The Role of Vitamin C in Tooth Growth

by Richard Bagnall
July 2015

SYNOPSIS

Six groups of ten guinea pigs were fed a diet supplemented with vitamin C at 0.5, 1.0 and 2.0 milligrams per day in the form of orange juice (OJ) or chemically pure vitamin C (VC). After 42 days, the length of the odontoblast cells were measured using optical microscopy. The tooth growth data therefore consist of 60 observations of the 3 variables: mean length of odontoblasts (microns), supplement type (OJ or VC) and vitamin C dose (miligrams/day).

EXPLORATORY ANALYSIS OF TOOTH GROWTH DATA

Aim: Use R to explore the sturcture of the tooth growth data

# load data
df <-ToothGrowth

# show structure of the data
str(df)
## 'data.frame':    60 obs. of  3 variables:
##  $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
##  $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...

Change ‘dose’ class from numeric to factor and show a summary of the data, split by supplement type.

# change dose to factor
df$dose <- as.factor(df$dose)

# summary of OJ and VC data
lapply(split(df$len, df$supp), function(x) {summary(x)})
## $OJ
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.20   15.52   22.70   20.66   25.72   30.90 
## 
## $VC
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    4.20   11.20   16.50   16.96   23.10   33.90
# compare variance of the OJ and VC data
lapply(split(df$len, df$supp), function(x) {var(x)})
## $OJ
## [1] 43.63344
## 
## $VC
## [1] 68.32723

Plot the data as a box plot, with a dot plot overlay, split by supplement dose and coloured by supplement type (R code is shown in Appendix 1).

Figure 1. Boxplot of tooth growth data split by vitamin C dose. Black horizontal lines in boxplot shows the mean value; red circles show orange juice supplement data points; blue circles show chemically pure vitamin C supplement data points.

CONCLUSIONS OF EXPLORATORY DATA ANALYSIS.

  • There are no missing data
  • There are no extreme outlier data points
  • The VC and OJ data sets are approximately normally distributed
  • The ‘dose’ variable class has been corrected from numeric to factor
  • The variance of the orange juce data (43.4) and the pure vitamin C data (68.3) are not equal, and this will inform the following t.test analyses.

COMPARE TOOTH GROWTH BY SUPPLEMENT

Perform a  to compare the odontoblast length between OJ and VC treated guinea pigs, and at each dose (see appendix 2 for R code).

Table 1. Comparison of Tooth Growth by Supplement Type

Supplement Comparison Group 95% CI p-value
OJ compared to VC (0.5 mg) -8.781, -1.719 0.006
OJ compared to VC (1.0 mg) -9.058, -2.802 0.001
OJ compared to VC (2.0 mg) -3.638, 3.798 0.964
OJ compared to VC (full data set) -0.171, 7.571 0.061

A 95% confidence interval measures the bounds where 95% of values fall within. Compared to chemically pure vitamin C, orange juice yields a shorter odontoblast length at a dose of 0.5 and 1.0 milligrams per day, since the interval is entirely below zero at 95% confidence. There is no difference in odontoblast length between vitamin C delivered in chemically pure form or as orange juice at a dose of 2.0 milligrams per day, since the interval contains zero at 95% confidence. In the overall data set, there is no difference in odontoblast length when vitamin C is delivered in chemically pure form or as orange juice as the confidence interval contains zero.

COMPARE TOOTH GROWTH BY DOSE

Perform a  to compare the odontoblast length between different doses of suppelment (see appendix 3 for R code).

Table 2. Comparison of Tooth Growth by Vitamin C Dose

Supplement Comparison Group 95% CI p-value
0.5 mg compared to 1.0 mg (VC) 6.314, 11.266 0.0000007
0.5 mg compared to 2.0 mg (VC) 14.418, 21.902 0.00000005
1.0 mg compared to 2.0 mg (VC) 5.686, 13.054 0.0000916
0.5 mg compared to 1.0 mg (OJ) 5.524, 13.416 0.0000878
0.5 mg compared to 2.0 mg (OJ) 9.325, 16.335 0.0000013
1.0 mg compared to 2.0 mg (OJ) 0.189, 6.531 0.039

Since none of the intervals include zero in any comparisons, increasing the dose of vitamin C from 0.5 to 1.0 or 2.0 milligrams per day, delivered in either chemically pure form or as orange juice, increases the odontoblast length.

ASSUMPTIONS MADE

The following assumptions were made in the t tests:

    1. The OJ data set and VC data set are normally distributed
    1. The variables are independent and identically distributed
    1. The variance of the OJ and VC data set are not equal

APPENDIX 1: R code for exploratory boxplot of tooth growth data (Figure 1)

# load ggplot2
suppressMessages(suppressWarnings(library(ggplot2)))

# box plot of data points
p <- ggplot(df, aes(x=dose, y=len, fill=supp)) + geom_boxplot()

# overlay dot points
p + geom_dotplot(binaxis='y', 
                 stackdir='center', 
                 position=position_dodge(0.75), 
                 dotsize=0.5, binwidth=1) 

# add title and legends
+ ggtitle("Distribution of Tooth Growth Data by Supplement Type") 
+ xlab("Vitamin C dose (milligrams/day)") 
+ ylab("Odontoblast length (microns)") 
+ theme(plot.title = element_text(size = 14.0), 
        axis.title = element_text(size = 10.0)) 
+ guides(fill = guide_legend(title="Supplement type")) 
+ scale_fill_discrete(labels=c("Orange Juice", "Pure Vitamin C"))

APPENDIX 2: R code for plot of tooth growth data by supplement type (Table 1)

low_supp_conf <-t.test(df[c(1:10),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$conf
low_supp_p <-t.test(df[c(1:10),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$p.value
mid_supp_conf <-t.test(df[c(11:20),1], df[c(41:50),1], paired=FALSE, var.equal = FALSE)$conf
mid_supp_p <-t.test(df[c(11:20),1], df[c(41:50),1], paired=FALSE, var.equal = FALSE)$p.value
high_supp_conf <-t.test(df[c(21:30),1], df[c(51:60),1], paired=FALSE, var.equal = FALSE)$conf
high_supp_p <-t.test(df[c(21:30),1], df[c(51:60),1], paired=FALSE, var.equal = FALSE)$p.value
full_supp_conf <- t.test(len ~ supp, paired=FALSE, var.equal = FALSE, data=df)$conf
full_supp_p <- t.test(len ~ supp, paired=FALSE, var.equal = FALSE, data=df)$p.value

APPENDIX 3: R code for plot of tooth growth data by dose (Table 2)

options(scipen=999)

vc_low_mid_conf <-t.test(df[c(11:20),1], df[c(1:10),1], paired=FALSE, var.equal = FALSE)$conf
vc_low_mid_p <-t.test(df[c(11:20),1], df[c(1:10),1], paired=FALSE, var.equal = FALSE)$p.value
vc_low_high_conf <-t.test(df[c(21:30),1], df[c(1:10),1], paired=FALSE, var.equal = FALSE)$conf
vc_low_high_p <-t.test(df[c(21:30),1], df[c(1:10),1], paired=FALSE, var.equal = FALSE)$p.value
vc_mid_high_conf <-t.test(df[c(21:30),1], df[c(11:20),1], paired=FALSE, var.equal = FALSE)$conf
vc_mid_high_p <-t.test(df[c(21:30),1], df[c(11:20),1], paired=FALSE, var.equal = FALSE)$p.value
oj_low_mid_conf <-t.test(df[c(41:50),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$conf
oj_low_mid_p <-t.test(df[c(41:50),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$p.value
oj_low_high_conf <-t.test(df[c(51:60),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$conf
oj_low_high_p <-t.test(df[c(51:60),1], df[c(31:40),1], paired=FALSE, var.equal = FALSE)$p.value
oj_mid_high_conf <-t.test(df[c(51:60),1], df[c(41:50),1], paired=FALSE, var.equal = FALSE)$conf
oj_mid_high_p <-t.test(df[c(51:60),1], df[c(41:50),1], paired=FALSE, var.equal = FALSE)$p.value