AHFR analysis
Juan Steibel
6/14/2021
Analysis of Capsid AHFR datasets
prepare all packages
library(tidyverse)
library(readxl)
library(lsmeans)
library(lme4)
library(ggplot2)
library(lmerTest)
setwd("C:/Users/marti/OneDrive/Documents/andras/AHFR/")Load data for AFHR and represent in a graphic
Read data and show graphics
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "AHFR")
ggplot(dts,aes(y=`Aqueous flow`,x=`Age (weeks)`,color=`ID`))+geom_point()+facet_grid(rows=vars(`Eye imaged`),cols=vars(`Group`))
ggplot(dts,aes(y=`Aqueous flow`,x=`Age (weeks)`))+facet_grid(rows=vars(`Eye imaged`),cols=vars(`Group`))+geom_point()+geom_smooth()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
The patter over age is not clear. But we can include a linear age term and let it interact with group.
ANOVA and mean comparisons
A linear mixed model was fit that included fixed effects of group and eye and fixed age*group term plus a random term for dog to account for repeated measures.
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Aqueous flow`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 78.709 78.709 1 17.789 16.2263 0.0008052 ***
## `Eye imaged` 0.544 0.544 1 50.834 0.1121 0.7391180
## age 3.236 3.236 1 41.748 0.6672 0.4186822
## Group:age 8.461 8.461 1 41.806 1.7442 0.1937896
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 3.52 0.442 23.6 2.61 4.43
## WT 5.95 0.409 13.0 5.06 6.83
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT -2.43 0.602 17.8 -4.028 0.0008
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogerDifferences between WT and mut are significant.The least square mean for WT larger than the mean for mut.
Repeat for IOP
Read data and show graphics
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "IOP")
ggplot(dts,aes(y=`Average IOP`,x=`Age (weeks)`,color=`ID`))+geom_point()+facet_grid(rows=vars(`Eye imaged`),cols=vars(`Group`))
ggplot(dts,aes(y=`Average IOP`,x=`Age (weeks)`))+facet_grid(rows=vars(`Eye imaged`),cols=vars(`Group`))+geom_point()+geom_smooth()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Here the interaction between age and group seems to be stronger
ANOVA and mean comparisons for (IOP)
A linear mixed model was fit that included fixed effects of group and eye and fixed age*group term plus a random term for dog to account for repeated measures.
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Average IOP`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 790.24 790.24 1 24.963 66.2047 1.742e-08 ***
## `Eye imaged` 0.36 0.36 1 46.460 0.0304 0.862424
## age 116.67 116.67 1 42.557 9.7742 0.003186 **
## Group:age 275.25 275.25 1 42.479 23.0601 1.976e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 28.3 1.17 25.9 25.9 30.7
## WT 14.1 1.30 24.2 11.4 16.8
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 14.2 1.75 25 8.137 <.0001
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `Average IOP` ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: 438.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6317 -0.3729 -0.0754 0.3606 2.9419
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 16.08 4.010
## Residual 11.94 3.455
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 28.41810 1.24120 30.70213 22.896 < 2e-16 ***
## GroupWT -14.22967 1.74661 23.42385 -8.147 2.74e-08 ***
## `Eye imaged`OS -0.14862 0.84936 44.94830 -0.175 0.862
## age 0.06770 0.01314 47.20504 5.152 4.97e-06 ***
## GroupWT:age -0.08201 0.01674 40.86180 -4.898 1.57e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.632
## `Eyimagd`OS -0.337 0.005
## age 0.141 -0.094 -0.026
## GroupWT:age -0.112 -0.023 0.025 -0.785Confirmed: there is a significant interaction effect of age and group on IOP. However, the marginal effect of group is strong enought for the IOP to still be significantly higher in mut compared to WT.
All other variables
ACD
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "ACD")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Acd-A`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 0.10525 0.10525 1 20.078 0.6907 0.41571
## `Eye imaged` 0.21214 0.21214 1 58.886 1.3921 0.24279
## age 0.54666 0.54666 1 42.623 3.5873 0.06502 .
## Group:age 0.84865 0.84865 1 42.578 5.5690 0.02294 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 4.26 0.0654 27.1 4.12 4.39
## WT 4.34 0.0682 15.3 4.19 4.48
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT -0.0785 0.0945 20.1 -0.831 0.4157
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `Acd-A` ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: 101.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.12797 -0.53621 -0.01017 0.72039 1.92011
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.0003677 0.01917
## Residual 0.1523880 0.39037
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.203772 0.079085 33.655868 53.155 <2e-16 ***
## GroupWT 0.078523 0.092332 9.579961 0.850 0.4158
## `Eye imaged`OS 0.108971 0.090904 48.010364 1.199 0.2365
## age 0.002291 0.000873 32.704684 2.624 0.0131 *
## GroupWT:age -0.002542 0.001068 26.747756 -2.380 0.0247 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.590
## `Eyimagd`OS -0.577 0.031
## age 0.157 -0.127 -0.016
## GroupWT:age -0.121 0.049 0.000 -0.817CCT
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "CCT")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`CCT`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 0.00090908 0.00090908 1 25.816 1.9634 0.1731
## `Eye imaged` 0.00003615 0.00003615 1 43.723 0.0781 0.7812
## age 0.00014172 0.00014172 1 61.421 0.3061 0.5821
## Group:age 0.00103310 0.00103310 1 61.316 2.2313 0.1404lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 0.633 0.0129 25.9 0.607 0.660
## WT 0.606 0.0144 25.7 0.576 0.636
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 0.0271 0.0193 25.8 1.401 0.1731
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: CCT ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: -232.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.37794 -0.45812 0.04689 0.43214 2.01508
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.002409 0.04908
## Residual 0.000463 0.02152
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.339e-01 1.314e-02 2.847e+01 48.252 <2e-16 ***
## GroupWT -2.711e-02 1.933e-02 2.620e+01 -1.402 0.173
## `Eye imaged`OS -1.498e-03 5.355e-03 4.410e+01 -0.280 0.781
## age 7.354e-05 1.132e-04 6.805e+01 0.650 0.518
## GroupWT:age -2.335e-04 1.520e-04 6.148e+01 -1.536 0.130
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.652
## `Eyimagd`OS -0.202 0.000
## age 0.113 -0.072 -0.035
## GroupWT:age -0.087 -0.044 0.042 -0.745CM-D
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "Crn diam")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Cornea diameter (mm)`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 0.94789 0.94789 1 26.162 10.4354 0.0033244 **
## `Eye imaged` 0.01545 0.01545 1 43.062 0.1700 0.6821235
## age 1.08531 1.08531 1 68.281 11.9482 0.0009454 ***
## Group:age 0.23127 0.23127 1 68.242 2.5461 0.1151888
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 17.5 0.236 26.1 17.0 17.9
## WT 16.3 0.265 26.2 15.8 16.9
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 1.15 0.355 26.2 3.230 0.0033
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `Cornea diameter (mm)` ~ Group + `Eye imaged` + age * Group +
## (1 | ID)
## Data: dts
##
## REML criterion at convergence: 145.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.12316 -0.30230 0.06611 0.20293 2.62575
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 0.84367 0.9185
## Residual 0.09083 0.3014
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 17.478604 0.239064 23.180051 73.113 < 2e-16 ***
## GroupWT -1.146708 0.354725 22.085339 -3.233 0.003813 **
## `Eye imaged`OS -0.031036 0.075199 38.732771 -0.413 0.682090
## age 0.006309 0.001753 67.169019 3.599 0.000606 ***
## GroupWT:age -0.003988 0.002430 68.020160 -1.641 0.105406
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.657
## `Eyimagd`OS -0.156 -0.001
## age 0.096 -0.061 -0.038
## GroupWT:age -0.073 -0.049 0.049 -0.722AS Vol
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "AS Vol")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Vol A.S.`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 15143 15143 1 25.036 5.6037 0.0259614 *
## `Eye imaged` 4670 4670 1 46.175 1.7282 0.1951325
## age 19555 19555 1 43.492 7.2364 0.0100939 *
## Group:age 39386 39386 1 43.410 14.5747 0.0004233 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 654 18.3 25.9 616 691
## WT 589 20.4 24.4 547 631
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 64.9 27.4 25 2.367 0.0260
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `Vol A.S.` ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: 814.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.10255 -0.53116 -0.05529 0.38512 2.34257
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 4043 63.59
## Residual 2702 51.98
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 645.2372 19.3499 31.6621 33.346 < 2e-16 ***
## GroupWT -64.8528 27.3635 24.8242 -2.370 0.025873 *
## `Eye imaged`OS 16.8877 12.7970 45.9714 1.320 0.193482
## age 0.8621 0.2031 49.7256 4.244 9.55e-05 ***
## GroupWT:age -1.0116 0.2596 43.1955 -3.897 0.000334 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.634
## `Eyimagd`OS -0.326 0.005
## age 0.140 -0.093 -0.027
## GroupWT:age -0.111 -0.025 0.026 -0.783AC Vol
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "AC Vol")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`AC Volume`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 7462.9 7462.9 1 24.899 3.6450 0.067827 .
## `Eye imaged` 3563.0 3563.0 1 46.716 1.7402 0.193538
## age 14771.8 14771.8 1 41.836 7.2148 0.010324 *
## Group:age 24698.5 24698.5 1 41.762 12.0631 0.001211 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 471 14.8 25.9 441 502
## WT 429 16.5 24.1 395 463
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 42.3 22.1 24.9 1.909 0.0678
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `AC Volume` ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: 792
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.85089 -0.51196 -0.06331 0.41832 2.29271
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 2522 50.22
## Residual 2047 45.25
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 464.0964 15.7834 32.1356 29.404 < 2e-16 ***
## GroupWT -42.2747 22.1126 24.2682 -1.912 0.067780 .
## `Eye imaged`OS 14.7217 11.1108 46.1104 1.325 0.191702
## age 0.6711 0.1682 47.0569 3.991 0.000229 ***
## GroupWT:age -0.7569 0.2138 41.1023 -3.540 0.001010 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.630
## `Eyimagd`OS -0.347 0.006
## age 0.142 -0.095 -0.026
## GroupWT:age -0.113 -0.021 0.024 -0.787Crn Vol
For all other variables, I conduct a single pass analysis, where I read data and fit the linear model described before
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "Crn Vol")
dts<-mutate(dts,age=as.numeric(`Age (weeks)`)-mean(`Age (weeks)`))
ah_lm<-lmer(`Kv-A`~Group+`Eye imaged`+age*Group+(1|ID),data=dts)
anova(ah_lm,ddf = "Kenward-Roger")## Type III Analysis of Variance Table with Kenward-Roger's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Group 806.72 806.72 1 25.657 9.0031 0.0059290 **
## `Eye imaged` 41.99 41.99 1 44.107 0.4686 0.4971906
## age 335.02 335.02 1 57.103 3.7389 0.0581221 .
## Group:age 1139.72 1139.72 1 56.990 12.7194 0.0007414 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeans(ah_lm,pairwise~Group)## NOTE: Results may be misleading due to involvement in interactions## $lsmeans
## Group lsmean SE df lower.CL upper.CL
## MUT 182 5.03 25.9 172 192
## WT 159 5.64 25.5 148 171
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## MUT - WT 22.7 7.56 25.7 3.001 0.0059
##
## Results are averaged over the levels of: Eye imaged
## Degrees-of-freedom method: kenward-rogersummary(ah_lm)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: `Kv-A` ~ Group + `Eye imaged` + age * Group + (1 | ID)
## Data: dts
##
## REML criterion at convergence: 601.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.66506 -0.44593 -0.00178 0.39323 1.91604
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 359.25 18.954
## Residual 89.61 9.466
## Number of obs: 74, groups: ID, 29
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 181.22941 5.16386 28.14128 35.096 < 2e-16 ***
## GroupWT -22.69283 7.55631 25.22391 -3.003 0.005957 **
## `Eye imaged`OS 1.61295 2.35195 43.67705 0.686 0.496469
## age 0.17655 0.04713 65.13794 3.746 0.000383 ***
## GroupWT:age -0.22901 0.06248 56.72089 -3.665 0.000546 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) GropWT `Ei`OS age
## GroupWT -0.649
## `Eyimagd`OS -0.225 0.001
## age 0.120 -0.077 -0.033
## GroupWT:age -0.094 -0.041 0.038 -0.755Correlation analyses
This part is to explore the possibility of using other variables as proxy for predicting AHFR. First thing to do is a simple pairwise correlation.
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "ALL")
cr<-cor(dts[,10:17])
cr[8,]## Acd-A Kt-A Kd-A Vas-A Acv-A Kv-A
## 0.055433020 -0.090480892 -0.004148388 0.022395588 0.037763202 -0.029746706
## Average IOP Aqueous flow
## -0.242384456 1.000000000The correlations are extremely small. With Absolute value lower than 0.25. let’s try with a multiple regression.
dts<-read_xlsx("Fluorophotometry organized data -VR_minus glaucoma drugs.xlsx",sheet = "ALL")
dt<-dts[,10:17]
lmm<-lm(dt$`Aqueous flow`~as.matrix(dt[,1:7]))
summary(lmm)##
## Call:
## lm(formula = dt$`Aqueous flow` ~ as.matrix(dt[, 1:7]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3014 -1.7701 -0.3809 0.9556 8.5702
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 91.93976 89.68428 1.025 0.3095
## as.matrix(dt[, 1:7])Acd-A -3.84437 8.96234 -0.429 0.6695
## as.matrix(dt[, 1:7])Kt-A -88.86714 61.01096 -1.457 0.1505
## as.matrix(dt[, 1:7])Kd-A -3.73258 4.51044 -0.828 0.4113
## as.matrix(dt[, 1:7])Vas-A 0.32830 0.23317 1.408 0.1644
## as.matrix(dt[, 1:7])Acv-A -0.34177 0.24733 -1.382 0.1722
## as.matrix(dt[, 1:7])Kv-A NA NA NA NA
## as.matrix(dt[, 1:7])Average IOP -0.10898 0.04663 -2.337 0.0228 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.481 on 59 degrees of freedom
## Multiple R-squared: 0.1236, Adjusted R-squared: 0.03443
## F-statistic: 1.386 on 6 and 59 DF, p-value: 0.2352pairs(dt)
This does not help either. One last thing that could be atempted is some sort of non-linear relation. But without any prior knowledge, it would be too easy to overfit the data.
We can discuss this on THU.