Project 1 Data Analysis: Sugars in Cereal

library(dplyr)
library(ggplot2)
library(rstatix)
library(tidyverse)

data = read_delim("Project_1_integration_data.csv", delim = ',')

Rows: 148 Columns: 7── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): Analyte
dbl (6): Concentration, Peak, Retention Time, Area, Height, Width
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

cereal_data = read_delim("cereal_samples.csv", delim = ',')

Rows: 18 Columns: 6── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): Sample
dbl (5): Peak, Ret_time, Area, Height, Width
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

#Separate peaks by variables
fructose = data %>% 
  filter(Analyte == "Fructose")

glucose = data %>% 
  filter(Analyte == "Glucose")

sucrose = data %>% 
  filter(Analyte == "Sucrose")

xylose = data %>% 
  filter(Analyte == "Xylose")

dsmo = data %>% 
  filter(Peak == 1)

fructose_peaks = fructose %>% 
  filter(Peak == 2) %>% 
  select(-Analyte) %>% 
  select(-Peak)

glucose_peaks = glucose %>% 
  filter(Peak == 2) %>% 
  select(-Analyte) %>% 
  select(-Peak)

sucrose_peaks = sucrose %>% 
  filter(Peak == 2) %>% 
  select(-Analyte) %>% 
  select(-Peak)

sucrose_peaks = sucrose_peaks[-c(3),]

xylose_peaks = xylose %>% 
  filter(`Retention Time`>10)

ggplot(data=fructose_peaks, mapping=aes(x=Concentration, y=Area)) + 
  geom_point(color = "blue", size = 2) + 
  ggtitle("Fructose")+
  theme(plot.title=element_text(face='bold', size = 20, hjust = 0.5), panel.background = element_rect('azure2'))

ggplot(data=glucose_peaks, mapping=aes(x=Concentration, y=Area)) + 
  geom_point(color = "blue", size = 2) + 
  ggtitle("Glucose")+
  theme(plot.title=element_text(face='bold', size = 20, hjust = 0.5), panel.background = element_rect('azure2'))

ggplot(data=sucrose_peaks, mapping=aes(x=Concentration, y=Area)) + 
  geom_point(color = "blue", size = 2) + 
  ggtitle("Sucrose")+
  theme(plot.title=element_text(face='bold', size = 20, hjust = 0.5), panel.background = element_rect('azure2')) +
  geom_smooth(method = 'lm') +
  xlab("Concentration (g/L)")

Grubbs_max = function(peaks = tibble()) {
  grubbs_max = max(peaks$Area)
  grubbs_avg = mean(peaks$Area)
  grubbs_reg = lm(Area ~ Concentration +0, data=peaks)
  
  G_calc = abs(grubbs_max-grubbs_avg)/grubbs_reg$coefficents[1]
  
  return(G_calc)
}

Sucrose_reg = lm(Area ~ Concentration+0, data= sucrose_peaks)
summary(Sucrose_reg)

Call:
lm(formula = Area ~ Concentration + 0, data = sucrose_peaks)

Residuals:
    Min      1Q  Median      3Q     Max 
-15.561  -7.797   1.930   4.166  32.884 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
Concentration   18.908      1.002   18.87 7.89e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 11.79 on 13 degrees of freedom
Multiple R-squared:  0.9648,    Adjusted R-squared:  0.9621 
F-statistic: 356.1 on 1 and 13 DF,  p-value: 7.893e-11

sucrose_peaks = sucrose_peaks %>% 
  mutate(sig_pred = Concentration * Sucrose_reg$coefficients[1]) %>% 
  mutate(resid = Area - sig_pred)

ggplot(data=sucrose_peaks, mapping=aes(x=Concentration, y=resid)) + 
  geom_point(color = "blue", size = 2) + 
  ggtitle("Sucrose Residual")+
  theme(plot.title=element_text(face='bold', size = 20, hjust = 0.5), panel.background = element_rect('azure2')) +
  geom_hline(yintercept = 0)

suc_res_sd = sd((sucrose_peaks %>% slice(3:5))$resid)
LOD = 3 *suc_res_sd / as.numeric(Sucrose_reg$coefficients[1])
LOQ = 10 *suc_res_sd / as.numeric(Sucrose_reg$coefficients[1])
LOD

[1] 0.1470493

LOQ

[1] 0.4901644

Fructose_reg = lm(Area ~ Concentration, data= fructose_peaks)
summary(Fructose_reg)

Call:
lm(formula = Area ~ Concentration, data = fructose_peaks)

Residuals:
    Min      1Q  Median      3Q     Max 
-32.471 -15.573 -14.070  -3.192 174.167 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)     46.747     23.400   1.998   0.0671 .
Concentration    5.142     15.388   0.334   0.7436  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 51.61 on 13 degrees of freedom
Multiple R-squared:  0.008517,  Adjusted R-squared:  -0.06775 
F-statistic: 0.1117 on 1 and 13 DF,  p-value: 0.7436

Glucose_reg = lm(Area ~ Concentration, data= glucose_peaks)
summary(Glucose_reg)

Call:
lm(formula = Area ~ Concentration, data = glucose_peaks)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.4570  -5.6250  -0.5563   2.9662  22.9004 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     25.027      4.228   5.919 5.07e-05 ***
Concentration   -5.413      2.780  -1.947   0.0735 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.326 on 13 degrees of freedom
Multiple R-squared:  0.2257,    Adjusted R-squared:  0.1662 
F-statistic:  3.79 on 1 and 13 DF,  p-value: 0.0735

R_times = data.frame(Analyte = character(), 
                     avg_r_time = numeric(),
                     sd_r_time = numeric(),
                     r_ci_low = numeric(), 
                     r_ci_high = numeric())

R_times = rbind(R_times, data.frame(Analyte = "Sucrose",
                                    avg_r_time = mean(sucrose_peaks$`Retention Time`),
                                    sd_r_time = sd(sucrose_peaks$`Retention Time`),
                                    r_ci_low = mean(sucrose_peaks$`Retention Time`)-2*sd(sucrose_peaks$`Retention Time`),
                                    r_ci_high = mean(sucrose_peaks$`Retention Time`)+2*sd(sucrose_peaks$`Retention Time`)))

R_times = rbind(R_times, data.frame(Analyte = "Fructose",
                                    avg_r_time = mean(fructose_peaks$`Retention Time`),
                                    sd_r_time = sd(fructose_peaks$`Retention Time`),
                                    r_ci_low = mean(fructose_peaks$`Retention Time`)-2*sd(fructose_peaks$`Retention Time`),
                                    r_ci_high = mean(fructose_peaks$`Retention Time`)+2*sd(fructose_peaks$`Retention Time`)))

R_times = rbind(R_times, data.frame(Analyte = "Glucose",
                                    avg_r_time = mean(glucose_peaks$`Retention Time`),
                                    sd_r_time = sd(glucose_peaks$`Retention Time`),
                                    r_ci_low = mean(glucose_peaks$`Retention Time`)-2*sd(glucose_peaks$`Retention Time`),
                                    r_ci_high = mean(glucose_peaks$`Retention Time`)+2*sd(glucose_peaks$`Retention Time`)))

R_times = rbind(R_times, data.frame(Analyte = "Xylose",
                                    avg_r_time = mean(xylose_peaks$`Retention Time`),
                                    sd_r_time = sd(xylose_peaks$`Retention Time`),
                                    r_ci_low = mean(xylose_peaks$`Retention Time`)-2*sd(xylose_peaks$`Retention Time`),
                                    r_ci_high = mean(xylose_peaks$`Retention Time`)+2*sd(xylose_peaks$`Retention Time`)))

R_times = rbind(R_times, data.frame(Analyte = "DSMO",
                                    avg_r_time = mean(dsmo$`Retention Time`),
                                    sd_r_time = sd(dsmo$`Retention Time`),
                                    r_ci_low = mean(dsmo$`Retention Time`)-2*sd(dsmo$`Retention Time`),
                                    r_ci_high = mean(dsmo$`Retention Time`)+2*sd(dsmo$`Retention Time`)))

dfructose_peaks = fructose %>% 
    filter(Peak == 1) %>% 
  select(-Analyte)

dglucose_peaks = glucose %>% 
  filter(Peak == 1) %>% 
  select(-Analyte)

dsucrose_peaks = sucrose %>% 
  filter(Peak == 1) %>% 
  select(-Analyte)

dsucrose_peaks = dsucrose_peaks[-c(3),]

xsucrose_peaks = sucrose %>% 
  filter(`Retention Time` < 12.80 & `Retention Time` > 10.97) %>% 
  mutate(Peak = as.character("IS"))

sucrose_x_is = data.frame(Peak = numeric(),
                          Retention_time = numeric(), 
                          Area = numeric()) 

sucrose_is = data.frame("Concentration" = sucrose_peaks$Concentration, "Fructose Peak" = sucrose_peaks$Area, "IS Peak" = xsucrose_peaks$Area)

sucrose_is = sucrose_is %>% 
  mutate(Response_Factor = (sucrose_is$Fructose.Peak/sucrose_is$Concentration)/(sucrose_is$IS.Peak/0.5))

sucrose_peaks = sucrose_peaks %>% 
  mutate(response_factor = (sucrose_peaks$Area/sucrose_peaks$Concentration)/dsucrose_peaks$Area)

print("Sucrose Peaks F Mean and SD")

[1] "Sucrose Peaks F Mean and SD"

mean(sucrose_peaks$response_factor)

[1] 3.869912

sd(sucrose_peaks$response_factor)

[1] 1.220331

print("DSMO Peaks Mean and SD")

[1] "DSMO Peaks Mean and SD"

mean(dsmo$Area)

[1] 11.10546

sd(dsmo$Area)

[1] 4.655197

print("DSMO F, sd, and CI")

[1] "DSMO F, sd, and CI"

dmso_RFF = mean(sucrose_peaks$response_factor)
dmso_RFF_sd = sd(sucrose_peaks$response_factor)
dmso_RFF

[1] 3.869912

dmso_RFF_sd

[1] 1.220331

dmso_RFF_low = mean(sucrose_peaks$response_factor) - 2 * sd(sucrose_peaks$response_factor)
dmso_RFF_low

[1] 1.42925

dmso_RFF_high = mean(sucrose_peaks$response_factor) + 2 * sd(sucrose_peaks$response_factor)
dmso_RFF_high

[1] 6.310574

print("Xylose F, sd, and CI")

[1] "Xylose F, sd, and CI"

mean(sucrose_is$Response_Factor)

[1] 1.17316

sd(sucrose_is$Response_Factor)

[1] 2.408369

mean(sucrose_is$Response_Factor) - 2 * sd(sucrose_is$Response_Factor)

[1] -3.643578

mean(sucrose_is$Response_Factor) + 2 * sd(sucrose_is$Response_Factor)

[1] 5.989898

cereal_data = cereal_data %>% 
  mutate(peak_type = case_when(
    Ret_time >= 5.676919 & Ret_time <= 7.391209 ~ "DSMO",
    Ret_time >= 8.363270 & Ret_time <= 8.595879 ~ "Sucrose",
    Ret_time >= 10.119791 & Ret_time < 10.296231 ~ "Fructose",
    Ret_time >= 10.296231 & Ret_time <= 10.653432 ~ "Fructose or Glucose",
    Ret_time >= 10.653432 & Ret_time <= 10.724288 ~ "Fructose",
    Ret_time >= 10.978320 & Ret_time <= 12.796417 ~ "Xylose",
    TRUE ~ "Outside of 95% CI"
  ))

choco = cereal_data %>% 
  filter(Sample =="Choco") %>% 
  select(-Sample)

special_k = cereal_data %>% 
  filter(Sample =="Special_k") %>% 
  select(-Sample)

corn = cereal_data %>% 
  filter(Sample =="corn") %>% 
  select(-Sample)

#sucrose in solution (lowest conc. to test LOQ)
(corn$Area[2] * 5.0 / (corn$Area[1] * dmso_RFF_high))

[1] 8.580379

 
#g sugar per 100 g if sugar is evenly distributed
((corn$Area[2] * 5.0 / (corn$Area[1] * dmso_RFF_low)) * 0.1 / 11.36) * 100

[1] 33.34945

((corn$Area[2] * 5.0 / (corn$Area[1] * dmso_RFF_high)) * 0.1 / 11.36) * 100

[1] 7.553151

#g sugar per 100 g if sugar is all in there
((corn$Area[2] * 5.0 / (corn$Area[1] * dmso_RFF_low)) * 0.1 / 11.36) * 100 * 56.1042 / 67.2568

[1] 27.81941

((corn$Area[2] * 5.0 / (corn$Area[1] * dmso_RFF_high)) * 0.1 / 11.36) * 100 * 56.1042 / 67.2568

[1] 6.300679

#Based on Calibration Curve
(corn$Area[2]/Sucrose_reg$coefficients[1]) #Concentration in solution

Concentration 
        4.741 

(corn$Area[2]/Sucrose_reg$coefficients[1]) * 0.1 #Mass in solution

Concentration 
       0.4741 

(((corn$Area[2]/Sucrose_reg$coefficients[1]) * 0.1)/11.36) * 100 #g/100 g in corn flakes

Concentration 
     4.173415 

corn_ci_low =((corn$Area[2]/(Sucrose_reg$coefficients[1]+(1.96*1.002)) * 0.1)/11.36) * 100 #g/100 g in corn flakes lower CI
corn_ci_high = ((corn$Area[2]/(Sucrose_reg$coefficients[1]-(1.96*1.002)) * 0.1)/11.36) * 100 #g/100 g in corn flakes lower CI
cat("The concentration of sucrose in cereal is between", corn_ci_low, "g/100 g and", corn_ci_high, "g/100 g")

The concentration of sucrose in cereal is between 3.780717 g/100 g and 4.657147 g/100 g