Load Data
- Determine Normality
- Determine Variable Correlation
RBP4 Model
TTR Model
- TTR Final Model
- TTR Model Plots
Retinol Model
Genotype effect on Retinol, RBP4, and TTR
Table S2, S3
Figure 2

Load Data

Determine Normality

for Shapiro-Wilk test p-value<0.05 indicates variables does not have normal distribution

Shapiro-Wilk Normality Test
Variable	p-value
BMI	0.078
HOMA-IR	1.56e-05
Age	0.274
eGFR	0.606
Adiponectin	0.008
Leptin	0.036
NAFLD-FS	0.927
Note: data with p-value<0.05 will be log-transformed

Determine Variable Correlation

ANOVA Results with Sex
Variable	p-value
BMI	8.04e-03
HOMA-IR	0.54
Age	0.59
eGFR	0.63
Adiponectin	0.92
Leptin	4.36e-05
NAFLD-FS	0.67

Spearman Correlation
Variable Pair	rho	p-value
BMI and Adiponectin	-0.35	0.06
BMI and Leptin	0.52	2.94e-03
HOMA-IR and Adiponectin	-0.59	6.19e-04
HOMA-IR and Leptin	0.25	0.17

ANOVA Results
Variable Pair	p-value
BMI and Sex	0.008
HOMA-IR and Sex	0.540
Age and Sex	0.587
Sex will be used for model building along with BMI, HOMA-IR, and Age

Spearman Correlation
Variable Pair	rho	p-value
BMI and Age	-0.37	0.042
BMI and HOMA-IR	0.52	0.003
Age and HOMA-IR	-0.41	0.022
These variables will be used for model building along with the variable Sex

RBP4 Model

#log transform RBP4 concentrations
vao$LRBP4<-log10(vao$RBP4)

#linear regression with BMI, Sex, Age and HOMAIR
model1=lm(LRBP4~BMI+Sex+Age+LHOMAIR,vao)
vif(model1)

##      BMI      Sex      Age  LHOMAIR 
## 1.597502 1.292650 1.233974 1.259206

#remove one variable at a time
model2=lm(LRBP4~BMI+Sex+Age,vao) #remove HOMAIR
model3=lm(LRBP4~BMI+Sex+LHOMAIR, vao) #remove Age
model4=lm(LRBP4~BMI+Age+LHOMAIR, vao) #remove Sex
model5=lm(LRBP4~Sex+Age+LHOMAIR, vao) #remove BMI

AIC<-AIC(model1,model2,model3,model4,model5) #summary of AIC
AIC_df<-data.frame(
  Model=c("Model 1: Full Model", "Model 2: No HOMA-IR", "Model 3: No Age",
          "Model 4: No Sex", "Model 5: No BMI"),
  AIC = round(AIC$AIC, 3),
  DF = AIC$df)

aic_table <- AIC_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aic_table

AIC Comparison of Models
Model Description	AIC Value	Degrees of Freedom
Model 1: Full Model	-34.866	6
Model 2: No HOMA-IR	-36.135	5
Model 3: No Age	-35.123	5
Model 4: No Sex	-33.703	5
Model 5: No BMI	-36.196	5
Note: Lower AIC values indicate a better model.

##remove BMI (lowest AIC), add interaction terms
model6=lm(LRBP4~Sex+Age+LHOMAIR+Age*Sex+LHOMAIR*Sex,vao)
summary(model6)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + LHOMAIR + Age * Sex + LHOMAIR * 
##     Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21429 -0.07825  0.02313  0.06886  0.20592 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     -0.071668   0.135146  -0.530  0.60058   
## SexMale          0.507136   0.207240   2.447  0.02177 * 
## Age              0.008636   0.002998   2.880  0.00803 **
## LHOMAIR         -0.048056   0.045468  -1.057  0.30065   
## SexMale:Age     -0.009698   0.004385  -2.212  0.03636 * 
## SexMale:LHOMAIR  0.072444   0.113449   0.639  0.52892   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1123 on 25 degrees of freedom
## Multiple R-squared:  0.4636, Adjusted R-squared:  0.3563 
## F-statistic: 4.322 on 5 and 25 DF,  p-value: 0.005699

AIC(model6,model5)

	df	AIC
model6	7	-40.24879
model5	5	-36.19628

#remove interaction terms one at a time
model7=lm(LRBP4~Sex+Age+LHOMAIR+LHOMAIR*Age,vao)
model8=lm(LRBP4~Sex+Age+LHOMAIR+Age*Sex,vao)
summary(model7)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + LHOMAIR + LHOMAIR * Age, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.24923 -0.06776  0.01125  0.07561  0.20708 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.183427   0.135373   1.355   0.1871  
## SexMale      0.106354   0.047271   2.250   0.0331 *
## Age          0.002726   0.002839   0.960   0.3458  
## LHOMAIR     -0.156739   0.218925  -0.716   0.4804  
## Age:LHOMAIR  0.002452   0.004827   0.508   0.6157  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1248 on 26 degrees of freedom
## Multiple R-squared:  0.3113, Adjusted R-squared:  0.2054 
## F-statistic: 2.939 on 4 and 26 DF,  p-value: 0.03955

summary(model8)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + LHOMAIR + Age * Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21447 -0.05720  0.02090  0.07151  0.20229 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.087232   0.131407  -0.664  0.51264   
## SexMale      0.571891   0.178663   3.201  0.00359 **
## Age          0.008906   0.002934   3.035  0.00541 **
## LHOMAIR     -0.036421   0.041179  -0.884  0.38456   
## SexMale:Age -0.010753   0.004015  -2.678  0.01267 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.111 on 26 degrees of freedom
## Multiple R-squared:  0.4549, Adjusted R-squared:  0.371 
## F-statistic: 5.424 on 4 and 26 DF,  p-value: 0.002596

AIC(model6,model7,model8) #remove HOMAIR x Age

	df	AIC
model6	7	-40.24879
model7	6	-34.50246
model8	6	-41.74725

AIC_RBP4_iterm<-AIC(model6,model7,model8) #summary of AIC
AIC_df_RBP4_iterm<-data.frame(
  Model=c("Model 6: Includes interaction terms", "Model 7: Remove Age x Sex", 
          "Model 8: Remove HOMA-IR x Sex"),
  AIC = round(AIC_RBP4_iterm$AIC,3),
  DF = AIC_RBP4_iterm$df)

aic_RBP4_iterm_table <- AIC_df_RBP4_iterm %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aic_RBP4_iterm_table

AIC Comparison of Models
Model Description	AIC Value	Degrees of Freedom
Model 6: Includes interaction terms	-40.249	7
Model 7: Remove Age x Sex	-34.502	6
Model 8: Remove HOMA-IR x Sex	-41.747	6
Note: Lower AIC values indicate a better model.

#remove HOMA-IR
model9=lm(LRBP4~Sex+Age+Age*Sex,vao)
summary(model9)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + Age * Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21781 -0.06921  0.01956  0.07634  0.19094 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.135948   0.118824  -1.144  0.26262   
## SexMale      0.591144   0.176615   3.347  0.00241 **
## Age          0.009749   0.002764   3.527  0.00152 **
## SexMale:Age -0.011126   0.003977  -2.798  0.00938 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1106 on 27 degrees of freedom
## Multiple R-squared:  0.4385, Adjusted R-squared:  0.3761 
## F-statistic: 7.027 on 3 and 27 DF,  p-value: 0.001216

AIC(model8,model9) # removing HOMA-IR leads to lower AIC

	df	AIC
model8	6	-41.74725
model9	5	-42.82834

#does adding BMI back into the model improve the model?
model10=lm(LRBP4~Sex+Age+Age*Sex+BMI,vao)
summary(model10)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + Age * Sex + BMI, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.195947 -0.053725  0.009708  0.071413  0.190375 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.007224   0.187983  -0.038  0.96964   
## SexMale      0.557203   0.181412   3.071  0.00494 **
## Age          0.008911   0.002932   3.040  0.00534 **
## BMI         -0.002252   0.002542  -0.886  0.38370   
## SexMale:Age -0.010792   0.004011  -2.691  0.01229 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.111 on 26 degrees of freedom
## Multiple R-squared:  0.4549, Adjusted R-squared:  0.3711 
## F-statistic: 5.425 on 4 and 26 DF,  p-value: 0.002593

AIC(model9,model10)

	df	AIC
model9	5	-42.82834
model10	6	-41.75058

anova(model9,model10) #no, both from ANOVA and AIC, BMI does not improve the model

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.3302089	NA	NA	NA	NA
26	0.3205299	1	0.009679	0.7851149	0.3837037

#does the interaction term improve the model?
model11=lm(LRBP4~Sex+Age,vao)
AIC(model9,model11)

	df	AIC
model9	5	-42.82834
model11	4	-36.93776

anova(model9,model11) #yes

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.3302089	NA	NA	NA	NA
28	0.4259237	-1	-0.0957148	7.82626	0.0093797

#is this the simplest model?
model12=lm(LRBP4~Sex,vao) #Sex alone
model13=lm(LRBP4~Age,vao) #Age alone

#summary of AIC
 AICR_3 <- AIC(model9,model12,model13)
 AICR_3df <- data.frame(
   Model = c("Age + Sex + Age x Sex", "Age", "Sex"),
   AIC = round(AICR_3$AIC, 3), 
   DF = AICR_3$df)
 AICR_3df %>%  flextable() %>%
   set_header_labels(Model = "Model Description", AIC = "AIC Value",
                     DF = "Degrees of Freedom") %>%
   add_header_lines(values = "AIC Comparison of Models for RBP4") %>%
   align(part = "header", align = "center") %>%
   add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
fontsize(part = "footer", size = 8) %>%
set_table_properties(layout = "autofit")

AIC Comparison of Models for RBP4
Model Description	AIC Value	Degrees of Freedom
Age + Sex + Age x Sex	-42.828	5
Age	-34.898	3
Sex	-33.200	3
Note: Lower AIC values indicate a better model.

#summary of anova results
 p_values<-data.frame(
   Comparison=c("Age+Sex+AgexSex v Age", "Age+Sex+AgexSex v Sex"),
   P_value=c(round(anova(model9,model12)$"Pr(>F)"[2],3),
             round(anova(model9,model13)$"Pr(>F)"[2],3)))
 
 p_values %>% flextable() %>%
     set_header_labels(Comparison="Models", P_value="P-value: Probability >F") %>%
     add_header_lines(values="Is this the simplest model that fits the data best?") %>%
     align(part="header", align="center" ) %>%
     set_table_properties(layout = "autofit") %>%
     add_footer_lines(values = "Note: p<0.05 cut-off for retaining more complex model") %>%
     fontsize(part = "footer", size = 8)

Is this the simplest model that fits the data best?
Models	P-value: Probability >F
Age+Sex+AgexSex v Age	0.006
Age+Sex+AgexSex v Sex	0.003
Note: p<0.05 cut-off for retaining more complex model

#lower AIC, and anova p<0.05 for the more complex model of Age + Sex + Age x Sex
##final model##
summary(model9)

## 
## Call:
## lm(formula = LRBP4 ~ Sex + Age + Age * Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21781 -0.06921  0.01956  0.07634  0.19094 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -0.135948   0.118824  -1.144  0.26262   
## SexMale      0.591144   0.176615   3.347  0.00241 **
## Age          0.009749   0.002764   3.527  0.00152 **
## SexMale:Age -0.011126   0.003977  -2.798  0.00938 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1106 on 27 degrees of freedom
## Multiple R-squared:  0.4385, Adjusted R-squared:  0.3761 
## F-statistic: 7.027 on 3 and 27 DF,  p-value: 0.001216

#variance inflation factors 
vif(model9,type=c("predictor")) #because this model has interaction terms we need to use the GVIF

	GVIF	Df	GVIF^(1/(2*Df))	Interacts With	Other Predictors
Sex	1	3	1	Age	–
Age	1	3	1	Sex	–

RBP4 Final Model

RBP4 Final Model: RBP4 ~ Age + Sex + Age x Sex (p=0.009)

RBP4 Model Plots

Post-hoc analysis of RBP4 and eGFR

summary(lm(LRBP4~eGFR,vao))

## 
## Call:
## lm(formula = LRBP4 ~ eGFR, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.277030 -0.051103  0.009991  0.070393  0.232258 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.673248   0.222715   3.023  0.00519 **
## eGFR        -0.003267   0.002029  -1.611  0.11810   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1364 on 29 degrees of freedom
## Multiple R-squared:  0.0821, Adjusted R-squared:  0.05045 
## F-statistic: 2.594 on 1 and 29 DF,  p-value: 0.1181

summary(lm(LRBP4~eGFR*Sex,vao))

## 
## Call:
## lm(formula = LRBP4 ~ eGFR * Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20730 -0.06922  0.01266  0.07022  0.23966 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.832255   0.224461   3.708 0.000954 ***
## eGFR         -0.005153   0.002057  -2.505 0.018573 *  
## SexMale      -0.546204   0.470518  -1.161 0.255861    
## eGFR:SexMale  0.006133   0.004256   1.441 0.161035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1206 on 27 degrees of freedom
## Multiple R-squared:  0.3319, Adjusted R-squared:  0.2576 
## F-statistic: 4.471 on 3 and 27 DF,  p-value: 0.0113

eGFR is not a significant correlate for RBP4 (p=0.12) eGFR as an interaction term with sex is also not significant (p=0.16)

TTR Model

vao$LTTR<-log10(vao$TTR)

#linear regression with BMI, Sex, Age and HOMA-IR
Tmodel1=lm(LTTR~BMI+Sex+Age+LHOMAIR,vao)
summary(Tmodel1)

## 
## Call:
## lm(formula = LTTR ~ BMI + Sex + Age + LHOMAIR, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.221583 -0.037441  0.002198  0.057781  0.207524 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.3295758  0.1437198   9.251 1.04e-09 ***
## BMI         -0.0021577  0.0023340  -0.924   0.3637    
## SexMale      0.0955022  0.0418519   2.282   0.0309 *  
## Age          0.0007957  0.0019475   0.409   0.6862    
## LHOMAIR     -0.0137659  0.0377648  -0.365   0.7184    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09806 on 26 degrees of freedom
## Multiple R-squared:  0.3276, Adjusted R-squared:  0.2242 
## F-statistic: 3.167 on 4 and 26 DF,  p-value: 0.0302

vif(Tmodel1)

##      BMI      Sex      Age  LHOMAIR 
## 1.597502 1.292650 1.233974 1.259206

#remove one variable at a time
Tmodel2=lm(LTTR~BMI+Sex+Age,vao) #remove HOMA-IR
Tmodel3=lm(LTTR~BMI+Sex+LHOMAIR, vao) #remove Age
Tmodel4=lm(LTTR~BMI+Age+LHOMAIR, vao) #remove Sex
Tmodel5=lm(LTTR~Sex+Age+LHOMAIR, vao) #remove BMI

AIC(Tmodel1,Tmodel2,Tmodel3,Tmodel4,Tmodel5) #summary of AIC

	df	AIC
Tmodel1	6	-49.45143
Tmodel2	5	-51.29340
Tmodel3	5	-51.25302
Tmodel4	5	-45.79239
Tmodel5	5	-50.44884

AICT<-AIC(Tmodel1,Tmodel2,Tmodel3,Tmodel4,Tmodel5) #summary of AIC
AICT_df<-data.frame(
  Model=c("Model 1: Full Model", "Model 2: No HOMA-IR", "Model 3: No Age", 
          "Model 4: No Sex", "Model 5: No BMI"),
  AIC = round(AICT$AIC,3), DF = AICT$df)

aicT_table <- AICT_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for TTR") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aicT_table

AIC Comparison of Models for TTR
Model Description	AIC Value	Degrees of Freedom
Model 1: Full Model	-49.451	6
Model 2: No HOMA-IR	-51.293	5
Model 3: No Age	-51.253	5
Model 4: No Sex	-45.792	5
Model 5: No BMI	-50.449	5
Note: Lower AIC values indicate a better model.

##remove HOMA-IR (lowest AIC)
#add interaction terms for Age and Sex which are not correlated
Tmodel6=lm(LTTR~Sex+Age+BMI+Age*Sex,vao)
summary(Tmodel6)

## 
## Call:
## lm(formula = LTTR ~ Sex + Age + BMI + Age * Sex, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.202202 -0.031876 -0.006347  0.048701  0.199926 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.150995   0.151538   7.595 4.61e-08 ***
## SexMale      0.421700   0.146241   2.884  0.00779 ** 
## Age          0.004725   0.002363   1.999  0.05613 .  
## BMI         -0.001957   0.002049  -0.955  0.34846    
## SexMale:Age -0.007491   0.003233  -2.317  0.02864 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08951 on 26 degrees of freedom
## Multiple R-squared:  0.4398, Adjusted R-squared:  0.3537 
## F-statistic: 5.104 on 4 and 26 DF,  p-value: 0.003592

AIC(Tmodel6,Tmodel2)

	df	AIC
Tmodel6	6	-55.11268
Tmodel2	5	-51.29340

anova(Tmodel6,Tmodel2)

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
26	0.2082919	NA	NA	NA	NA
27	0.2513029	-1	-0.043011	5.368841	0.0286386

##inclusion of interaction term improves model
###Model now TTR~Sex+BMI+Age+Age*Sex

#remove terms
Tmodel7=lm(LTTR~Sex+Age+Age*Sex,vao) # remove BMI
Tmodel8=lm(LTTR~Sex+BMI,vao) # remove Age
Tmodel9=lm(LTTR~Age+BMI,vao) #remove Sex

AICT_iterm<-AIC(Tmodel6,Tmodel7,Tmodel8,Tmodel9) #summary of AIC
AICT_iterm_df<-data.frame(
  Model=c("Full Model: Sex+Age+BMI+AgexSex",
          "Remove BMI: Sex+Age+AgexSex",
          "Remove Age: Sex+BMI",
          "Remove Sex: Age+BMI"),
  AIC = round(AICT_iterm$AIC,3), DF = AICT_iterm$df)

aicT_iterm_table <- AICT_iterm_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for TTR") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aicT_iterm_table

AIC Comparison of Models for TTR
Model Description	AIC Value	Degrees of Freedom
Full Model: Sex+Age+BMI+AgexSex	-55.113	6
Remove BMI: Sex+Age+AgexSex	-56.044	5
Remove Age: Sex+BMI	-52.979	4
Remove Sex: Age+BMI	-47.742	4
Note: Lower AIC values indicate a better model.

#lowest AIC removing BMI
#confirm with anova
anova(Tmodel7,Tmodel8)

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.2155956	NA	NA	NA	NA
28	0.2538616	-1	-0.038266	4.792217	0.0374116

anova(Tmodel6,Tmodel7) # removing BMI leads to lower AIC, stat. sig.

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
26	0.2082919	NA	NA	NA	NA
27	0.2155956	-1	-0.0073038	0.911693	0.3484596

###Model now TTR ~ Sex + Age + Age * Sex

#does adding HOMA-IR back into the model improve the model?
Tmodel10=lm(LTTR~Sex+Age+Age*Sex+LHOMAIR,vao)
summary(Tmodel10)

## 
## Call:
## lm(formula = LTTR ~ Sex + Age + Age * Sex + LHOMAIR, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.219463 -0.034099 -0.000104  0.048686  0.205280 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.060046   0.107323   9.877 2.74e-10 ***
## SexMale      0.442935   0.145917   3.036   0.0054 ** 
## Age          0.005092   0.002397   2.124   0.0433 *  
## LHOMAIR     -0.015603   0.033632  -0.464   0.6465    
## SexMale:Age -0.007621   0.003279  -2.324   0.0282 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09069 on 26 degrees of freedom
## Multiple R-squared:  0.425,  Adjusted R-squared:  0.3365 
## F-statistic: 4.803 on 4 and 26 DF,  p-value: 0.004906

AIC(Tmodel7, Tmodel10)

	df	AIC
Tmodel7	5	-56.04428
Tmodel10	6	-54.29986

anova(Tmodel7, Tmodel10) #no, both from ANOVA and AIC, HOMA does not improve the model

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.2155956	NA	NA	NA	NA
26	0.2138255	1	0.0017702	0.2152428	0.6465498

#does the interaction term improve the model?
Tmodel11=lm(LTTR~Sex+Age,vao)
AIC(Tmodel7,Tmodel11)

	df	AIC
Tmodel7	5	-56.04428
Tmodel11	4	-51.95223

anova(Tmodel7,Tmodel11) #yes

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.2155956	NA	NA	NA	NA
28	0.2624138	-1	-0.0468181	5.863243	0.022454

#is this the simplest model?
Tmodel12=lm(LTTR~Sex,vao) #Sex alone
Tmodel13=lm(LTTR~Age,vao) #Age alone


AICT2<-AIC(Tmodel7,Tmodel11,Tmodel12,Tmodel13) #summary of AIC
AICT2_df<-data.frame(
  Model=c("Sex + Age + Sex x Age",
          "Sex + Age","Sex", "Age"),
  AIC = round(AICT2$AIC,3), DF = AICT2$df)

aicT2_table <- AICT2_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for TTR") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values="Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aicT2_table

AIC Comparison of Models for TTR
Model Description	AIC Value	Degrees of Freedom
Sex + Age + Sex x Age	-56.044	5
Sex + Age	-51.952	4
Sex	-52.919	3
Age	-44.500	3
Note: Lower AIC values indicate a better model.

 #summary of anova results
  p_values<-data.frame(
    Comparison=c("Age+Sex+AgexSex v Age+Sex", "Age+Sex+AgexSex v Age", 
                 "Age+Sex+AgexSex v Sex"),
    P_value=c(round(anova(Tmodel7,Tmodel11)$"Pr(>F)"[2],3),
              round(anova(Tmodel7,Tmodel12)$"Pr(>F)"[2],3),
              round(anova(Tmodel7,Tmodel13)$"Pr(>F)"[2],3)))
  
  p_values %>% flextable() %>%
      set_header_labels(Comparison="Models", P_value="P-value: Probability >F") %>%
      add_header_lines(values="Is this the simplest model that fits the data best?") %>%
      align(part="header", align="center" ) %>%
      set_table_properties(layout = "autofit") %>%
      add_footer_lines(values = "Note: p<0.05 cut-off for retaining more complex model") %>%
      fontsize(part = "footer", size = 8)

Is this the simplest model that fits the data best?
Models	P-value: Probability >F
Age+Sex+AgexSex v Age+Sex	0.022
Age+Sex+AgexSex v Age	0.045
Age+Sex+AgexSex v Sex	0.001
Note: p<0.05 cut-off for retaining more complex model

  ##final model for TTR
summary(Tmodel7)

## 
## Call:
## lm(formula = LTTR ~ Sex + Age + Age * Sex, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.219703 -0.039820  0.003317  0.047080  0.200418 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.039175   0.096013  10.823 2.53e-11 ***
## SexMale      0.451183   0.142710   3.162  0.00385 ** 
## Age          0.005453   0.002233   2.442  0.02145 *  
## SexMale:Age -0.007781   0.003213  -2.421  0.02245 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08936 on 27 degrees of freedom
## Multiple R-squared:  0.4202, Adjusted R-squared:  0.3558 
## F-statistic: 6.522 on 3 and 27 DF,  p-value: 0.00184

#variance inflation factors 
vif(Tmodel7,type=c("predictor")) #because this model has interaction terms we need to use the GVIF

	GVIF	Df	GVIF^(1/(2*Df))	Interacts With	Other Predictors
Sex	1	3	1	Age	–
Age	1	3	1	Sex	–

TTR Final Model

TTR Final Model: TTR ~ Age + Sex + Age x Sex (p=0.02)

TTR Model Plots

Retinol Model

vao$LROL<-log10(vao$Sretinol)

#linear regression with BMI, Sex, Age and HOMAIR
Rmodel1=lm(LROL~BMI+Sex+Age+LHOMAIR,vao)
vif(Rmodel1)

##      BMI      Sex      Age  LHOMAIR 
## 1.597502 1.292650 1.233974 1.259206

#remove one variable at a time
Rmodel2=lm(LROL~BMI+Sex+Age,vao) #remove HOMA-IR
Rmodel3=lm(LROL~BMI+Sex+LHOMAIR, vao) #remove Age
Rmodel4=lm(LROL~BMI+Age+LHOMAIR, vao) #remove Sex
Rmodel5=lm(LROL~Sex+Age+LHOMAIR, vao) #remove BMI

AIC(Rmodel1,Rmodel2,Rmodel3,Rmodel4,Rmodel5) #summary of AIC

	df	AIC
Rmodel1	6	-37.11641
Rmodel2	5	-38.95172
Rmodel3	5	-37.12858
Rmodel4	5	-37.23750
Rmodel5	5	-38.03374

AICR<-AIC(Rmodel1,Rmodel2,Rmodel3,Rmodel4,Rmodel5) #summary of AIC
AICR_df<-data.frame(
  Model=c("Model 1: Full Model", "Model 2: No HOMA-IR", "Model 3: No Age",
          "Model 4: No Sex", "Model 5: No BMI"),
  AIC = AICR$AIC,
  DF = AICR$df)
aicR_table <- AICR_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for Retinol") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aicR_table

AIC Comparison of Models for Retinol
Model Description	AIC Value	Degrees of Freedom
Model 1: Full Model	-37.11641	6
Model 2: No HOMA-IR	-38.95172	5
Model 3: No Age	-37.12858	5
Model 4: No Sex	-37.23750	5
Model 5: No BMI	-38.03374	5
Note: Lower AIC values indicate a better model.

##remove HOMA-IR (lowest AIC), add interaction term
Rmodel6=lm(LROL~Age+BMI+Sex+Age*Sex,vao)
summary(Rmodel6)

## 
## Call:
## lm(formula = LROL ~ Age + BMI + Sex + Age * Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23533 -0.07032  0.00921  0.05459  0.24907 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.005764   0.197897  -0.029   0.9770  
## Age          0.005830   0.003086   1.889   0.0701 .
## BMI         -0.002747   0.002676  -1.026   0.3142  
## SexMale      0.281136   0.190980   1.472   0.1530  
## Age:SexMale -0.004974   0.004222  -1.178   0.2494  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1169 on 26 degrees of freedom
## Multiple R-squared:  0.3144, Adjusted R-squared:  0.2089 
## F-statistic:  2.98 on 4 and 26 DF,  p-value: 0.03764

#can we justify inclusion of interaction terms?
AIC(Rmodel6,Rmodel2)

	df	AIC
Rmodel6	6	-38.56389
Rmodel2	5	-38.95172

anova(Rmodel6,Rmodel2)

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
26	0.3552323	NA	NA	NA	NA
27	0.3741953	-1	-0.0189629	1.387927	0.2494263

#cannot justify interaction terms

#remove each term
Rmodel7=lm(LROL~Age+BMI,vao) #remove Sex
Rmodel8=lm(LROL~Age+Sex,vao) # remove BMI
Rmodel9=lm(LROL~BMI+Sex,vao) # remove Age

p_values<-data.frame(
  Comparison=c("Age+Sex+BMI v Age+BMI", "Age+Sex+BMI v Age+Sex", 
               "Age+Sex+BMI v BMI+Sex"),
  P_value=c(round(anova(Rmodel2,Rmodel7)$"Pr(>F)"[2],3),
            round(anova(Rmodel2,Rmodel8)$"Pr(>F)"[2],3),
            round(anova(Rmodel2,Rmodel9)$"Pr(>F)"[2],3)))
  
  p_values %>% flextable() %>%
    set_header_labels(Comparison="Comparison", P_value="P-value: Probability >F") %>%
    add_header_lines(values="ANOVA Comparison") %>%
    align(part="header", align="center" ) %>%
    set_table_properties(layout = "autofit") %>%
    add_footer_lines(values = "Note: p<0.05 cut-off for retaining more complex model") %>%
    fontsize(part = "footer", size = 8)

ANOVA Comparison
Comparison	P-value: Probability >F
Age+Sex+BMI v Age+BMI	0.213
Age+Sex+BMI v Age+Sex	0.267
Age+Sex+BMI v BMI+Sex	0.152
Note: p<0.05 cut-off for retaining more complex model

{AICR_2<-AIC(Rmodel2,Rmodel7,Rmodel8,Rmodel9) #summary of AIC
AICR_2df<-data.frame(
  Model=c("Age + BMI + Sex","Age + BMI","Age + Sex", 
          "BMI + Sex"),
  AIC = AICR_2$AIC, DF = AICR_2$df)

aicR_2_table <- AICR_2df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for Retinol") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")}
aicR_2_table

AIC Comparison of Models for Retinol
Model Description	AIC Value	Degrees of Freedom
Age + BMI + Sex	-38.95172	5
Age + BMI	-39.14023	4
Age + Sex	-39.50958	4
BMI + Sex	-38.55048	4
Note: Lower AIC values indicate a better model.

#Age and Sex has the lowest AIC
#single regressions
Rmodel10=lm(LROL~Age,vao) 
Rmodel11=lm(LROL~Sex,vao)
AIC(Rmodel11, Rmodel10,Rmodel8)

	df	AIC
Rmodel11	3	-37.36999
Rmodel10	3	-37.28122
Rmodel8	4	-39.50958

anova(Rmodel10,Rmodel8) #not better than Age alone

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
29	0.4493028	NA	NA	NA	NA
28	0.3920143	1	0.0572885	4.09189	0.0527329

anova(Rmodel11,Rmodel8) #not better than Sex alone

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
29	0.4480181	NA	NA	NA	NA
28	0.3920143	1	0.0560038	4.000128	0.0552816

summary(Rmodel10)

## 
## Call:
## lm(formula = LROL ~ Age, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.31522 -0.04495  0.01325  0.06391  0.26545 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.040082   0.097843  -0.410   0.6851  
## Age          0.004689   0.002225   2.107   0.0438 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1245 on 29 degrees of freedom
## Multiple R-squared:  0.1328, Adjusted R-squared:  0.1029 
## F-statistic: 4.441 on 1 and 29 DF,  p-value: 0.04385

summary(Rmodel11)

## 
## Call:
## lm(formula = LROL ~ Sex, data = vao)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32125 -0.04191  0.00414  0.05189  0.23507 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.12539    0.02779   4.512 9.83e-05 ***
## SexMale      0.09938    0.04666   2.130   0.0418 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1243 on 29 degrees of freedom
## Multiple R-squared:  0.1353, Adjusted R-squared:  0.1055 
## F-statistic: 4.537 on 1 and 29 DF,  p-value: 0.04178

#what about BMI alone
Rmodel12=lm(LROL~BMI,vao)
summary(Rmodel12)

## 
## Call:
## lm(formula = LROL ~ BMI, data = vao)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.254853 -0.039187  0.007799  0.053518  0.304417 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.382573   0.089540   4.273  0.00019 ***
## BMI         -0.005809   0.002274  -2.555  0.01615 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1208 on 29 degrees of freedom
## Multiple R-squared:  0.1837, Adjusted R-squared:  0.1555 
## F-statistic: 6.526 on 1 and 29 DF,  p-value: 0.01615

#best p-value for BMI alone

{AICR_3<-AIC(Rmodel7,Rmodel8,Rmodel9,Rmodel10,Rmodel11,Rmodel12) #summary of AIC
AICR_3df<-data.frame(
  Model=c("Age + BMI","Age + Sex", 
          "BMI + Sex", "Age", "Sex", "BMI"),
  AIC = AICR_3$AIC, DF = AICR_3$df)

aicR_3_table <- AICR_3df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for Retinol") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")}
aicR_3_table

AIC Comparison of Models for Retinol
Model Description	AIC Value	Degrees of Freedom
Age + BMI	-39.14023	4
Age + Sex	-39.50958	4
BMI + Sex	-38.55048	4
Age	-37.28122	3
Sex	-37.36999	3
BMI	-39.15575	3
Note: Lower AIC values indicate a better model.

#BMI alone also has lowest AIC
##final model is ROL ~ BMI

Retinol Final Model

Retinol Final Model: Retinol ~ BMI (p=0.016)

Retinol Model Plots

Sensitivity Analysis of Retinol and BMI

vaono23 <-vao %>% filter(ID!= "51-3523") #omit 23 from data set
Rmodel12no23<-lm(LROL~BMI,vaono23)
summary(Rmodel12no23)

## 
## Call:
## lm(formula = LROL ~ BMI, data = vaono23)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.258376 -0.049593  0.003565  0.047807  0.293192 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.321821   0.086169   3.735 0.000852 ***
## BMI         -0.003968   0.002226  -1.783 0.085468 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1114 on 28 degrees of freedom
## Multiple R-squared:  0.1019, Adjusted R-squared:  0.06987 
## F-statistic: 3.178 on 1 and 28 DF,  p-value: 0.08547

Omission of participant with liver fibrosis and overt retinol deficiency from the regression model increased the p-value of correlation between BMI and retinol to p=0.09

Retinol Regressions Omitting Participant with Retinol Deficiency and Apparent Liver Fibrosis

Rno23model1=lm(LROL~BMI+Sex+Age+LHOMAIR,vaono23)
summary(Rno23model1)

## 
## Call:
## lm(formula = LROL ~ BMI + Sex + Age + LHOMAIR, data = vaono23)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.255391 -0.062874 -0.002688  0.052888  0.230952 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.0639189  0.1612890   0.396    0.695
## BMI         -0.0008989  0.0027014  -0.333    0.742
## SexMale      0.0677670  0.0466130   1.454    0.158
## Age          0.0028660  0.0021708   1.320    0.199
## LHOMAIR     -0.0193169  0.0420587  -0.459    0.650
## 
## Residual standard error: 0.1092 on 25 degrees of freedom
## Multiple R-squared:  0.2294, Adjusted R-squared:  0.1061 
## F-statistic:  1.86 on 4 and 25 DF,  p-value: 0.1489

#remove one variable at a time
Rno23model2=lm(LROL~BMI+Sex+Age,vaono23) #remove HOMAIR
Rno23model3=lm(LROL~BMI+Sex+LHOMAIR, vaono23) #remove Age
Rno23model4=lm(LROL~BMI+Age+LHOMAIR, vaono23) #remove Sex
Rno23model5=lm(LROL~Sex+Age+LHOMAIR, vaono23) #remove BMI

AICR<-AIC(Rno23model1, Rno23model2, Rno23model3, Rno23model4,Rno23model5) #summary of AIC
AICR_df<-data.frame(
  Model=c("Model 1: Full Model", "Model 2: No HOMA-IR", "Model 3: No Age", 
          "Model 4: No Sex", "Model 5: No BMI"),
  AIC = AICR$AIC,
  DF = AICR$df)
aicR_table <- AICR_df %>%
  flextable() %>%
  set_header_labels(Model = "Model Description", AIC = "AIC Value",
                    DF="Degrees of Freedom") %>%
  add_header_lines(values = "AIC Comparison of Models for Retinol (Omitting 23)") %>%
  align(part="header", align="center" ) %>%
  add_footer_lines(values = "Note: Lower AIC values indicate a better model.") %>%
  fontsize(part = "footer", size = 8) %>%
  set_table_properties(layout = "autofit")
aicR_table

AIC Comparison of Models for Retinol (Omitting 23)
Model Description	AIC Value	Degrees of Freedom
Model 1: Full Model	-41.21348	6
Model 2: No HOMA-IR	-42.96142	5
Model 3: No Age	-41.19143	5
Model 4: No Sex	-40.77869	5
Model 5: No BMI	-43.08092	5
Note: Lower AIC values indicate a better model.

#remove BMI, add interaction terms
Rno23model6=lm(LROL~Sex+Age+LHOMAIR+Sex*Age,vaono23)
Rno23model7=lm(LROL~Sex+Age+Sex*Age,vaono23) #remove HOMA
Rno23model8=lm(LROL~Sex+Age,vaono23) #remove HOMA and Sex * Age
Rno23model9=lm(LROL~Sex+LHOMAIR,vaono23) #remove Age
Rno23model10=lm(LROL~Age+LHOMAIR,vaono23) #remove Sex

AIC(Rno23model5, Rno23model6,Rno23model7,Rno23model8,Rno23model9,Rno23model10)

	df	AIC
Rno23model5	5	-43.08092
Rno23model6	6	-42.14048
Rno23model7	5	-43.85300
Rno23model8	4	-44.68606
Rno23model9	4	-42.70304
Rno23model10	4	-41.45723

#model 8 has the lowest AIC
#Sex + Age
summary(Rno23model8)

## 
## Call:
## lm(formula = LROL ~ Sex + Age, data = vaono23)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.26566 -0.06596 -0.01165  0.04795  0.21500 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.004218   0.085347  -0.049   0.9609  
## SexMale      0.076579   0.040293   1.901   0.0681 .
## Age          0.003450   0.001926   1.791   0.0845 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.106 on 27 degrees of freedom
## Multiple R-squared:  0.2157, Adjusted R-squared:  0.1576 
## F-statistic: 3.713 on 2 and 27 DF,  p-value: 0.03763

#how does this compare to the predictors alone
Rno23model11=lm(LROL~Sex,vaono23) #Sex alone
Rno23model12=lm(LROL~Age,vaono23) #Age alone
AIC(Rno23model8, Rno23model11, Rno23model12)

	df	AIC
Rno23model8	4	-44.68606
Rno23model11	3	-43.31838
Rno23model12	3	-42.91924

anova(Rno23model8,Rno23model11) #not better than Sex alone

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.3033459	NA	NA	NA	NA
28	0.3393832	-1	-0.0360373	3.207581	0.0845163

anova(Rno23model8,Rno23model12) #not better than Age alone

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
27	0.3033459	NA	NA	NA	NA
28	0.3439287	-1	-0.0405828	3.612165	0.0680846

summary(Rno23model11) #p>0.05

## 
## Call:
## lm(formula = LROL ~ Sex, data = vaono23)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.287994 -0.050487  0.001027  0.044673  0.235073 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.14230    0.02526   5.634 4.92e-06 ***
## SexMale      0.08247    0.04171   1.977   0.0579 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1101 on 28 degrees of freedom
## Multiple R-squared:  0.1225, Adjusted R-squared:  0.09117 
## F-statistic: 3.909 on 1 and 28 DF,  p-value: 0.05794

summary(Rno23model12) #p>0.05

## 
## Call:
## lm(formula = LROL ~ Age, data = vaono23)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.291619 -0.052172  0.005761  0.063472  0.261440 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.010978   0.088847   0.124   0.9025  
## Age         0.003749   0.002007   1.868   0.0723 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1108 on 28 degrees of freedom
## Multiple R-squared:  0.1108, Adjusted R-squared:  0.079 
## F-statistic: 3.488 on 1 and 28 DF,  p-value: 0.07233

summary(lm(LROL~BMI,vaono23))

## 
## Call:
## lm(formula = LROL ~ BMI, data = vaono23)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.258376 -0.049593  0.003565  0.047807  0.293192 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.321821   0.086169   3.735 0.000852 ***
## BMI         -0.003968   0.002226  -1.783 0.085468 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1114 on 28 degrees of freedom
## Multiple R-squared:  0.1019, Adjusted R-squared:  0.06987 
## F-statistic: 3.178 on 1 and 28 DF,  p-value: 0.08547

No significant correlates for retinol after omission participant with gross morphology of liver fibrosis and overt retinol deficiency

Genotype effect on Retinol, RBP4, and TTR

ANOVA Results Table
Analyte	SNP	p-value
Retinol	TTRsnp	0.63
Retinol	RBP4snp	0.86
RBP4	TTRsnp	0.48
RBP4	RBP4snp	0.70
TTR	TTRsnp	0.64
TTR	RBP4snp	0.36

Table S2, S3

Analyte Conc. Stratified by RBP4 Genotype (rs10882272)
Genotype	RBP4 (μM)	TTR (μM)	Retinol (μM)
1/1	1.91 (1.00, 3.16)	19.20 (10.37, 26.61)	1.35 (0.71, 2.88)
1/2	2.15 (1.19, 3.24)	21.27 (13.07, 29.81)	1.52 (1.00, 2.16)
2/2	2.10 (0.95, 3.18)	20.24 (12.03, 29.55)	1.42 (0.64, 1.97)
Concentrations shown as geometric mean and range
For the RBP4 genotype, 1/1 refers to T/T, 1/2 to T/C and 2/2 to C/C for single nucleotide polymorphism in the 3’ untranslated region

Analyte Conc. Stratified by TTR Genotype (rs1667255)
Genotype	RBP4 (μM)	TTR (μM)	Retinol (μM)
1/1	1.88 (0.95, 3.16)	18.84 (12.03, 26.61)	1.42 (0.64, 2.88)
1/2	2.10 (1.00, 3.04)	20.39 (10.37, 29.81)	1.38 (0.71, 1.69)
2/2	2.27 (1.50, 3.24)	22.27 (16.46, 29.79)	1.56 (1.21, 2.16)
Concentrations shown as geometric mean and range
For the TTR genotype, 1/1 refers to A/A, 1/2 to A/C and 2/2 to C/C for intronic single nucleotide polymorphism

Sex and Age but not Body Mass Index (BMI) are Significant Predictors of Serum Retinol Binding Protein 4 (RBP4) and Transthyretin (TTR) Concentrations

Statistical Analysis Code and Output

Aprajita S. Yadav

2025-06-25

Load Data

Determine Normality

Determine Variable Correlation

RBP4 Model

RBP4 Final Model

RBP4 Model Plots

Post-hoc analysis of RBP4 and eGFR

TTR Model

TTR Final Model

TTR Model Plots

Retinol Model

Retinol Final Model

Retinol Model Plots

Sensitivity Analysis of Retinol and BMI

Retinol Regressions Omitting Participant with Retinol Deficiency and Apparent Liver Fibrosis

Genotype effect on Retinol, RBP4, and TTR

Table S2, S3

Figure 2