.677326 0.1 0.2812384 - R
67 Gene67 88.445307 0.1 0.3110092 - R
29 Gene29 88.439498 0.1 0.3097112 - R
6 Gene6 84.472748 0.1 0.3047120 - R
23 Gene23 76.090339 0.1 0.2390754 - R
90 Gene91 52.915735 0.1 0.3281189 - R
21 Gene21 50.880954 0.1 0.3199397 - R
96 Gene97 48.442793 0.1 0.2908925 - R
42 Gene42 44.777559 0.1 0.5999895 - R
1 Gene1 40.134270 0.1 0.3922824 - R
82 Gene83 39.639383 0.1 0.4893582 - R
14 Gene14 38.549461 0.1 0.4340459 - R
78 Gene79 35.045910 0.1 0.3481011 - R
32 Gene32 144.807897 0.2 0.1803355 - R
7 Gene7 143.422005 0.2 0.1889123 - R
10 Gene10 130.618427 0.2 0.2217622 - R
36 Gene36 120.829166 0.2 0.2507271 - R
92 Gene93 103.662961 0.2 0.3341376 - R
65 Gene65 98.361779 0.2 0.3128623 - R
24 Gene24 92.201463 0.2 0.3046823 - R
17 Gene17 84.100832 0.2 0.3811577 - R
11 Gene11 68.716381 0.2 0.4969852 - R
88 Gene89 64.385061 0.2 0.4804907 - R
54 Gene54 59.933443 0.2 0.5642517 - R
26 Gene26 58.385493 0.2 0.6215621 - R
25 Gene25 51.702722 0.2 0.7066071 - R
3 Gene3 46.001939 0.2 0.8028123 - R
91 Gene92 45.903855 0.2 0.4838004 - R
58 Gene58 45.506047 0.2 0.7348415 - R
16 Gene16 43.849973 0.2 0.9786969 - R
89 Gene90 42.720397 0.2 0.8680919 - R
9 Gene9 42.017388 0.2 0.9558635 - R
48 Gene48 41.820112 0.2 1.0728645 - R
22 Gene22 40.453281 0.2 0.8163934 - R
76 Gene76 38.549919 0.2 0.8814084 - R
87 Gene88 35.147004 0.2 0.8821751 - R
79 Gene80 34.412237 0.2 0.6539720 - R
56 Gene56 34.258620 0.2 0.6983485 - R
37 Gene37 64.092504 0.3 0.7072218 - R
98 Gene99 48.721447 0.3 0.8812622 - R
86 Gene87 44.274336 0.3 1.1906371 - R
4 Gene4 38.792334 0.3 1.0669108 - R
83 Gene84 31.738086 0.3 0.9771723 - R
5 Gene5 73.184401 0.4 0.8496894 - R
8 Gene8 35.751730 0.4 1.1839906 - R
85 Gene86 31.395715 0.4 1.1725224 - R
72 Gene72 54.068005 0.5 1.1406095 - R
39 Gene39 44.218182 0.5 1.6425369 - R
99 Gene100 30.785716 0.5 1.9949584 - R
63 Gene63 65.358008 0.6 1.4317514 - R
35 Gene35 34.617445 0.6 2.0142300 - R
13 Gene13 33.959616 0.7 2.2632251 - R
20 Gene20 29.471714 0.8 2.3888816 - R
47 Gene47 38.606681 1.0 2.7468553 - R
66 Gene66 24.244624 1.8 5.6432982 - R
60 Gene60 23.047096 2.2 7.7529417 - R
94 Gene95 19.429654 2.3 8.4947719 - R
59 Gene59 18.742760 2.4 9.8450535 - R
27 Gene27 24.793410 3.0 8.4300048 - R
55 Gene55 26.192692 3.1 9.9946725 - R
12 Gene12 20.625201 3.1 10.0703651 - R
97 Gene98 18.328136 3.1 12.8366699 - R
49 Gene49 23.117921 3.3 10.2350192 - R
30 Gene30 18.374832 3.3 7.4443107 - R
69 Gene69 22.766881 3.5 11.4504084 - R
57 Gene57 18.911661 3.5 12.7353833 - R
95 Gene96 16.859134 3.6 14.4007254 - R
46 Gene46 14.632071 4.3 15.7980896 - R
31 Gene31 17.597946 4.9 19.2909380 - R
45 Gene45 14.734285 4.9 20.3482096 - R
74 Gene74 17.892081 5.2 16.3031581 - R
84 Gene85 13.488933 5.2 21.9485478 - R
43 Gene43 14.577235 5.8 26.0905728 - R
33 Gene33 11.898146 5.9 22.8645499 - R
77 Gene78 10.339745 5.9 37.9577425 - R
75 Gene75 14.767943 6.5 30.3861762 - R
18 Gene18 9.955954 6.7 39.7876362 - R
19 Gene19 11.400038 6.8 32.1898937 - R
51 Gene51 11.009624 7.1 42.7965016 - R
93 Gene94 8.452682 8.0 58.8259400 - R
102 Gene399 7.992158 8.1 63.4303484 - R
100 Gene104 9.543673 8.3 55.4369711 - -
44 Gene44 9.085678 8.6 60.6833925 - -
38 Gene38 8.201157 8.7 75.1981087 - -
41 Gene41 14.155428 9.3 32.6547299 - -
103 Gene598 7.385797 9.9 45.7547190 - -
101 Gene277 8.133859 10.0 35.8366225 - -
104 Gene618 8.115440 10.0 83.1822532 - -
107 Gene946 8.108665 10.0 55.5536499 - -
105 Gene651 7.659571 10.0 50.6472306 - -
106 Gene670 7.613712 10.0 81.8036205 - -
A plot with a representation of the potential genes based on OR (vertical axis), FP (horizontal axis) and dFP (size of the circle is inversely proportional to its value) can also be obtained. Genes that fulfil the relaxed criterion are drawn with triangles. The resulting plot is similar to Fig.3b in [1].
plot(myORdensity)
By default, the number of clusters computed by the ORdensity method is used. Other values for the number of clusters can be specified.
plot(myORdensity, k = 5)
The plot of k values against the silhouette measure is also provided.
silhouetteAnalysis(myORdensity)
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