1 Linear Correlation: “Cancer”

# install.packages("remotes")
# remotes::install_github("sarbearschwartz/apaSupp")
# remotes::install_github("ddsjoberg/gtsummary")

library(tidyverse)    # Loads several very helpful 'tidy' packages
library(haven)        # Read in SPSS datasets
library(psych)        # Lots of nice tid-bits
library(GGally)       # Extension to 'ggplot2' (ggpairs)
library(corrplot)     # Correlation Matrix plots
library(apaSupp)      # APA 7th ed tables

1.1 PURPOSE

1.1.1 Research Question

Is there a relationship between the demographics and oral condition over the 6 weeks?

1.1.2 Data Description

The Cancer data set contains 4 repeated measure of oral condition for 25 cancer patients to see if an aloe treatment helps with oral condition (ulcers).

cancer_raw <- haven::read_spss("https://raw.githubusercontent.com/CEHS-research/eBook_ANOVA/master/data/Cancer.sav")
tibble::glimpse(cancer_raw)
Rows: 25
Columns: 9
$ ID       <dbl> 1, 5, 6, 9, 11, 15, 21, 26, 31, 35, 39, 41, 45, 2, 12, 14, 16…
$ TRT      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1…
$ AGE      <dbl> 52, 77, 60, 61, 59, 69, 67, 56, 61, 51, 46, 65, 67, 46, 56, 4…
$ WEIGHIN  <dbl> 124.0, 160.0, 136.5, 179.6, 175.8, 167.6, 186.0, 158.0, 212.8…
$ STAGE    <dbl> 2, 1, 4, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 2, 4, 1, 2, 1, 4, 2, 1…
$ TOTALCIN <dbl> 6, 9, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 8, 7, 6, 4, 6, 6, 12, 5, …
$ TOTALCW2 <dbl> 6, 6, 9, 7, 7, 6, 11, 11, 9, 4, 8, 6, 8, 16, 10, 6, 11, 7, 11…
$ TOTALCW4 <dbl> 6, 10, 17, 9, 16, 6, 11, 15, 6, 8, 11, 9, 9, 9, 11, 8, 11, 6,…
$ TOTALCW6 <dbl> 7, 9, 19, 3, 13, 11, 10, 15, 8, 7, 11, 6, 10, 10, 9, 7, 14, 6…
cancer_clean <- cancer_raw %>% 
  dplyr::rename_all(tolower) %>% 
  dplyr::mutate(id = factor(id)) %>% 
  dplyr::mutate(trt = factor(trt,
                             labels = c("Placebo", 
                                        "Aloe Juice"))) %>% 
  dplyr::mutate(stage = factor(stage))
tibble::glimpse(cancer_clean)
Rows: 25
Columns: 9
$ id       <fct> 1, 5, 6, 9, 11, 15, 21, 26, 31, 35, 39, 41, 45, 2, 12, 14, 16…
$ trt      <fct> Placebo, Placebo, Placebo, Placebo, Placebo, Placebo, Placebo…
$ age      <dbl> 52, 77, 60, 61, 59, 69, 67, 56, 61, 51, 46, 65, 67, 46, 56, 4…
$ weighin  <dbl> 124.0, 160.0, 136.5, 179.6, 175.8, 167.6, 186.0, 158.0, 212.8…
$ stage    <fct> 2, 1, 4, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 2, 4, 1, 2, 1, 4, 2, 1…
$ totalcin <dbl> 6, 9, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 8, 7, 6, 4, 6, 6, 12, 5, …
$ totalcw2 <dbl> 6, 6, 9, 7, 7, 6, 11, 11, 9, 4, 8, 6, 8, 16, 10, 6, 11, 7, 11…
$ totalcw4 <dbl> 6, 10, 17, 9, 16, 6, 11, 15, 6, 8, 11, 9, 9, 9, 11, 8, 11, 6,…
$ totalcw6 <dbl> 7, 9, 19, 3, 13, 11, 10, 15, 8, 7, 11, 6, 10, 10, 9, 7, 14, 6…
cancer_clean %>% 
  dplyr::arrange(trt, stage, age, weighin) %>% 
  dplyr::select("Treatment" = trt,
                "ID" = id,
                "Stage" = stage,
                "Age" = age,
                "Weight" = weighin,
                "Intake" = totalcin,
                "Week 2" = totalcw2,
                "Week 4" = totalcw4,
                "Week 6" = totalcw6) %>% 
  flextable::as_grouped_data(groups = "Treatment") %>% 
  flextable::flextable() %>% 
  flextable::add_header_row(values = c("" , "Oral Condition"),
                            colwidths = c(5, 4)) %>% 
  apaSupp::theme_apa(caption = "Cancer Dataset",
                     general_note = "Age is in years and Weight is in pounds.  Age, Weight, and Stage as well as the first oral condition refer to baseline or intake appointment. Yellow denotes missing values.",
                     d = 0) %>%  
  flextable::hline( part = "header", i = 1,   j = 6:9) %>% 
  flextable::hline( part = "body",   i = 15) %>% 
  flextable::bg(bg = "yellow", i = c(17, 23), j = 9)
(#tab:df_cancer)Cancer Dataset

Oral Condition

Treatment

ID

Stage

Age

Weight

Intake

Week 2

Week 4

Week 6

Placebo

35

1

51

189

6

4

8

7

9

1

61

180

6

7

9

3

31

1

61

213

6

9

6

8

41

1

65

157

6

6

9

6

21

1

67

186

6

11

11

10

45

1

67

186

8

8

9

10

15

1

69

168

6

6

6

11

5

1

77

160

9

6

10

9

2

2

46

164

7

16

9

10

1

2

52

124

6

6

6

7

11

2

59

176

6

7

16

13

26

3

56

158

6

11

15

15

39

4

46

149

7

8

11

11

6

4

60

136

7

9

17

19

Aloe Juice

42

0

73

182

8

11

16

22

1

27

225

6

7

6

6

14

1

42

163

4

6

8

7

44

1

67

187

5

7

7

7

37

1

86

140

6

7

7

7

16

2

44

261

6

11

11

14

50

2

60

164

6

8

16

34

2

77

164

5

7

13

12

58

4

54

173

7

8

10

8

12

4

56

227

6

10

11

9

24

4

68

226

12

11

12

9

Note. Age is in years and Weight is in pounds. Age, Weight, and Stage as well as the first oral condition refer to baseline or intake appointment. Yellow denotes missing values.

1.2 EXPLORATORY DATA ANALYSIS

1.2.1 Scatterplot

Always plot your data first! 

cancer_clean %>% 
  ggplot(aes(x = age,
             y = weighin)) +
  geom_count() +
  geom_smooth(method = "lm") +
  theme_bw()

1.3 PEARSON’S CORRELATION

1.3.1 Using the Default Settings

The cor.test() function needs at least TWO arguments:

  • formula - The formula specifies the two variabels between which you would like to calcuate the correlation. Note at the two variable names come AFTER the tilda symbol and are separated with a plus sign: ~ continuous_var1 + continuous_var2

  • data - Since the datset is not the first argument in the function, you must use the period to signify that the datset is being piped from above data = . 

cancer_clean %>% 
  cor.test(~ age + weighin,  # formula: order doesn't matter
           data = .)         # data piped from above

    Pearson's product-moment correlation

data:  age and weighin
t = -1.4401, df = 23, p-value = 0.1633
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.6130537  0.1213316
sample estimates:
       cor 
-0.2875868

1.3.2 Additional Arguments

  • alternative - The cor.test() function defaults to the alternative = “two.sided”. If you would like a one-sided alternative, you must choose which side you would like to test: alternative = “greater” to test for POSITIVE correlation or alternative = “less” to test for NEGATIVE correlation.

  • method - The default is to calculate the Pearson correlation coefficient (method = “pearson”), but you may also specify the Kendall’s tau (method = “kendall”)or Spearman’s rho (method = “spearman”), which are both non-parametric methods.

  • conf.int - It also defaults to testing for the two-sided alternative and computing a 95% confidence interval (conf.level = 0.95), but this may be changed.

Since the following code only specifies thedefaults, it Will give the same results as if you did not type out the last three lines (see above).

cancer_clean %>% 
  cor.test(~ age + weighin,
           data = .,
           alternative = "two.sided",  # or "greater" (positive r) or "less" (negative r)
           method = "pearson",          # or "kendall" (tau) or "spearman" (rho)
           conf.level = .95)            # or .90 or .99 (ect)

    Pearson's product-moment correlation

data:  age and weighin
t = -1.4401, df = 23, p-value = 0.1633
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.6130537  0.1213316
sample estimates:
       cor 
-0.2875868

Non-Significant Correlation

APA Results: There was no evidence of an association in overall oral condition from baseline to two week follow-up, $r(25) = -0.288 \(p < .163\).

1.3.3 Statistical Significance

cancer_clean %>% 
  ggplot(aes(x = totalcin,
             y = totalcw4)) +
  geom_count() +
  geom_smooth(method = "lm") +
  theme_bw()

cancer_clean %>% 
  cor.test(~ totalcin + totalcw4,
           data = .)

    Pearson's product-moment correlation

data:  totalcin and totalcw4
t = 1.0911, df = 23, p-value = 0.2865
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.1899343  0.5672525
sample estimates:
      cor 
0.2218459 
cancer_clean %>% 
  cor.test(~ totalcw2 + totalcw4,
           data = .)

    Pearson's product-moment correlation

data:  totalcw2 and totalcw4
t = 1.718, df = 23, p-value = 0.09923
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.06678726  0.64625711
sample estimates:
      cor 
0.3372434

NOT Statistically Significant Correlation

APA Results: No evidence of a correlation between oral between weeks two and four was found, t(23) = 1.72, p = .099.

cancer_clean %>% 
  ggplot(aes(x = totalcw4,
             y = totalcw6)) +
  geom_point() +
  geom_smooth(method = "lm") +
  theme_bw()

cancer_clean %>% 
  cor.test(~ totalcw4 + totalcw6,
           data = .)

    Pearson's product-moment correlation

data:  totalcw4 and totalcw6
t = 5.4092, df = 21, p-value = 2.296e-05
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.5117459 0.8940223
sample estimates:
     cor 
0.762999

Statistically Significant Correlation

APA Results: Overall oral condition was positively correlated (r = .763) between weeks four and six, t(21) = 5.41, p < .001.

1.4 CORRELATION TABLES

Missing Values - Listwise Deletion vs. Pairwise Deletion

cancer_clean %>% 
  dplyr::filter(complete.cases(totalcin, totalcw2, totalcw4, totalcw6)) %>% 
  dplyr::select("Baseline" = totalcin, 
                "Week 2" = totalcw2, 
                "Week 4" = totalcw4, 
                "Week 6" = totalcw6) %>% 
  apaSupp::tab_cor(caption = "Correlations Between Repeated Measures of Total Oral Condition, Listwise Deletion",
                   general_note = "Listwise deletion applied, thus only participants with oral condition captured at all four occations are utilized.",
                   p_note = "apa3")
Table 1.1
Correlations Between Repeated Measures of Total Oral Condition, Listwise Deletion

Variable Pair

r

p

Week 2

Baseline

.280

.192

Week 4

Baseline

.210

.346

Week 6

Baseline

.098

.657

Week 4

Week 2

.310

.145

Week 6

Week 2

.380

.075

Week 6

Week 4

.760

< .001***

Note. N = 23. r = Pearson's Product-Moment correlation coefficient.Listwise deletion applied, thus only participants with oral condition captured at all four occations are utilized.

*** p < .001. 

cancer_clean %>% 
  dplyr::select("Baseline" = totalcin, 
                "Week 2" = totalcw2, 
                "Week 4" = totalcw4, 
                "Week 6" = totalcw6) %>% 
  apaSupp::tab_cor(caption = "Correlations Between Repeated Measures of Total Oral Condition, Pairwise Deletion",
                   general_note = "Pairwise-deletion used for each pair of obseration times.",
                   p_note = "apa3")
Table 1.2
Correlations Between Repeated Measures of Total Oral Condition, Pairwise Deletion

Variable Pair

r

p

Week 2

Baseline

.310

.126

Week 4

Baseline

.220

.287

Week 6

Baseline

.098

.657

Week 4

Week 2

.340

.099

Week 6

Week 2

.380

.075

Week 6

Week 4

.760

< .001***

Note. N = 25. r = Pearson's Product-Moment correlation coefficient.Pairwise-deletion used for each pair of obseration times.

*** p < .001.

1.5 PAIRS PLOTS

1.5.1 Using Base R

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  pairs()

1.5.2 Using the psych package

cancer_clean %>% 
  dplyr::select(age, weighin,
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  psych::pairs.panels()

1.5.3 Using the ggplot2 and GGally packages

cancer_clean %>% 
  dplyr::select(age, weighin,
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  data.frame %>% 
  ggscatmat() +
  theme_bw()

cancer_clean %>% 
  data.frame %>% 
  ggscatmat(columns = c("age", "weighin",
                        "totalcin", "totalcw2", "totalcw4", "totalcw6"),
            color = "trt") +
  theme_bw()

1.6 CORROLAGRAMS

1.6.1 Simple Correlation Matrix (Base R)

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") 
                 age     weighin   totalcin   totalcw2    totalcw4    totalcw6
age       1.00000000 -0.29909121 0.22386540 -0.1613892  0.09918029  0.03015273
weighin  -0.29909121  1.00000000 0.16403694  0.2763478 -0.08013506 -0.07750304
totalcin  0.22386540  0.16403694 1.00000000  0.2819648  0.20604650  0.09786664
totalcw2 -0.16138924  0.27634783 0.28196479  1.0000000  0.31354250  0.37809488
totalcw4  0.09918029 -0.08013506 0.20604650  0.3135425  1.00000000  0.76299899
totalcw6  0.03015273 -0.07750304 0.09786664  0.3780949  0.76299899  1.00000000

1.6.2 Using the Default Settings

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") %>% 
  corrplot::corrplot()

1.6.3 Changing the shape

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") %>% 
  corrplot::corrplot(method = "square")

1.6.4 Only Displaying Half

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") %>% 
  corrplot::corrplot(method = "ellipse",
                     type = "lower")

1.6.5 Mixing it up

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") %>% 
  corrplot::corrplot.mixed()

1.6.6 Getting Fancy

cancer_clean %>% 
  dplyr::select(age, weighin, 
                totalcin, totalcw2, totalcw4, totalcw6) %>% 
  cor(method = "pearson",
      use = "complete.obs") %>% 
  corrplot::corrplot.mixed(upper = "number",
                           lower = "ellipse")