| tags: [ Data Cleaning Imputation Bivariate Correlations R ] categories: [Coding Experiments ]
Pearson's correlations on imputed data set
# required packages
require(corrplot)
require(missMDA)
require(FactoMineR)
library(Hmisc)Introduction
Prior to performing principal component analyses, bivariate correlations need to be performed between variables to determine any underlying relationships. This is because PCA indentifies components that may better explain relationships or variability among variables that are related. If none of the variables are correlated, it would be futile to perform a PCA.
Methods and Results
1. Load data
phen.data.age <- read.csv('C:/Users/Martha/Documents/Honours/Project/honours.project/Data/NIES_master_database-age.csv')
phen.data.adults<-phen.data.age[phen.data.age$Age.excel>17,]
quant.variables<- c("Logmar.VA.Right", "Logmar.VA.Left", "R.Sph..pre.dilate.", "R.Cyl..pre.dilate.",
"R.Axis..pre.dilate.", "L.Sph..pre.dilate.", "L.Cyl..pre.dilate.", "L.Axis..pre.dilate.",
"R.K.value.H", "R.K.Value.H.Axis", "R.K.value.V", "R.K.value.V.Axis", "L.K.value.H",
"L.K.value.H.Axis", "L.K.value.V", "L.K.value.V.Axis", "R.Pachimetry", "L.Pachimetry", "R.Axial.Length",
"L.Axial.Length", "AC.Depth.R", "AC.Depth.L", "R.IOP.mmHg", "L.IOP.mmHg", "CDR.RE", "CDR.LE")
quant.data.adults<- phen.data.adults[quant.variables]
ocular_data <- quant.data.adults
ocular_data <- as.matrix(ocular_data)2. Perform imputation
nbdim = estim_ncpPCA(ocular_data, method = 'EM', method.cv="Kfold")##
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|=================================================================| 100%nbdim## $ncp
## [1] 5
##
## $criterion
## 0 1 2 3 4 5
## 810867.1 812754.7 807844.4 810153.7 802944.9 790850.0res.comp = MIPCA(ocular_data, ncp = nbdim$ncp, nboot = 1000)
imputed_phen_data<-res.comp$res.imputePCA
head(imputed_phen_data)## Logmar.VA.Right Logmar.VA.Left R.Sph..pre.dilate. R.Cyl..pre.dilate.
## 1 0.02 -0.04 0.25 0.00
## 2 0.10 0.16 0.00 -0.75
## 3 0.00 0.00 1.25 -1.25
## 4 0.30 0.08 1.25 -0.25
## 5 0.00 -0.10 1.25 -0.25
## 6 0.24 0.36 4.00 -0.50
## R.Axis..pre.dilate. L.Sph..pre.dilate. L.Cyl..pre.dilate.
## 1 0 0.25 -0.50
## 2 28 -0.50 -0.25
## 3 148 1.25 -0.25
## 4 97 1.50 -0.50
## 5 37 1.25 -0.75
## 6 46 3.75 -0.75
## L.Axis..pre.dilate. R.K.value.H R.K.Value.H.Axis R.K.value.V
## 1 79 42.00000 2.0000 43.00000
## 2 164 41.25000 7.0000 42.25000
## 3 24 43.77619 147.5682 44.76719
## 4 81 44.75000 5.0000 45.00000
## 5 164 44.75000 0.0000 44.75000
## 6 180 42.00000 8.0000 43.25000
## R.K.value.V.Axis L.K.value.H L.K.value.H.Axis L.K.value.V
## 1 92.00000 42.50000 5.00000 43.50000
## 2 97.00000 41.50000 168.00000 42.00000
## 3 48.29713 43.92883 36.60368 44.74071
## 4 95.00000 45.00000 60.00000 45.25000
## 5 90.00000 44.25000 178.00000 44.75000
## 6 98.00000 42.25000 177.00000 43.25000
## L.K.value.V.Axis R.Pachimetry L.Pachimetry R.Axial.Length L.Axial.Length
## 1 95.0000 532 554 24.31 24.10
## 2 78.0000 608 612 25.02 25.21
## 3 138.2271 507 510 22.78 22.80
## 4 150.0000 560 559 23.02 22.98
## 5 88.0000 556 562 21.75 22.04
## 6 87.0000 498 501 23.06 23.17
## AC.Depth.R AC.Depth.L R.IOP.mmHg L.IOP.mmHg CDR.RE CDR.LE
## 1 3.09 3.03 14 14 0.9 0.9
## 2 3.38 3.92 16 15 0.9 0.7
## 3 3.40 3.45 26 22 0.7 0.7
## 4 3.00 2.85 14 14 0.2 0.2
## 5 2.60 2.53 22 21 0.3 0.3
## 6 2.94 3.04 18 20 0.6 0.63. Perform Pearson’s correlation
pearson_imputed_data_2<-rcorr(imputed_phen_data, type="pearson")
pearson_coeff_2<-rcorr(imputed_phen_data, type="pearson")$r #extract pearson correlation coefficients
pearson_pval_2<-rcorr(imputed_phen_data, type="pearson")$P #extract p-values of correlations
pearson_phen_data_F<-rbind(pearson_coeff_2, pearson_pval_2) #bind p-values and coefficients
pearson_phen_data_F## Logmar.VA.Right Logmar.VA.Left R.Sph..pre.dilate.
## Logmar.VA.Right 1.000000e+00 4.454011e-01 0.017186736
## Logmar.VA.Left 4.454011e-01 1.000000e+00 0.054838125
## R.Sph..pre.dilate. 1.718674e-02 5.483813e-02 1.000000000
## R.Cyl..pre.dilate. -3.688587e-01 -2.525133e-01 -0.033743995
## R.Axis..pre.dilate. 1.388061e-01 9.961581e-02 0.050047958
## L.Sph..pre.dilate. 3.398164e-02 4.620814e-02 0.730333039
## L.Cyl..pre.dilate. -2.159157e-01 -3.359285e-01 0.005389548
## L.Axis..pre.dilate. 5.328228e-02 1.128061e-01 0.037417632
## R.K.value.H -1.345955e-02 -3.206278e-02 -0.108338149
## R.K.Value.H.Axis -1.867260e-02 -1.569874e-02 -0.048477396
## R.K.value.V 8.898591e-02 3.149647e-02 -0.066520015
## R.K.value.V.Axis 1.218296e-02 9.111135e-03 0.060012089
## L.K.value.H -9.494568e-03 -8.878938e-02 -0.100504485
## L.K.value.H.Axis 3.708237e-02 9.400021e-02 0.080258840
## L.K.value.V 7.708716e-02 7.511794e-02 -0.084444300
## L.K.value.V.Axis -5.464628e-02 -2.996776e-02 -0.031844529
## R.Pachimetry -7.176747e-02 -7.079376e-02 -0.028152645
## L.Pachimetry -5.312824e-02 -4.732768e-02 -0.022178378
## R.Axial.Length -5.713710e-03 3.170483e-02 -0.482319027
## L.Axial.Length -1.433367e-02 3.680919e-02 -0.396076139
## AC.Depth.R -3.333595e-02 -3.139923e-02 -0.361096066
## AC.Depth.L -2.866435e-02 -5.256072e-02 -0.343645600
## R.IOP.mmHg -2.582148e-02 -1.552415e-02 -0.049335731
## L.IOP.mmHg -2.689835e-02 2.648440e-02 -0.047631682
## CDR.RE 1.773177e-01 1.915697e-01 0.063687069
## CDR.LE 1.159215e-01 1.735255e-01 0.073417171
## Logmar.VA.Right NA 0.000000e+00 0.633289018
## Logmar.VA.Left 0.000000e+00 NA 0.127674480
## R.Sph..pre.dilate. 6.332890e-01 1.276745e-01 NA
## R.Cyl..pre.dilate. 0.000000e+00 1.040723e-12 0.348795212
## R.Axis..pre.dilate. 1.080692e-04 5.570931e-03 0.164499525
## L.Sph..pre.dilate. 3.454094e-01 1.993780e-01 0.000000000
## L.Cyl..pre.dilate. 1.319169e-09 0.000000e+00 0.881077415
## L.Axis..pre.dilate. 1.388586e-01 1.682054e-03 0.298805584
## R.K.value.H 7.086829e-01 3.733457e-01 0.002560324
## R.K.Value.H.Axis 6.042091e-01 6.629886e-01 0.178166580
## R.K.value.V 1.332466e-02 3.818501e-01 0.064529664
## R.K.value.V.Axis 7.352232e-01 8.003369e-01 0.095452464
## L.K.value.H 7.921228e-01 1.353080e-02 0.005159925
## L.K.value.H.Axis 3.031591e-01 8.921719e-03 0.025653573
## L.K.value.V 3.211583e-02 3.679188e-02 0.018864872
## L.K.value.V.Axis 1.290145e-01 4.053928e-01 0.376609310
## R.Pachimetry 4.607717e-02 4.911935e-02 0.434442168
## L.Pachimetry 1.400057e-01 1.886938e-01 0.538092138
## R.Axial.Length 8.739826e-01 3.787074e-01 0.000000000
## L.Axial.Length 6.907091e-01 3.067375e-01 0.000000000
## AC.Depth.R 3.546576e-01 3.833223e-01 0.000000000
## AC.Depth.L 4.261335e-01 1.442946e-01 0.000000000
## R.IOP.mmHg 4.734549e-01 6.665095e-01 0.170596380
## L.IOP.mmHg 4.551985e-01 4.621690e-01 0.185866753
## CDR.RE 7.001193e-07 7.989846e-08 0.076791292
## CDR.LE 1.243866e-03 1.212600e-06 0.041284650
## R.Cyl..pre.dilate. R.Axis..pre.dilate.
## Logmar.VA.Right -3.688587e-01 1.388061e-01
## Logmar.VA.Left -2.525133e-01 9.961581e-02
## R.Sph..pre.dilate. -3.374399e-02 5.004796e-02
## R.Cyl..pre.dilate. 1.000000e+00 -1.693042e-01
## R.Axis..pre.dilate. -1.693042e-01 1.000000e+00
## L.Sph..pre.dilate. -2.717719e-02 6.865934e-02
## L.Cyl..pre.dilate. 5.973295e-01 -7.356295e-02
## L.Axis..pre.dilate. -7.230666e-02 -1.425961e-01
## R.K.value.H 8.765792e-02 2.146923e-02
## R.K.Value.H.Axis 1.688868e-02 2.298502e-01
## R.K.value.V -2.580297e-01 4.735102e-02
## R.K.value.V.Axis -1.105367e-02 -1.916153e-01
## L.K.value.H 7.823322e-02 3.857773e-02
## L.K.value.H.Axis -1.981146e-02 -1.091434e-01
## L.K.value.V -2.143308e-01 4.740708e-02
## L.K.value.V.Axis -3.319770e-03 1.462404e-01
## R.Pachimetry 6.221456e-02 -3.707056e-02
## L.Pachimetry 6.196682e-02 -3.224088e-02
## R.Axial.Length -8.062329e-02 -3.639616e-02
## L.Axial.Length -9.725968e-02 -6.518836e-02
## AC.Depth.R -8.751128e-02 -1.209965e-02
## AC.Depth.L -6.091203e-02 -1.761891e-02
## R.IOP.mmHg 4.339635e-02 8.290154e-03
## L.IOP.mmHg 2.894962e-02 -7.485854e-03
## CDR.RE -1.361865e-01 5.588392e-02
## CDR.LE -1.066871e-01 6.567715e-02
## Logmar.VA.Right 0.000000e+00 1.080692e-04
## Logmar.VA.Left 1.040723e-12 5.570931e-03
## R.Sph..pre.dilate. 3.487952e-01 1.644995e-01
## R.Cyl..pre.dilate. NA 2.204190e-06
## R.Axis..pre.dilate. 2.204190e-06 NA
## L.Sph..pre.dilate. 4.505366e-01 5.637958e-02
## L.Cyl..pre.dilate. 0.000000e+00 4.088220e-02
## L.Axis..pre.dilate. 4.446177e-02 6.934744e-05
## R.K.value.H 1.477316e-02 5.511691e-01
## R.K.Value.H.Axis 6.391930e-01 1.000124e-10
## R.K.value.V 3.190781e-13 1.884756e-01
## R.K.value.V.Axis 7.589682e-01 7.932498e-08
## L.K.value.H 2.963590e-02 2.840638e-01
## L.K.value.H.Axis 5.823344e-01 2.376240e-03
## L.K.value.V 1.750038e-09 1.879524e-01
## L.K.value.V.Axis 9.265788e-01 4.478748e-05
## R.Pachimetry 8.387722e-02 3.033133e-01
## L.Pachimetry 8.511976e-02 3.706955e-01
## R.Axial.Length 2.498840e-02 3.122006e-01
## L.Axial.Length 6.807011e-03 7.007616e-02
## AC.Depth.R 1.494131e-02 7.369667e-01
## AC.Depth.L 9.057720e-02 6.247697e-01
## R.IOP.mmHg 2.281421e-01 8.179977e-01
## L.IOP.mmHg 4.215422e-01 8.353895e-01
## CDR.RE 1.458928e-04 1.205587e-01
## CDR.LE 2.979093e-03 6.799657e-02
## L.Sph..pre.dilate. L.Cyl..pre.dilate.
## Logmar.VA.Right 0.0339816391 -2.159157e-01
## Logmar.VA.Left 0.0462081411 -3.359285e-01
## R.Sph..pre.dilate. 0.7303330391 5.389548e-03
## R.Cyl..pre.dilate. -0.0271771939 5.973295e-01
## R.Axis..pre.dilate. 0.0686593364 -7.356295e-02
## L.Sph..pre.dilate. 1.0000000000 -1.168117e-01
## L.Cyl..pre.dilate. -0.1168116609 1.000000e+00
## L.Axis..pre.dilate. 0.0523287613 -1.496289e-01
## R.K.value.H -0.0844018236 2.761341e-02
## R.K.Value.H.Axis -0.0080634243 1.164528e-02
## R.K.value.V -0.0562417035 -2.250674e-01
## R.K.value.V.Axis 0.0398679186 -5.210953e-02
## L.K.value.H -0.1532123389 1.951523e-01
## L.K.value.H.Axis 0.0506513880 -5.920490e-02
## L.K.value.V -0.0837598728 -2.826019e-01
## L.K.value.V.Axis -0.0209120347 -8.567104e-04
## R.Pachimetry -0.0220820589 4.228394e-02
## L.Pachimetry -0.0089273430 6.010379e-02
## R.Axial.Length -0.4634724349 -6.678543e-02
## L.Axial.Length -0.4499419623 -9.160339e-02
## AC.Depth.R -0.3257406411 -7.188980e-02
## AC.Depth.L -0.2919984785 -7.073071e-02
## R.IOP.mmHg -0.0735415773 6.014899e-02
## L.IOP.mmHg -0.0781540536 8.973181e-02
## CDR.RE 0.0853704666 -1.071664e-01
## CDR.LE 0.0954691132 -9.545223e-02
## Logmar.VA.Right 0.3454094044 1.319169e-09
## Logmar.VA.Left 0.1993779612 0.000000e+00
## R.Sph..pre.dilate. 0.0000000000 8.810774e-01
## R.Cyl..pre.dilate. 0.4505365714 0.000000e+00
## R.Axis..pre.dilate. 0.0563795825 4.088220e-02
## L.Sph..pre.dilate. NA 1.139570e-03
## L.Cyl..pre.dilate. 0.0011395699 NA
## L.Axis..pre.dilate. 0.1460761913 2.954872e-05
## R.K.value.H 0.0189249969 4.432979e-01
## R.K.Value.H.Axis 0.8228917321 7.464989e-01
## R.K.value.V 0.1181967288 2.471263e-10
## R.K.value.V.Axis 0.2682553404 1.477755e-01
## L.K.value.H 0.0000188467 4.508289e-08
## L.K.value.H.Axis 0.1594634143 1.000016e-01
## L.K.value.V 0.0198542568 1.110223e-15
## L.K.value.V.Axis 0.5615523197 9.810277e-01
## R.Pachimetry 0.5398591522 2.402997e-01
## L.Pachimetry 0.8042821165 9.494632e-02
## R.Axial.Length 0.0000000000 6.346858e-02
## L.Axial.Length 0.0000000000 1.083190e-02
## AC.Depth.R 0.0000000000 4.570640e-02
## AC.Depth.L 0.0000000000 4.932203e-02
## R.IOP.mmHg 0.0409409885 9.469756e-02
## L.IOP.mmHg 0.0298017542 1.256729e-02
## CDR.RE 0.0175946999 2.851500e-03
## CDR.LE 0.0079052609 7.916331e-03
## L.Axis..pre.dilate. R.K.value.H R.K.Value.H.Axis
## Logmar.VA.Right 5.328228e-02 -0.0134595504 -1.867260e-02
## Logmar.VA.Left 1.128061e-01 -0.0320627832 -1.569874e-02
## R.Sph..pre.dilate. 3.741763e-02 -0.1083381491 -4.847740e-02
## R.Cyl..pre.dilate. -7.230666e-02 0.0876579186 1.688868e-02
## R.Axis..pre.dilate. -1.425961e-01 0.0214692297 2.298502e-01
## L.Sph..pre.dilate. 5.232876e-02 -0.0844018236 -8.063424e-03
## L.Cyl..pre.dilate. -1.496289e-01 0.0276134111 1.164528e-02
## L.Axis..pre.dilate. 1.000000e+00 -0.0678690496 -1.355030e-01
## R.K.value.H -6.786905e-02 1.0000000000 -1.375863e-04
## R.K.Value.H.Axis -1.355030e-01 -0.0001375863 1.000000e+00
## R.K.value.V -4.120723e-02 0.8561504469 3.776652e-02
## R.K.value.V.Axis 1.502140e-01 0.0128834714 -3.312986e-01
## L.K.value.H -7.564871e-02 0.8488819993 2.885870e-02
## L.K.value.H.Axis 2.801829e-01 -0.0112961381 -2.054109e-01
## L.K.value.V -1.850401e-02 0.8098742743 3.417124e-02
## L.K.value.V.Axis -1.131125e-01 0.0064695392 1.620715e-01
## R.Pachimetry 2.169897e-02 -0.0244702866 1.110650e-02
## L.Pachimetry 2.417753e-02 -0.0316941263 -1.131536e-02
## R.Axial.Length 3.405846e-02 -0.5219316083 3.139872e-02
## L.Axial.Length 6.198091e-02 -0.4620957026 -9.910078e-03
## AC.Depth.R 6.827092e-03 -0.0268476943 1.880086e-02
## AC.Depth.L 1.860522e-02 -0.0721486880 2.550189e-02
## R.IOP.mmHg -2.398815e-02 0.0703163249 1.681101e-02
## L.IOP.mmHg 1.604946e-02 0.0592916819 1.854371e-02
## CDR.RE 1.819876e-04 -0.1114921184 -1.774599e-02
## CDR.LE -7.978182e-03 -0.1151646678 -1.774908e-02
## Logmar.VA.Right 1.388586e-01 0.7086829060 6.042091e-01
## Logmar.VA.Left 1.682054e-03 0.3733456613 6.629886e-01
## R.Sph..pre.dilate. 2.988056e-01 0.0025603236 1.781666e-01
## R.Cyl..pre.dilate. 4.446177e-02 0.0147731633 6.391930e-01
## R.Axis..pre.dilate. 6.934744e-05 0.5511691479 1.000124e-10
## L.Sph..pre.dilate. 1.460762e-01 0.0189249969 8.228917e-01
## L.Cyl..pre.dilate. 2.954872e-05 0.4432979234 7.464989e-01
## L.Axis..pre.dilate. NA 0.0592846697 1.576383e-04
## R.K.value.H 5.928467e-02 NA 9.969528e-01
## R.K.Value.H.Axis 1.576383e-04 0.9969528036 NA
## R.K.value.V 2.524945e-01 0.0000000000 2.943194e-01
## R.K.value.V.Axis 2.747572e-05 0.7206181623 0.000000e+00
## L.K.value.H 3.547783e-02 0.0000000000 4.230023e-01
## L.K.value.H.Axis 2.220446e-15 0.7538500000 8.246671e-09
## L.K.value.V 6.074783e-01 0.0000000000 3.427232e-01
## L.K.value.V.Axis 1.633392e-03 0.8574802634 5.933771e-06
## R.Pachimetry 5.469155e-01 0.4969192146 7.578522e-01
## L.Pachimetry 5.020834e-01 0.3788685290 7.534446e-01
## R.Axial.Length 3.443194e-01 0.0000000000 3.833300e-01
## L.Axial.Length 8.504870e-02 0.0000000000 7.832474e-01
## AC.Depth.R 8.496948e-01 0.4560483399 6.017272e-01
## AC.Depth.L 6.055148e-01 0.0449300399 4.789492e-01
## R.IOP.mmHg 5.054392e-01 0.0506714417 6.407352e-01
## L.IOP.mmHg 6.559385e-01 0.0995044000 6.067078e-01
## CDR.RE 9.959694e-01 0.0019062081 6.222741e-01
## CDR.LE 8.247335e-01 0.0013393827 6.222134e-01
## R.K.value.V R.K.value.V.Axis L.K.value.H
## Logmar.VA.Right 8.898591e-02 1.218296e-02 -9.494568e-03
## Logmar.VA.Left 3.149647e-02 9.111135e-03 -8.878938e-02
## R.Sph..pre.dilate. -6.652001e-02 6.001209e-02 -1.005045e-01
## R.Cyl..pre.dilate. -2.580297e-01 -1.105367e-02 7.823322e-02
## R.Axis..pre.dilate. 4.735102e-02 -1.916153e-01 3.857773e-02
## L.Sph..pre.dilate. -5.624170e-02 3.986792e-02 -1.532123e-01
## L.Cyl..pre.dilate. -2.250674e-01 -5.210953e-02 1.951523e-01
## L.Axis..pre.dilate. -4.120723e-02 1.502140e-01 -7.564871e-02
## R.K.value.H 8.561504e-01 1.288347e-02 8.488820e-01
## R.K.Value.H.Axis 3.776652e-02 -3.312986e-01 2.885870e-02
## R.K.value.V 1.000000e+00 1.310378e-02 7.601752e-01
## R.K.value.V.Axis 1.310378e-02 1.000000e+00 -3.390998e-02
## L.K.value.H 7.601752e-01 -3.390998e-02 1.000000e+00
## L.K.value.H.Axis -3.035603e-02 1.365079e-01 -4.844737e-02
## L.K.value.V 8.992973e-01 1.534125e-02 7.870445e-01
## L.K.value.V.Axis 2.632216e-03 -1.842536e-01 4.676476e-02
## R.Pachimetry -4.110367e-02 3.704538e-03 -7.850495e-03
## L.Pachimetry -5.771585e-02 1.141139e-02 -8.525538e-03
## R.Axial.Length -5.070540e-01 -5.888528e-02 -4.762205e-01
## L.Axial.Length -4.450582e-01 -2.916098e-02 -4.453847e-01
## AC.Depth.R -2.866161e-02 -3.710637e-02 -2.666432e-02
## AC.Depth.L -7.294788e-02 -3.942675e-02 -4.592850e-02
## R.IOP.mmHg 4.119578e-02 -3.456348e-02 8.453247e-02
## L.IOP.mmHg 2.794598e-02 -1.408438e-02 9.490281e-02
## CDR.RE -7.374125e-02 6.105801e-03 -1.201137e-01
## CDR.LE -9.081069e-02 -3.206109e-03 -1.240358e-01
## Logmar.VA.Right 1.332466e-02 7.352232e-01 7.921228e-01
## Logmar.VA.Left 3.818501e-01 8.003369e-01 1.353080e-02
## R.Sph..pre.dilate. 6.452966e-02 9.545246e-02 5.159925e-03
## R.Cyl..pre.dilate. 3.190781e-13 7.589682e-01 2.963590e-02
## R.Axis..pre.dilate. 1.884756e-01 7.932498e-08 2.840638e-01
## L.Sph..pre.dilate. 1.181967e-01 2.682553e-01 1.884670e-05
## L.Cyl..pre.dilate. 2.471263e-10 1.477755e-01 4.508289e-08
## L.Axis..pre.dilate. 2.524945e-01 2.747572e-05 3.547783e-02
## R.K.value.H 0.000000e+00 7.206182e-01 0.000000e+00
## R.K.Value.H.Axis 2.943194e-01 0.000000e+00 4.230023e-01
## R.K.value.V NA 7.160456e-01 0.000000e+00
## R.K.value.V.Axis 7.160456e-01 NA 3.464282e-01
## L.K.value.H 0.000000e+00 3.464282e-01 NA
## L.K.value.H.Axis 3.993328e-01 1.406603e-04 1.784358e-01
## L.K.value.V 0.000000e+00 6.702058e-01 0.000000e+00
## L.K.value.V.Axis 9.417545e-01 2.486420e-07 1.940121e-01
## R.Pachimetry 2.536896e-01 9.180975e-01 8.274942e-01
## L.Pachimetry 1.088449e-01 7.514208e-01 8.129243e-01
## R.Axial.Length 0.000000e+00 1.018499e-01 0.000000e+00
## L.Axial.Length 0.000000e+00 4.181589e-01 0.000000e+00
## AC.Depth.R 4.261779e-01 3.028461e-01 4.591321e-01
## AC.Depth.L 4.260305e-02 2.735915e-01 2.021142e-01
## R.IOP.mmHg 2.526264e-01 3.372083e-01 1.874060e-02
## L.IOP.mmHg 4.378240e-01 6.958180e-01 8.284183e-03
## CDR.RE 4.039447e-02 8.654146e-01 8.191989e-04
## CDR.LE 1.153914e-02 9.290858e-01 5.475918e-04
## L.K.value.H.Axis L.K.value.V L.K.value.V.Axis
## Logmar.VA.Right 3.708237e-02 7.708716e-02 -5.464628e-02
## Logmar.VA.Left 9.400021e-02 7.511794e-02 -2.996776e-02
## R.Sph..pre.dilate. 8.025884e-02 -8.444430e-02 -3.184453e-02
## R.Cyl..pre.dilate. -1.981146e-02 -2.143308e-01 -3.319770e-03
## R.Axis..pre.dilate. -1.091434e-01 4.740708e-02 1.462404e-01
## L.Sph..pre.dilate. 5.065139e-02 -8.375987e-02 -2.091203e-02
## L.Cyl..pre.dilate. -5.920490e-02 -2.826019e-01 -8.567104e-04
## L.Axis..pre.dilate. 2.801829e-01 -1.850401e-02 -1.131125e-01
## R.K.value.H -1.129614e-02 8.098743e-01 6.469539e-03
## R.K.Value.H.Axis -2.054109e-01 3.417124e-02 1.620715e-01
## R.K.value.V -3.035603e-02 8.992973e-01 2.632216e-03
## R.K.value.V.Axis 1.365079e-01 1.534125e-02 -1.842536e-01
## L.K.value.H -4.844737e-02 7.870445e-01 4.676476e-02
## L.K.value.H.Axis 1.000000e+00 1.987050e-03 -3.107153e-01
## L.K.value.V 1.987050e-03 1.000000e+00 2.167432e-02
## L.K.value.V.Axis -3.107153e-01 2.167432e-02 1.000000e+00
## R.Pachimetry -8.080029e-02 -5.278222e-02 2.080932e-02
## L.Pachimetry -9.378962e-02 -6.441326e-02 1.246881e-02
## R.Axial.Length -4.102191e-02 -4.779763e-01 3.031773e-02
## L.Axial.Length -6.588596e-03 -4.373384e-01 4.772779e-03
## AC.Depth.R -5.023448e-02 -1.551928e-02 6.716837e-03
## AC.Depth.L -2.427959e-02 -3.894027e-02 2.946164e-02
## R.IOP.mmHg -5.145410e-03 4.328532e-02 5.318492e-02
## L.IOP.mmHg -1.052531e-02 3.226861e-02 6.153925e-02
## CDR.RE 3.150660e-02 -9.608155e-02 4.070920e-02
## CDR.LE 1.360234e-02 -1.127845e-01 6.517838e-02
## Logmar.VA.Right 3.031591e-01 3.211583e-02 1.290145e-01
## Logmar.VA.Left 8.921719e-03 3.679188e-02 4.053928e-01
## R.Sph..pre.dilate. 2.565357e-02 1.886487e-02 3.766093e-01
## R.Cyl..pre.dilate. 5.823344e-01 1.750038e-09 9.265788e-01
## R.Axis..pre.dilate. 2.376240e-03 1.879524e-01 4.478748e-05
## L.Sph..pre.dilate. 1.594634e-01 1.985426e-02 5.615523e-01
## L.Cyl..pre.dilate. 1.000016e-01 1.110223e-15 9.810277e-01
## L.Axis..pre.dilate. 2.220446e-15 6.074783e-01 1.633392e-03
## R.K.value.H 7.538500e-01 0.000000e+00 8.574803e-01
## R.K.Value.H.Axis 8.246671e-09 3.427232e-01 5.933771e-06
## R.K.value.V 3.993328e-01 0.000000e+00 9.417545e-01
## R.K.value.V.Axis 1.406603e-04 6.702058e-01 2.486420e-07
## L.K.value.H 1.784358e-01 0.000000e+00 1.940121e-01
## L.K.value.H.Axis NA 9.560139e-01 0.000000e+00
## L.K.value.V 9.560139e-01 NA 5.473713e-01
## L.K.value.V.Axis 0.000000e+00 5.473713e-01 NA
## R.Pachimetry 2.467078e-02 1.426088e-01 5.634765e-01
## L.Pachimetry 9.076617e-03 7.348045e-02 7.292515e-01
## R.Axial.Length 2.546361e-01 0.000000e+00 3.999282e-01
## L.Axial.Length 8.548863e-01 0.000000e+00 8.946023e-01
## AC.Depth.R 1.629303e-01 6.666077e-01 8.520940e-01
## AC.Depth.L 5.002799e-01 2.795594e-01 4.133742e-01
## R.IOP.mmHg 8.864271e-01 2.293355e-01 1.395827e-01
## L.IOP.mmHg 7.701578e-01 3.702840e-01 8.729914e-02
## CDR.RE 3.816971e-01 7.512974e-03 2.582782e-01
## CDR.LE 7.057355e-01 1.685535e-03 7.011918e-02
## R.Pachimetry L.Pachimetry R.Axial.Length
## Logmar.VA.Right -7.176747e-02 -5.312824e-02 -0.005713710
## Logmar.VA.Left -7.079376e-02 -4.732768e-02 0.031704833
## R.Sph..pre.dilate. -2.815264e-02 -2.217838e-02 -0.482319027
## R.Cyl..pre.dilate. 6.221456e-02 6.196682e-02 -0.080623290
## R.Axis..pre.dilate. -3.707056e-02 -3.224088e-02 -0.036396163
## L.Sph..pre.dilate. -2.208206e-02 -8.927343e-03 -0.463472435
## L.Cyl..pre.dilate. 4.228394e-02 6.010379e-02 -0.066785428
## L.Axis..pre.dilate. 2.169897e-02 2.417753e-02 0.034058457
## R.K.value.H -2.447029e-02 -3.169413e-02 -0.521931608
## R.K.Value.H.Axis 1.110650e-02 -1.131536e-02 0.031398721
## R.K.value.V -4.110367e-02 -5.771585e-02 -0.507053975
## R.K.value.V.Axis 3.704538e-03 1.141139e-02 -0.058885283
## L.K.value.H -7.850495e-03 -8.525538e-03 -0.476220515
## L.K.value.H.Axis -8.080029e-02 -9.378962e-02 -0.041021905
## L.K.value.V -5.278222e-02 -6.441326e-02 -0.477976267
## L.K.value.V.Axis 2.080932e-02 1.246881e-02 0.030317729
## R.Pachimetry 1.000000e+00 9.515023e-01 0.019358611
## L.Pachimetry 9.515023e-01 1.000000e+00 0.008546207
## R.Axial.Length 1.935861e-02 8.546207e-03 1.000000000
## L.Axial.Length 4.117183e-02 3.134055e-02 0.876781035
## AC.Depth.R -2.251240e-02 -2.642278e-02 0.369048909
## AC.Depth.L -3.213576e-02 -3.998663e-02 0.401267212
## R.IOP.mmHg 2.017683e-01 2.101310e-01 -0.012607365
## L.IOP.mmHg 1.911503e-01 2.106094e-01 0.011325604
## CDR.RE -8.530554e-02 -6.842084e-02 0.066642423
## CDR.LE -8.335143e-02 -7.859245e-02 0.074704798
## Logmar.VA.Right 4.607717e-02 1.400057e-01 0.873982621
## Logmar.VA.Left 4.911935e-02 1.886938e-01 0.378707430
## R.Sph..pre.dilate. 4.344422e-01 5.380921e-01 0.000000000
## R.Cyl..pre.dilate. 8.387722e-02 8.511976e-02 0.024988404
## R.Axis..pre.dilate. 3.033133e-01 3.706955e-01 0.312200566
## L.Sph..pre.dilate. 5.398592e-01 8.042821e-01 0.000000000
## L.Cyl..pre.dilate. 2.402997e-01 9.494632e-02 0.063468583
## L.Axis..pre.dilate. 5.469155e-01 5.020834e-01 0.344319444
## R.K.value.H 4.969192e-01 3.788685e-01 0.000000000
## R.K.Value.H.Axis 7.578522e-01 7.534446e-01 0.383330028
## R.K.value.V 2.536896e-01 1.088449e-01 0.000000000
## R.K.value.V.Axis 9.180975e-01 7.514208e-01 0.101849917
## L.K.value.H 8.274942e-01 8.129243e-01 0.000000000
## L.K.value.H.Axis 2.467078e-02 9.076617e-03 0.254636072
## L.K.value.V 1.426088e-01 7.348045e-02 0.000000000
## L.K.value.V.Axis 5.634765e-01 7.292515e-01 0.399928178
## R.Pachimetry NA 0.000000e+00 0.590988274
## L.Pachimetry 0.000000e+00 NA 0.812479166
## R.Axial.Length 5.909883e-01 8.124792e-01 NA
## L.Axial.Length 2.529025e-01 3.842124e-01 0.000000000
## AC.Depth.R 5.319869e-01 4.632117e-01 0.000000000
## AC.Depth.L 3.722584e-01 2.668317e-01 0.000000000
## R.IOP.mmHg 1.522909e-08 3.662165e-09 0.726362941
## L.IOP.mmHg 8.537516e-08 3.369284e-09 0.753228721
## CDR.RE 1.768124e-02 5.724356e-02 0.064038493
## CDR.LE 2.046598e-02 2.889321e-02 0.037843165
## L.Axial.Length AC.Depth.R AC.Depth.L R.IOP.mmHg
## Logmar.VA.Right -0.014333673 -0.033335953 -0.02866435 -2.582148e-02
## Logmar.VA.Left 0.036809189 -0.031399229 -0.05256072 -1.552415e-02
## R.Sph..pre.dilate. -0.396076139 -0.361096066 -0.34364560 -4.933573e-02
## R.Cyl..pre.dilate. -0.097259682 -0.087511275 -0.06091203 4.339635e-02
## R.Axis..pre.dilate. -0.065188362 -0.012099648 -0.01761891 8.290154e-03
## L.Sph..pre.dilate. -0.449941962 -0.325740641 -0.29199848 -7.354158e-02
## L.Cyl..pre.dilate. -0.091603393 -0.071889804 -0.07073071 6.014899e-02
## L.Axis..pre.dilate. 0.061980911 0.006827092 0.01860522 -2.398815e-02
## R.K.value.H -0.462095703 -0.026847694 -0.07214869 7.031632e-02
## R.K.Value.H.Axis -0.009910078 0.018800865 0.02550189 1.681101e-02
## R.K.value.V -0.445058210 -0.028661605 -0.07294788 4.119578e-02
## R.K.value.V.Axis -0.029160985 -0.037106372 -0.03942675 -3.456348e-02
## L.K.value.H -0.445384671 -0.026664319 -0.04592850 8.453247e-02
## L.K.value.H.Axis -0.006588596 -0.050234478 -0.02427959 -5.145410e-03
## L.K.value.V -0.437338447 -0.015519283 -0.03894027 4.328532e-02
## L.K.value.V.Axis 0.004772779 0.006716837 0.02946164 5.318492e-02
## R.Pachimetry 0.041171831 -0.022512403 -0.03213576 2.017683e-01
## L.Pachimetry 0.031340548 -0.026422784 -0.03998663 2.101310e-01
## R.Axial.Length 0.876781035 0.369048909 0.40126721 -1.260737e-02
## L.Axial.Length 1.000000000 0.343819477 0.38058288 -3.173895e-02
## AC.Depth.R 0.343819477 1.000000000 0.80814429 -6.165880e-02
## AC.Depth.L 0.380582884 0.808144290 1.00000000 -7.141801e-02
## R.IOP.mmHg -0.031738950 -0.061658797 -0.07141801 1.000000e+00
## L.IOP.mmHg 0.003745218 -0.077963692 -0.09197031 7.819438e-01
## CDR.RE 0.042041218 -0.094371263 -0.03837619 5.983441e-02
## CDR.LE 0.052671354 -0.100985499 -0.06186336 5.621917e-02
## Logmar.VA.Right 0.690709145 0.354657638 0.42613355 4.734549e-01
## Logmar.VA.Left 0.306737539 0.383322328 0.14429455 6.665095e-01
## R.Sph..pre.dilate. 0.000000000 0.000000000 0.00000000 1.705964e-01
## R.Cyl..pre.dilate. 0.006807011 0.014941311 0.09057720 2.281421e-01
## R.Axis..pre.dilate. 0.070076163 0.736966685 0.62476970 8.179977e-01
## L.Sph..pre.dilate. 0.000000000 0.000000000 0.00000000 4.094099e-02
## L.Cyl..pre.dilate. 0.010831903 0.045706395 0.04932203 9.469756e-02
## L.Axis..pre.dilate. 0.085048695 0.849694820 0.60551482 5.054392e-01
## R.K.value.H 0.000000000 0.456048340 0.04493004 5.067144e-02
## R.K.Value.H.Axis 0.783247428 0.601727167 0.47894924 6.407352e-01
## R.K.value.V 0.000000000 0.426177934 0.04260305 2.526264e-01
## R.K.value.V.Axis 0.418158939 0.302846093 0.27359155 3.372083e-01
## L.K.value.H 0.000000000 0.459132104 0.20211423 1.874060e-02
## L.K.value.H.Axis 0.854886304 0.162930258 0.50027989 8.864271e-01
## L.K.value.V 0.000000000 0.666607673 0.27955937 2.293355e-01
## L.K.value.V.Axis 0.894602276 0.852094014 0.41337417 1.395827e-01
## R.Pachimetry 0.252902534 0.531986873 0.37225836 1.522909e-08
## L.Pachimetry 0.384212379 0.463211657 0.26683171 3.662165e-09
## R.Axial.Length 0.000000000 0.000000000 0.00000000 7.263629e-01
## L.Axial.Length NA 0.000000000 0.00000000 3.781944e-01
## AC.Depth.R 0.000000000 NA 0.00000000 8.668531e-02
## AC.Depth.L 0.000000000 0.000000000 NA 4.715027e-02
## R.IOP.mmHg 0.378194350 0.086685311 0.04715027 NA
## L.IOP.mmHg 0.917201338 0.030203839 0.01051777 0.000000e+00
## CDR.RE 0.243011952 0.008654521 0.28658887 9.643939e-02
## CDR.LE 0.143450682 0.004949057 0.08564305 1.183444e-01
## L.IOP.mmHg CDR.RE CDR.LE
## Logmar.VA.Right -2.689835e-02 1.773177e-01 0.1159214896
## Logmar.VA.Left 2.648440e-02 1.915697e-01 0.1735255038
## R.Sph..pre.dilate. -4.763168e-02 6.368707e-02 0.0734171713
## R.Cyl..pre.dilate. 2.894962e-02 -1.361865e-01 -0.1066870536
## R.Axis..pre.dilate. -7.485854e-03 5.588392e-02 0.0656771523
## L.Sph..pre.dilate. -7.815405e-02 8.537047e-02 0.0954691132
## L.Cyl..pre.dilate. 8.973181e-02 -1.071664e-01 -0.0954522276
## L.Axis..pre.dilate. 1.604946e-02 1.819876e-04 -0.0079781819
## R.K.value.H 5.929168e-02 -1.114921e-01 -0.1151646678
## R.K.Value.H.Axis 1.854371e-02 -1.774599e-02 -0.0177490829
## R.K.value.V 2.794598e-02 -7.374125e-02 -0.0908106873
## R.K.value.V.Axis -1.408438e-02 6.105801e-03 -0.0032061094
## L.K.value.H 9.490281e-02 -1.201137e-01 -0.1240357857
## L.K.value.H.Axis -1.052531e-02 3.150660e-02 0.0136023359
## L.K.value.V 3.226861e-02 -9.608155e-02 -0.1127844786
## L.K.value.V.Axis 6.153925e-02 4.070920e-02 0.0651783770
## R.Pachimetry 1.911503e-01 -8.530554e-02 -0.0833514295
## L.Pachimetry 2.106094e-01 -6.842084e-02 -0.0785924463
## R.Axial.Length 1.132560e-02 6.664242e-02 0.0747047983
## L.Axial.Length 3.745218e-03 4.204122e-02 0.0526713536
## AC.Depth.R -7.796369e-02 -9.437126e-02 -0.1009854992
## AC.Depth.L -9.197031e-02 -3.837619e-02 -0.0618633578
## R.IOP.mmHg 7.819438e-01 5.983441e-02 0.0562191681
## L.IOP.mmHg 1.000000e+00 1.047319e-01 0.1046829951
## CDR.RE 1.047319e-01 1.000000e+00 0.9606262010
## CDR.LE 1.046830e-01 9.606262e-01 1.0000000000
## Logmar.VA.Right 4.551985e-01 7.001193e-07 0.0012438656
## Logmar.VA.Left 4.621690e-01 7.989846e-08 0.0000012126
## R.Sph..pre.dilate. 1.858668e-01 7.679129e-02 0.0412846499
## R.Cyl..pre.dilate. 4.215422e-01 1.458928e-04 0.0029790933
## R.Axis..pre.dilate. 8.353895e-01 1.205587e-01 0.0679965662
## L.Sph..pre.dilate. 2.980175e-02 1.759470e-02 0.0079052609
## L.Cyl..pre.dilate. 1.256729e-02 2.851500e-03 0.0079163314
## L.Axis..pre.dilate. 6.559385e-01 9.959694e-01 0.8247335171
## R.K.value.H 9.950440e-02 1.906208e-03 0.0013393827
## R.K.Value.H.Axis 6.067078e-01 6.222741e-01 0.6222134051
## R.K.value.V 4.378240e-01 4.039447e-02 0.0115391384
## R.K.value.V.Axis 6.958180e-01 8.654146e-01 0.9290858486
## L.K.value.H 8.284183e-03 8.191989e-04 0.0005475918
## L.K.value.H.Axis 7.701578e-01 3.816971e-01 0.7057355363
## L.K.value.V 3.702840e-01 7.512974e-03 0.0016855345
## L.K.value.V.Axis 8.729914e-02 2.582782e-01 0.0701191832
## R.Pachimetry 8.537516e-08 1.768124e-02 0.0204659837
## L.Pachimetry 3.369284e-09 5.724356e-02 0.0288932098
## R.Axial.Length 7.532287e-01 6.403849e-02 0.0378431648
## L.Axial.Length 9.172013e-01 2.430120e-01 0.1434506815
## AC.Depth.R 3.020384e-02 8.654521e-03 0.0049490567
## AC.Depth.L 1.051777e-02 2.865889e-01 0.0856430537
## R.IOP.mmHg 0.000000e+00 9.643939e-02 0.1183444246
## L.IOP.mmHg NA 3.555109e-03 0.0035707260
## CDR.RE 3.555109e-03 NA 0.0000000000
## CDR.LE 3.570726e-03 0.000000e+00 NA4. Plot significant results from correlation
title <- "Pearson correlation of imputed phenotypic data"
corrplot.mixed(pearson_coeff_2, p.mat=pearson_pval_2, sig.level = 0.05, insig="blank", tl.pos = 'lt',
tl.col="black", tl.cex=0.60, mar=c(0,0,1,1), number.cex = 0.65, title=title)
Discussion
The correlation plots show very strong relationships between the left and right measurements for the same test, as expected. It is also evident that negative correlations exist between axial length and corneal curvature (keratometry), while there are positive correlations between axial length and anterior chamber depth, and corneal thickness and intraocular pressure. These relationships are expected as they overlap in function. Interestingly, there are very weak negative correlations between corneal curvature (keratometry / K-values) and cup-to-disc ratio. This has been reported in other studies (https://www.nature.com/articles/eye201098.pdf?origin=ppub), although the biological reason for this relationship is not well-established. There is also a very weak positive correlaton between the intraocular pressure for left eye, but not right, measurements and cup-to-disc ratio measurements for both eyes. And weak negative correlations between the anterior chamber depth for the right eye, but not left, and cup-to-disc ratio for both eyes.