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DESCRIPTION
Project classifing human carcinoid cells. The application uses SAS Base Programing. PROC ACCECLUS, PROC VARCLUS PROC FASTCLUS are being . Given a data set of profiles of mRNA expression that contain distinct adenocarcinoma subclasses classify human lung carcinomas.
Citation preview
Project Scope
Given a data set of profiles of mRNA expression that contain distinct adenocarcinoma subclasses classify human lung carcinomas.
Data Set
This data set contains 56 variables measured on 12,625 genes using Affymetrix GeneChip 95av2 (dedicated to acquiring, analyzing and managing complex genetic information). Of the 56 variables measured 20 lung carcinoid (Carcinoid), 13 are related to the metastasis of colon cancer (colon) 17 normal lung function (Normal) and 6 to lung small cell carcinoma (SmallCell).
STEP 1: Data Manipulation
Missing data & Format
The first step is assuring that the data set is suitable for the analysis. We are checking whether the format of the data is suitable for our analysis and whether there are missing values. The format has been changed to numeric in order for the analyze to be taken care of . No missing data was in the data set.
Extreme values
We are using PROC UNIVARIATE to search for extreme values among out 56 variables. We see that our data set has indeed extreme values. We expect somehow this behavior as we are analyzing cancer cells which vary in size. As a consequence we will eliminate the outliers which have high values for the normal cells as this cells should have values that are not further from 3 standard deviation from the mean and smallcells. Data was standardized, although as the data set consists of variables measured in the same unit of measurement it would not affect the calculation of distances between clusters. We will keep in consequence the outliers for the colon cells and carcinoid. From our initial data base of 12,625 observations we will end up with a 11279 observation data base.
Getting an intuition over the data
We are interested to know whether or not the variables are linked between. As the results from PROC CORR indicate, the variables are strongly correlated. Our intuition that each type of variable Normal, Colon, Carcinoid and SmallCell are more correlated between
their own type then let’s say Colon and Normal cell is confirmed by the results given by the division into clusters using principal components as a criteria. We will specify the number of clusters to be 4. We will obtain a cluster (CLUSTER 1) with Normal Cells and half of the Small Cells, a cluster(CLUSTER 3) with colon cells and 2 clusters with Carcinoids, one of them having the rest of the small cells (CLUSTER 2) and the other one variable concerning Colon variables. The full table is to be found in the ANNEX.
STEP 2: Choosing the right number of clusters
In finding the right clusters, three approaches in manipulating our initial variables have been used:
1. Computing 56 canonical variables – PROC ACECLUS2. Reducing the number of variables to 10 – PROC VARCLUS3. Standardizing our initial 56 variables – PROC STANDARD However when comparing the Cubic Clustering Criteria, only the latter was found appropriate to continue our analysis.
As we do not know prior the number of clusters, we will apply automatic clustering methods to figure out the exact number. The data set is to vast to apply directly the SAS procedure CLUSTER, so we will first apply FASTCLUS to find a set of initial cluters which will be used as input for PROC CLUSTER.
We choose the number of maximum clusters for the FASTCLUST procedure 53 as the square root of our total number of observations (11279) devided by 2. As there were clusters with few observations, those with fewer than 9 were deleted and the rest became seeds for a second FASTCLUST procedure. We are using the output containing clusters as an input for the CLUSTER procedure.
The criteria used in our clusterisation is the Ward distance. This meant that a loss of inertia resulted in the fusion of two classes, as a consequence it seeks to have a low interclass inertia. It is calculates using the square of the distances of two barycenteres divided by 1/the number of individuals in the corresponding class.
1. Computing 56 canonical variables – PROC ACECLUS
In order to compute canonical variables for subsequent cluster analysis we obtain approximate estimates of the pooled within-cluster covariance matrix by using PROC ACECLUS. As our database contained a big number of data we choose 0.1 to be our within cluster covariance coefficient. Data with poorly separated or elongated patterns need to be transformed. Also, variables with different units of measurement or with different size variances will need to be transformed as well. In our case only the former is true as all the variables use the same unit of measure. For clusterization to be done it is advisable to have spherical clusters rather than elongates elliptical clusters.
We can apply this technique directly on the data without prior clusterization as there is no need for prior knowledge on cluster membership or number of clusters.
However the Clustering Criteria below fail to validate the data as appropriate for our analysis. The negative value of the CCC indicates a strong presence of outliers in the data set, which makes it difficult to find an appropriate number of clusters.
In consequence we will try to reduce the number of variables that are being used.
FIG1. Clustering Criteria for the clusters obtained on canonical variables
2. Reducing the number of variables to 10 – PROC VARCLUS
The correlation between our variables is high as the result from the PROC CORR show .
FIG2- PROC CORR-best 8- correlation between variables.
In consequence we can reduce our number of variables. In order to reduce our 56 variables to a smaller number we will use PROC VARCLUS. This procedure will output our variables into a number of clusters from which we will select a few variables that are most representative for the subsequent cluster and use it in our analysis. This procedure is closely related to the principal component procedure, finding the groups of variables that are as correlated as possible among themselves and as uncorrelated as possible with variables in other clusters.
For our analysis we choose rather than the number of clusters the threshold for identifying additional dimensions within equal to 0.8. From each cluster we choose one variable which had the lowest 1-R**2 value as it contributed the most to the subsequent cluster .
We choosed as a consequence : Normal7 Carcinoid4 Carcinoid19 Carcinoid18 Carcinoid6 Colon5 Colon12 Colon3 SmallCell3 SmallCell4 Colon10. Table 1 Classification of variables in 10 distinct clusters
10 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Cluster 1 Normal1 0.5776 0.4322 0.7440 Normal1
10 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Normal2 0.7216 0.4075 0.4699 Normal2
Normal3 0.7099 0.3027 0.4161 Normal3
Normal4 0.6246 0.3060 0.5409 Normal4
Normal5 0.8154 0.3919 0.3036 Normal5
Normal6 0.7852 0.4063 0.3618 Normal6
Normal7 0.7112 0.4114 0.4907 Normal7
Normal8 0.7808 0.4384 0.3904 Normal8
Normal9 0.7855 0.3485 0.3292 Normal9
Normal10 0.7179 0.4627 0.5250 Normal10
Normal11 0.6125 0.2770 0.5359 Normal11
Normal13 0.5408 0.3959 0.7603 Normal13
Normal14 0.6168 0.3040 0.5506 Normal14
Normal15 0.5465 0.3721 0.7222 Normal15
Normal16 0.6182 0.2556 0.5129 Normal16
Normal17 0.6962 0.3395 0.4600 Normal17
Cluster 2 Carcinoid2 0.7208 0.4011 0.4663 Carcinoid2
Carcinoid3 0.5375 0.1325 0.5332 Carcinoid3
Carcinoid4 0.7874 0.2760 0.2937 Carcinoid4
Carcinoid9 0.7170 0.3094 0.4097 Carcinoid9
Carcinoid14 0.6630 0.1973 0.4199 Carcinoid14
Carcinoid15 0.7679 0.3107 0.3368 Carcinoid15
Carcinoid16 0.6685 0.1959 0.4122 Carcinoid16
Carcinoid17 0.7478 0.4225 0.4367 Carcinoid17
Cluster 3 Colon2 0.5300 0.1949 0.5837 Colon2
Colon4 0.6529 0.3772 0.5573 Colon4
Colon5 0.6688 0.1567 0.3928 Colon5
Colon7 0.5610 0.2561 0.5901 Colon7
10 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Colon8 0.5945 0.2326 0.5283 Colon8
Colon9 0.4309 0.1879 0.7008 Colon9
Colon10 0.5334 0.1981 0.5818 Colon10
Colon11 0.5477 0.2664 0.6166 Colon11
Cluster 4 Carcinoid1 0.7041 0.3215 0.4360 Carcinoid1
Carcinoid5 0.3161 0.1972 0.8519 Carcinoid5
Carcinoid7 0.6917 0.3549 0.4778 Carcinoid7
Carcinoid10 0.3658 0.1754 0.7691 Carcinoid10
Carcinoid12 0.7055 0.3482 0.4519 Carcinoid12
Carcinoid13 0.7094 0.3875 0.4745 Carcinoid13
Carcinoid19 0.7206 0.3585 0.4355 Carcinoid19
Carcinoid20 0.7007 0.4087 0.5062 Carcinoid20
Normal12 0.4108 0.3121 0.8565 Normal12
Cluster 5 Carcinoid6 0.8378 0.2576 0.2185 Carcinoid6
Carcinoid8 0.8310 0.3032 0.2425 Carcinoid8
Carcinoid11 0.7852 0.2763 0.2968 Carcinoid11
Cluster 6 SmallCell2 0.5349 0.1577 0.5522 SmallCell2
SmallCell3 0.7381 0.1753 0.3176 SmallCell3
SmallCell5 0.7062 0.2283 0.3807 SmallCell5
SmallCell6 0.5383 0.2274 0.5976 SmallCell6
Cluster 7 Colon6 0.6001 0.1719 0.4829 Colon6
Colon12 0.7246 0.2947 0.3904 Colon12
Colon13 0.5620 0.2061 0.5517 Colon13
Cluster 8 Carcinoid18 0.6827 0.1944 0.3939 Carcinoid18
Colon1 0.6827 0.2248 0.4093 Colon1
Cluster 9 SmallCell1 0.6772 0.1897 0.3983 SmallCell1
SmallCell4 0.6772 0.1536 0.3814 SmallCell4
10 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Cluster 10 Colon3 1.0000 0.0970 0.0000 Colon3
FIG 3 Variable classification result
When we executed our clustering procedure we obtained an improvement in the criteria , but still not good enough for a further analysis. The CCC criteria indicates a lower presence of a outliers and thus a better chance for obtaining a satisfying clusterisation . However the pseudo t square indicates in the are where CCC value allows for a clusterisation, a good number of clusters to be 15, as it is the number which indicates a surge followed by a drop. This number is rather big for our data of 10 variables and difficult to interpret in a proper manner as a consequence. We will continue our analysis on all the variables on which standardization has been performed.
FIG4. Clustering Criteria for the clusters obtained on 10 variables
3. Standardized variables – PROC STANDARD
Our third attempt consists in running PROC CLUSTER on standardized data with no outliers for the normal and smallcell variables.
We are looking for a Cubic Clustering Criteria (CCC) which is greater than 0 as well as local maximum and local maximum for the Pseudo F and Pseudo t square Criteria. As we do not observe a local spike in the Pseudo F statistic plot, we will use the pseudo t square as a criteria. We see that there are several local spikes, but we will take into consideration only those grater or equal to 11, ass for the others the CCC is negative indicating the presence of outliers. We will choose 12 clusters which is equal to K+1, K being the number of clusters where pseudo T square was a local maximum.
FIG5. Clustering Criteria for the clusters standardize variables
The resulted classification is comprised in the table below. The results are robust as there is no class with few observations.FIG 6 – Final clusters
FIG 7 Dendogram obtained from the cluster procedure
We want to study the characteristics of each cluster. In order to do that we will look at the classification obtained by the VARCLUS procedure and we will create 4 variables which we will use to highlight the difference between the clusters we obtained.
FIG 8 Characteristics of clusters found
Interpretation of cluster values
The clusters which include most of our observations are cluster number 3, 4 and 11. Clusters 3 and 11 are distinguishable as they contain values closer to 0. We can interpret this observations as being less prone to having a medical problem. Cluster 1 contains the fewest number of observations, however all the variables displayed high values, indicating a set of individuals which have a medical condition that is worst then the rest of the observations. Individuals from the 5th Cluster also exhibit a salient pattern as the value for the Colon cell is greater than the rest of the Colon values. The Carcinoid1 and Carcinoid2 have also striking low negative values. The values from the Carcinoid1 and Carcinoid2 display values that are somehow similar for each cluster.
REFERENCES
Variable Reduction for Modeling using PROC VARCLUS, Bryan D. Nelsonhttp://www2.sas.com/proceedings/sugi26/p261-26.pdf
A Methodological approach to performing cluster analysis with SAS®, William F. McCarthyhttp://analytics.ncsu.edu/sesug/2007/DM05.pdf
SAS Institute Inc.SAS/STAT ® User’s Guide, Version 8, Cary, NC: SAS Institute Inc., 1999https://ciser.cornell.edu/sasdoc/saspdf/stat/chap16.pdf
Data Mining et Statistique Decisionelle, Stéphane Tufféryhttp://data.mining.free.fr/cours/Descriptives.pdf
ANNEX
Results of PROC VARCLUS on a given number of 4 clusters4 classes r carré avec Rapport
1-R**2Libellé dela variableClasse Variable Propre
classeLe plusproche
Cluster 1 Normal1 0.5759 0.4497 0.7707 Normal1
Normal2 0.7123 0.4297 0.5045 Normal2
Normal3 0.7042 0.3347 0.4446 Normal3
Normal4 0.6145 0.3086 0.5575 Normal4
Normal5 0.8057 0.3996 0.3236 Normal5
Normal6 0.7870 0.4343 0.3765 Normal6
Normal7 0.7050 0.4419 0.5286 Normal7
Normal8 0.7764 0.4810 0.4308 Normal8
Normal9 0.7807 0.3743 0.3505 Normal9
Normal10 0.7144 0.4917 0.5620 Normal10
Normal11 0.6122 0.2759 0.5355 Normal11
Normal13 0.5389 0.4305 0.8098 Normal13
Normal14 0.6134 0.3293 0.5764 Normal14
Normal15 0.5398 0.3839 0.7469 Normal15
Normal16 0.6145 0.2525 0.5157 Normal16
Normal17 0.6947 0.3544 0.4729 Normal17
SmallCell2 0.1319 0.0173 0.8835 SmallCell2
SmallCell3 0.1727 0.0407 0.8624 SmallCell3
SmallCell6 0.2829 0.1281 0.8225 SmallCell6
Cluster 2 Carcinoid2 0.7112 0.4379 0.5138 Carcinoid2
Carcinoid3 0.5221 0.1459 0.5595 Carcinoid3
Carcinoid4 0.7768 0.2583 0.3009 Carcinoid4
Carcinoid9 0.6935 0.3199 0.4506 Carcinoid9
Carcinoid14 0.6603 0.1824 0.4155 Carcinoid14
4 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Carcinoid15 0.7405 0.3248 0.3843 Carcinoid15
Carcinoid16 0.6643 0.2120 0.4260 Carcinoid16
Carcinoid17 0.7396 0.4638 0.4857 Carcinoid17
SmallCell1 0.2858 0.1533 0.8435 SmallCell1
SmallCell4 0.0617 0.0057 0.9437 SmallCell4
SmallCell5 0.1136 0.0698 0.9529 SmallCell5
Cluster 3 Colon2 0.4956 0.0987 0.5597 Colon2
Colon3 0.1472 0.0642 0.9113 Colon3
Colon4 0.6775 0.0912 0.3549 Colon4
Colon5 0.5922 0.1323 0.4700 Colon5
Colon6 0.2904 0.0362 0.7363 Colon6
Colon7 0.5091 0.2763 0.6783 Colon7
Colon8 0.5530 0.2569 0.6015 Colon8
Colon9 0.4197 0.1813 0.7087 Colon9
Colon10 0.4903 0.1314 0.5868 Colon10
Colon11 0.5567 0.1919 0.5486 Colon11
Colon12 0.4449 0.0553 0.5876 Colon12
Colon13 0.3369 0.0934 0.7315 Colon13
Cluster 4 Carcinoid1 0.6485 0.3165 0.5142 Carcinoid1
Carcinoid5 0.3241 0.1925 0.8369 Carcinoid5
Carcinoid6 0.4246 0.2670 0.7850 Carcinoid6
Carcinoid7 0.6180 0.3510 0.5887 Carcinoid7
Carcinoid8 0.4619 0.2834 0.7509 Carcinoid8
Carcinoid10 0.3452 0.1753 0.7940 Carcinoid10
Carcinoid11 0.3911 0.2645 0.8279 Carcinoid11
Carcinoid12 0.6441 0.3407 0.5398 Carcinoid12
Carcinoid13 0.6721 0.3800 0.5288 Carcinoid13
4 classes r carré avec Rapport1-R**2
Libellé dela variableClasse Variable Propre
classeLe plusproche
Carcinoid18 0.2518 0.1611 0.8919 Carcinoid18
Carcinoid19 0.6462 0.3467 0.5415 Carcinoid19
Carcinoid20 0.6727 0.3954 0.5414 Carcinoid20
Colon1 0.2930 0.2116 0.8967 Colon1
Normal12 0.4199 0.3089 0.8395 Normal12
Best 8 correlation between the 56 variablesCoefficients de corrélation de Pearson, N = 12625
Carcinoid1
Carcinoid1
Carcinoid1
1.00000
Carcinoid7
0.76043
Carcinoid12
0.66852
Carcinoid13
0.65419
Carcinoid19
0.64338
Carcinoid20
0.61351
Normal1
-0.55903
Normal10
-0.51519
Carcinoid2
Carcinoid2
Carcinoid2
1.00000
Carcinoid17
0.82788
Carcinoid9
0.70795
Carcinoid4
0.70294
Carcinoid15
0.69357
Carcinoid14
0.60661
Carcinoid16
0.60145
Carcinoid20
0.59006
Carcinoid3
Carcinoid3
Carcinoid3
1.00000
Carcinoid16
0.66630
Carcinoid4
0.64394
Carcinoid15
0.55431
Carcinoid14
0.54885
Carcinoid17
0.52568
Carcinoid2
0.51971
Carcinoid9
0.51357
Carcinoid4
Carcinoid4
Carcinoid4
1.00000
Carcinoid15
0.73755
Carcinoid14
0.73427
Carcinoid9
0.70689
Carcinoid2
0.70294
Carcinoid16
0.70230
Carcinoid17
0.69915
Carcinoid3
0.64394
Carcinoid5
Carcinoid5
Carcinoid5
1.00000
Carcinoid2
0.45567
Carcinoid6
0.43501
Carcinoid7
0.43160
Carcinoid17
0.43127
Carcinoid1
0.42381
Carcinoid19
0.42197
Carcinoid15
0.41406
Coefficients de corrélation de Pearson, N = 12625
Carcinoid6
Carcinoid6
Carcinoid6
1.00000
Carcinoid8
0.76986
Carcinoid11
0.70985
Carcinoid17
0.49237
Normal1
-0.48927
Carcinoid2
0.48818
Normal10
-0.47197
Carcinoid9
0.46320
Carcinoid7
Carcinoid7
Carcinoid7
1.00000
Carcinoid1
0.76043
Carcinoid19
0.66637
Carcinoid13
0.65993
Carcinoid12
0.64727
Carcinoid20
0.61242
Normal10
-0.55620
Normal1
-0.54062
Carcinoid8
Carcinoid8
Carcinoid8
1.00000
Carcinoid6
0.76986
Carcinoid11
0.70054
Carcinoid17
0.55688
Carcinoid2
0.54662
Normal1
-0.52602
Normal8
-0.51673
Normal10
-0.51604
Carcinoid9
Carcinoid9
Carcinoid9
1.00000
Carcinoid15
0.77872
Carcinoid2
0.70795
Carcinoid4
0.70689
Carcinoid17
0.68714
Carcinoid14
0.64445
Carcinoid16
0.60833
Carcinoid3
0.51357
Carcinoid10
Carcinoid10
Carcinoid10
1.00000
Carcinoid1
0.46498
Carcinoid13
0.43394
Carcinoid19
0.42922
Normal8
-0.42764
Carcinoid7
0.42744
Carcinoid12
0.42491
Carcinoid20
0.42129
Carcinoid11
Carcinoid11
Carcinoid11
1.00000
Carcinoid6
0.70985
Carcinoid8
0.70054
Normal8
-0.52161
Normal10
-0.51058
Normal2
-0.47851
Normal7
-0.47280
Normal13
-0.46092
Carcinoid12
Carcinoid12
Carcinoid12
1.00000
Carcinoid13
0.71217
Carcinoid19
0.68722
Carcinoid1
0.66852
Carcinoid20
0.66621
Carcinoid7
0.64727
Normal10
-0.5449
Normal8
-0.5348
Coefficients de corrélation de Pearson, N = 12625
2 9
Carcinoid13
Carcinoid13
Carcinoid13
1.00000
Carcinoid20
0.72258
Carcinoid12
0.71217
Carcinoid19
0.67641
Carcinoid7
0.65993
Carcinoid1
0.65419
Normal8
-0.58342
Normal7
-0.58017
Carcinoid14
Carcinoid14
Carcinoid14
1.00000
Carcinoid4
0.73427
Carcinoid15
0.68809
Carcinoid9
0.64445
Carcinoid17
0.63565
Carcinoid2
0.60661
Carcinoid16
0.59469
Carcinoid3
0.54885
Carcinoid15
Carcinoid15
Carcinoid15
1.00000
Carcinoid9
0.77872
Carcinoid4
0.73755
Carcinoid17
0.72976
Carcinoid2
0.69357
Carcinoid14
0.68809
Carcinoid16
0.65930
Carcinoid3
0.55431
Carcinoid16
Carcinoid16
Carcinoid16
1.00000
Carcinoid4
0.70230
Carcinoid3
0.66630
Carcinoid15
0.65930
Carcinoid17
0.65897
Carcinoid9
0.60833
Carcinoid2
0.60145
Carcinoid14
0.59469
Carcinoid17
Carcinoid17
Carcinoid17
1.00000
Carcinoid2
0.82788
Carcinoid15
0.72976
Carcinoid4
0.69915
Carcinoid9
0.68714
Carcinoid16
0.65897
Carcinoid14
0.63565
Carcinoid20
0.62751
Carcinoid18
Carcinoid18
Carcinoid18
1.00000
Carcinoid12
0.40774
Carcinoid20
0.39237
Carcinoid13
0.38769
Normal6
-0.38244
Normal8
-0.37752
Colon1
-0.36538
Normal3
-0.36512
Carcinoid19
Carcinoid19
Carcinoid19
1.00000
Carcinoid20
0.75603
Carcinoid12
0.68722
Carcinoid13
0.67641
Carcinoid7
0.66637
Carcinoid1
0.64338
Carcinoid17
0.57726
Carcinoid2
0.56875
Coefficients de corrélation de Pearson, N = 12625
Carcinoid20
Carcinoid20
Carcinoid20
1.00000
Carcinoid19
0.75603
Carcinoid13
0.72258
Carcinoid12
0.66621
Normal10
-0.62818
Carcinoid17
0.62751
Carcinoid1
0.61351
Carcinoid7
0.61242
Colon1
Colon1
Colon1
1.00000
Colon10
0.52391
Colon8
0.47107
Carcinoid20
-0.46948
Carcinoid13
-0.46442
Colon7
0.46279
Carcinoid12
-0.42695
Colon5
0.39584
Colon2
Colon2
Colon2
1.00000
Colon5
0.53715
Colon8
0.50553
Colon11
0.50005
Colon4
0.49674
Colon10
0.48671
Colon9
0.45048
Colon7
0.41451
Colon3
Colon3
Colon3
1.00000
Colon7
0.34298
Colon13
0.30004
Carcinoid15
-0.29628
Colon11
0.27278
Colon9
0.25388
Colon10
0.24795
Carcinoid17
-0.24515
Colon4
Colon4
Colon4
1.00000
Colon5
0.76511
Colon11
0.57350
Colon12
0.55389
Colon8
0.54034
Colon10
0.50760
Colon2
0.49674
Colon7
0.48757
Colon5
Colon5
Colon5
1.00000
Colon4
0.76511
Colon10
0.61925
Colon7
0.53726
Colon2
0.53715
Colon8
0.51923
Colon11
0.47195
Colon9
0.40288
Colon6
Colon6
Colon6
1.00000
Colon12
0.51281
Colon4
0.41797
Colon11
0.39771
Colon9
0.34628
Colon13
0.33400
Colon2
0.32768
Colon8
0.31242
Colon Colon Colon Colon Colon Colon Colon Colon Colon
Coefficients de corrélation de Pearson, N = 12625
7
Colon7
7
1.00000
8
0.55466
5
0.53726
11
0.53362
10
0.49063
4
0.48757
9
0.48755
1
0.46279
Colon8
Colon8
Colon8
1.00000
Colon7
0.55466
Colon4
0.54034
Colon10
0.53437
Colon11
0.52166
Colon5
0.51923
Colon2
0.50553
Colon12
0.47912
Colon9
Colon9
Colon9
1.00000
Colon7
0.48755
Colon11
0.46316
Carcinoid7
-0.45329
Colon2
0.45048
Colon8
0.44571
Colon4
0.42571
Carcinoid15
-0.41483
Colon10
Colon10
Colon10
1.00000
Colon5
0.61925
Colon8
0.53437
Colon1
0.52391
Colon4
0.50760
Colon7
0.49063
Colon2
0.48671
Colon13
0.41241
Colon11
Colon11
Colon11
1.00000
Colon4
0.57350
Colon7
0.53362
Colon8
0.52166
Colon2
0.50005
Colon12
0.47237
Colon5
0.47195
Colon9
0.46316
Colon12
Colon12
Colon12
1.00000
Colon4
0.55389
Colon6
0.51281
Colon8
0.47912
Colon13
0.47698
Colon11
0.47237
Colon2
0.39536
Colon5
0.37724
Colon13
Colon13
Colon13
1.00000
Colon4
0.48486
Colon12
0.47698
Colon10
0.41241
Colon11
0.35161
Colon6
0.33400
Colon2
0.32347
Normal14
-0.32289
Normal1
Norma
Normal1
1.0000
Normal6
0.7158
Normal8
0.6832
Normal13
0.6564
Normal9
0.6551
Normal10
0.6410
Normal5
0.6378
Normal15
0.6091
Coefficients de corrélation de Pearson, N = 12625
l1 0 0 7 2 3 9 9 6
Normal2
Normal2
Normal2
1.00000
Normal10
0.81377
Normal5
0.76149
Normal7
0.75402
Normal17
0.73383
Normal8
0.73289
Normal9
0.72105
Normal3
0.68483
Normal3
Normal3
Normal3
1.00000
Normal9
0.78681
Normal7
0.77417
Normal5
0.76386
Normal6
0.76234
Normal8
0.75050
Normal16
0.68702
Normal14
0.68599
Normal4
Normal4
Normal4
1.00000
Normal5
0.74139
Normal8
0.69502
Normal6
0.68872
Normal3
0.64913
Normal2
0.64644
Normal16
0.64563
Normal17
0.63615
Normal5
Normal5
Normal5
1.00000
Normal9
0.79233
Normal17
0.77752
Normal3
0.76386
Normal2
0.76149
Normal6
0.75498
Normal8
0.75131
Normal4
0.74139
Normal6
Normal6
Normal6
1.00000
Normal9
0.77519
Normal8
0.77407
Normal3
0.76234
Normal5
0.75498
Normal7
0.73208
Normal1
0.71580
Normal10
0.71054
Normal7
Normal7
Normal7
1.00000
Normal8
0.78269
Normal10
0.78147
Normal3
0.77417
Normal9
0.76339
Normal2
0.75402
Normal5
0.73753
Normal6
0.73208
Normal8
Normal8
Normal8
1.00000
Normal9
0.82385
Normal7
0.78269
Normal6
0.77407
Normal5
0.75131
Normal3
0.75050
Normal10
0.74076
Normal2
0.73289
Normal9
Normal9
Normal8
Normal5
Normal3
Normal6
Normal7
Normal17
Normal16
Coefficients de corrélation de Pearson, N = 12625
Normal9
1.00000
0.82385
0.79233
0.78681
0.77519
0.76339
0.76014
0.72997
Normal10
Normal10
Normal10
1.00000
Normal2
0.81377
Normal7
0.78147
Normal8
0.74076
Normal5
0.71437
Normal6
0.71054
Normal17
0.70908
Normal9
0.70497
Normal11
Normal11
Normal11
1.00000
Normal5
0.70896
Normal17
0.70307
Normal16
0.69957
Normal6
0.67592
Normal9
0.67177
Normal10
0.66273
Normal2
0.63507
Normal12
Normal12
Normal12
1.00000
Normal1
0.60477
Normal10
0.57498
Normal13
0.54883
Normal8
0.51963
Carcinoid20
-0.51910
Normal6
0.51896
Carcinoid17
-0.51502
Normal13
Normal13
Normal13
1.00000
Normal10
0.68100
Normal6
0.68037
Normal1
0.65642
Normal2
0.63214
Normal5
0.62261
Normal8
0.60417
Normal7
0.58099
Normal14
Normal14
Normal14
1.00000
Normal8
0.72169
Normal3
0.68599
Normal9
0.67728
Normal5
0.67636
Normal7
0.67364
Normal2
0.67173
Normal6
0.64870
Normal15
Normal15
Normal15
1.00000
Normal5
0.69502
Normal6
0.65994
Normal4
0.61474
Normal1
0.60916
Normal8
0.59538
Normal16
0.59358
Normal3
0.59067
Normal16
Normal16
Normal16
1.00000
Normal5
0.73010
Normal9
0.72997
Normal6
0.70484
Normal11
0.69957
Normal3
0.68702
Normal4
0.64563
Normal17
0.61784
Coefficients de corrélation de Pearson, N = 12625
Normal17
Normal17
Normal17
1.00000
Normal5
0.77752
Normal9
0.76014
Normal2
0.73383
Normal8
0.72886
Normal10
0.70908
Normal11
0.70307
Normal6
0.68954
SmallCell1
SmallCell1
SmallCell1
1.00000
SmallCell5
0.43470
Carcinoid4
-0.41770
Carcinoid17
-0.40781
Carcinoid2
-0.39123
Carcinoid16
-0.38007
Carcinoid14
-0.37400
SmallCell3
0.37240
SmallCell2
SmallCell2
SmallCell2
1.00000
SmallCell5
0.52080
SmallCell3
0.48107
SmallCell4
0.41688
Normal17
-0.35743
SmallCell6
0.35288
Normal11
-0.31516
Normal16
-0.29002
SmallCell3
SmallCell3
SmallCell3
1.00000
SmallCell5
0.65225
SmallCell6
0.55030
SmallCell2
0.48107
SmallCell1
0.37240
Normal6
-0.35422
Normal9
-0.33901
Normal8
-0.32282
SmallCell4
SmallCell4
SmallCell4
1.00000
SmallCell2
0.41688
SmallCell1
0.35445
SmallCell5
0.35163
SmallCell3
0.31675
Colon13
-0.23498
Carcinoid2
-0.20339
Carcinoid17
-0.19663
SmallCell5
SmallCell5
SmallCell5
1.00000
SmallCell3
0.65225
SmallCell2
0.52080
SmallCell6
0.45510
SmallCell1
0.43470
SmallCell4
0.35163
Carcinoid3
-0.29408
Carcinoid18
0.28815
SmallCell6
SmallCell6
SmallCell6
1.00000
SmallCell3
0.55030
Normal6
-0.4681
Normal8
-0.4621
SmallCell5
0.45510
Normal10
-0.4432
Normal7
-0.4420
Normal9
-0.4231
Coefficients de corrélation de Pearson, N = 12625
6 0 8 3 4