How to Calculate Odds Ratios in R With Examples Using epitools

Introduction

If you’re an R programmer working with categorical data, you’ll often need to measure the association between two binary variables. That’s where odds ratios come in handy! The epitools package in R makes calculating odds ratios simple with its oddsratio() function .

In this guide, we’ll walk through everything you need to know about calculating odds ratios in R. You’ll learn the function syntax, see practical examples, and understand how to interpret the results. Whether you’re analyzing medical data, conducting epidemiological research, or exploring any binary relationships, this tutorial has you covered.

What Are Odds Ratios?

An odds ratio (OR) compares the odds of an event happening in one group versus another group. It’s especially useful when you have two binary variables (yes/no, exposed/unexposed, success/failure) .

Here’s what the values mean:

• OR = 1: No association between the variables
• OR > 1: Positive association (higher odds in the first group)
• OR < 1: Negative association (lower odds in the first group)

For example, if the odds ratio is 3.0, the odds of the outcome are 3 times higher in the exposed group compared to the unexposed group.

Installing and Loading epitools

Before we dive into calculations, let’s get the epitools package ready:

# Install the package (only need to do this once)
#install.packages("epitools")

# Load the package
library(epitools)

Understanding oddsratio() Syntax

The oddsratio() function has a straightforward syntax with several customizable options :

oddsratio(x, y = NULL, 
          method = c("midp", "fisher", "wald", "small"), 
          conf.level = 0.95, 
          rev = c("neither", "rows", "columns", "both"), 
          correction = FALSE, 
          verbose = FALSE)

Let’s break down each parameter:

Parameter	Description	Default
x	A 2x2 matrix or table of counts	Required
y	Optional second vector (rarely used)	NULL
method	Estimation method	“midp”
conf.level	Confidence level (e.g., 0.95 for 95%)	0.95
rev	Reverse table orientation	“neither”
correction	Apply continuity correction	FALSE
verbose	Print detailed output	FALSE

Creating 2x2 Tables in R

Odds ratios work with 2x2 contingency tables. Here’s how to create them :

Method 1: Using matrix()

# Create a 2x2 table
data <- matrix(c(30, 70, 10, 90), nrow = 2, byrow = TRUE)

# Add row and column names for clarity
rownames(data) <- c("Exposed", "Unexposed")
colnames(data) <- c("Disease", "No Disease")

# View the table
print(data)

          Disease No Disease
Exposed        30         70
Unexposed      10         90

Method 2: Using a Data Frame

# Create a data frame
df <- data.frame(
  exposure = c(rep("Exposed", 100), rep("Unexposed", 100)),
  disease = c(rep("Yes", 30), rep("No", 70), 
              rep("Yes", 10), rep("No", 90))
)

# Convert to table
my_table <- table(df$exposure, df$disease)
print(my_table)

           
            No Yes
  Exposed   70  30
  Unexposed 90  10

Basic Examples with oddsratio()

Let’s calculate odds ratios with real examples :

Example 1: Simple Calculation

# Create the data
data1 <- matrix(c(30, 70, 10, 90), nrow = 2, byrow = TRUE)
rownames(data1) <- c("Exposed", "Unexposed")
colnames(data1) <- c("Disease", "No Disease")

# Calculate odds ratio
result <- oddsratio(data1, method = "wald")
print(result)

$data
          Disease No Disease Total
Exposed        30         70   100
Unexposed      10         90   100
Total          40        160   200

$measure
                        NA
odds ratio with 95% C.I. estimate    lower   upper
               Exposed   1.000000       NA      NA
               Unexposed 3.857143 1.766603 8.42156

$p.value
           NA
two-sided     midp.exact fisher.exact  chi.square
  Exposed             NA           NA          NA
  Unexposed 0.0004024082 0.0006504107 0.000406952

$correction
[1] FALSE

attr(,"method")
[1] "Unconditional MLE & normal approximation (Wald) CI"

Based on our computation results, this would give us:

• Odds Ratio: 3.857
• 95% CI: 1.767 to 8.422
• p-value: 0.0007

Example 2: Different Method Options

# Using Fisher's exact method
result_fisher <- oddsratio(data1, method = "fisher")
cat("Fisher's Exact Method Results:\n")

Fisher's Exact Method Results:

print(result_fisher)

$data
          Disease No Disease Total
Exposed        30         70   100
Unexposed      10         90   100
Total          40        160   200

$measure
                        NA
odds ratio with 95% C.I. estimate    lower    upper
               Exposed   1.000000       NA       NA
               Unexposed 3.831525 1.684537 9.405984

$p.value
           NA
two-sided     midp.exact fisher.exact  chi.square
  Exposed             NA           NA          NA
  Unexposed 0.0004024082 0.0006504107 0.000406952

$correction
[1] FALSE

attr(,"method")
[1] "Conditional MLE & exact CI from 'fisher.test'"

# Using mid-p method (default)
result_midp <- oddsratio(data1, method = "midp")
cat("Mid-P Method Results:\n")

Mid-P Method Results:

print(result_midp)

$data
          Disease No Disease Total
Exposed        30         70   100
Unexposed      10         90   100
Total          40        160   200

$measure
                        NA
odds ratio with 95% C.I. estimate    lower    upper
               Exposed   1.000000       NA       NA
               Unexposed 3.796852 1.783145 8.728312

$p.value
           NA
two-sided     midp.exact fisher.exact  chi.square
  Exposed             NA           NA          NA
  Unexposed 0.0004024082 0.0006504107 0.000406952

$correction
[1] FALSE

attr(,"method")
[1] "median-unbiased estimate & mid-p exact CI"

# Using small sample adjustment
result_small <- oddsratio(data1, method = "small")

Warning in any(or, na.rm = TRUE): coercing argument of type 'double' to logical

cat("Small Sample Adjustment Results:\n")

Small Sample Adjustment Results:

print(result_small)

$data
          Disease No Disease Total
Exposed        30         70   100
Unexposed      10         90   100
Total          40        160   200

$measure
                        NA
odds ratio with 95% C.I. estimate    lower    upper
               Exposed   1.000000       NA       NA
               Unexposed 3.457106 1.731167 8.031582

$p.value
           NA
two-sided     midp.exact fisher.exact  chi.square
  Exposed             NA           NA          NA
  Unexposed 0.0004024082 0.0006504107 0.000406952

$correction
[1] FALSE

attr(,"method")
[1] "small sample-adjusted UMLE & normal approx (Wald) CI"

Interpreting the Results

When you run oddsratio(), you get several key outputs :

Output	What It Means
Odds Ratio	The strength of association
95% CI Lower	Lower bound of confidence interval
95% CI Upper	Upper bound of confidence interval
p-value	Statistical significance test

Key Takeaway: If the confidence interval includes 1, the association is not statistically significant at your chosen confidence level.

Real-World Examples

Let’s look at some practical scenarios:

Medical Study Example

# Smoking and lung cancer data
smoking_data <- matrix(c(15, 25, 5, 35), nrow = 2, byrow = TRUE)
rownames(smoking_data) <- c("Smokers", "Non-smokers")
colnames(smoking_data) <- c("Cancer", "No Cancer")

result <- oddsratio(smoking_data, method = "wald")
cat("Smoking and Lung Cancer Results:\n")

Smoking and Lung Cancer Results:

print(result)

$data
            Cancer No Cancer Total
Smokers         15        25    40
Non-smokers      5        35    40
Total           20        60    80

$measure
                        NA
odds ratio with 95% C.I. estimate    lower   upper
             Smokers          1.0       NA      NA
             Non-smokers      4.2 1.350224 13.0645

$p.value
             NA
two-sided     midp.exact fisher.exact  chi.square
  Smokers             NA           NA          NA
  Non-smokers 0.01128547   0.01877238 0.009823275

$correction
[1] FALSE

attr(,"method")
[1] "Unconditional MLE & normal approximation (Wald) CI"

From our calculations, this gives:

• Odds Ratio: 4.200
• 95% CI: 1.350 to 13.065
• p-value: 0.011

This means smokers have 4.2 times higher odds of cancer compared to non-smokers.

Small Sample Example

When dealing with small samples, use appropriate methods:

# Sparse data
sparse_data <- matrix(c(2, 8, 1, 19), nrow = 2, byrow = TRUE)
result_sparse <- oddsratio(sparse_data, method = "fisher")

Warning in chisq.test(xx, correct = correction): Chi-squared approximation may
be incorrect

cat("Sparse Data Results:\n")

Sparse Data Results:

print(result_sparse)

$data
          Outcome
Predictor  Disease1 Disease2 Total
  Exposed1        2        8    10
  Exposed2        1       19    20
  Total           3       27    30

$measure
          odds ratio with 95% C.I.
Predictor  estimate     lower    upper
  Exposed1 1.000000        NA       NA
  Exposed2 4.480431 0.2060739 293.9622

$p.value
          two-sided
Predictor  midp.exact fisher.exact chi.square
  Exposed1         NA           NA         NA
  Exposed2  0.2807882    0.2512315  0.1967056

$correction
[1] FALSE

attr(,"method")
[1] "Conditional MLE & exact CI from 'fisher.test'"

Results:

• Odds Ratio: 4.48
• 95% CI: 0.206 to 293.962
• p-value: 0.251

Note the wide confidence interval due to small sample size!

Visualizing Odds Ratios

Visual representations help communicate your findings. Here are the odds ratios from our examples:

# Load necessary libraries
library(ggplot2)
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

# Create a data frame for plotting
odds_data <- data.frame(
  Group = c("Exposed", "Unexposed", "Smokers", "Non-smokers"),
  Odds_Ratio = c(3.857, 1, 4.200, 1),
  Lower_CI = c(1.767, NA, 1.350, NA),
  Upper_CI = c(8.422, NA, 13.065, NA)
)
# Plot the odds ratios with confidence intervals
ggplot(odds_data, aes(x = Group, y = Odds_Ratio)) +
  geom_point() +
  geom_errorbar(aes(ymin = Lower_CI, ymax = Upper_CI), width = 0.2) +
  geom_hline(yintercept = 1, linetype = "dashed", color = "red") +
  labs(title = "Odds Ratios with 95% Confidence Intervals",
       y = "Odds Ratio",
       x = "Group") +
  theme_minimal()

The plot shows odds ratios with 95% confidence intervals. The dashed line at OR=1 represents no association.

Here’s how the data looks in a contingency table:

# Create a contingency table for visualization
contingency_table <- matrix(c(30, 70, 10, 90), nrow = 2, byrow = TRUE)
rownames(contingency_table) <- c("Exposed", "Unexposed")
colnames(contingency_table) <- c("Disease", "No Disease")
# Display the contingency table
print(contingency_table)

          Disease No Disease
Exposed        30         70
Unexposed      10         90

Common Use Cases

Odds ratios are widely used in:

1. Case-Control Studies: Comparing disease cases with healthy controls
2. Clinical Trials: Evaluating treatment effectiveness
3. Epidemiology: Identifying risk factors for diseases
4. Cross-Sectional Studies: Analyzing prevalence relationships
5. Public Health: Informing policy decisions

Your Turn!

Try calculating an odds ratio yourself! Given this vaccination data:

	Got Flu	No Flu
Vaccinated	10	90
Unvaccinated	30	70

Challenge: Calculate the odds ratio using the oddsratio() function. What does it tell you about vaccine effectiveness?

Click here for Solution!

# Create the table
vaccine_data <- matrix(c(10, 90, 30, 70), nrow = 2, byrow = TRUE)
rownames(vaccine_data) <- c("Vaccinated", "Unvaccinated")
colnames(vaccine_data) <- c("Got Flu", "No Flu")

# Calculate odds ratio
library(epitools)
result <- oddsratio(vaccine_data, method = "wald")
print(result)

$data
             Got Flu No Flu Total
Vaccinated        10     90   100
Unvaccinated      30     70   100
Total             40    160   200

$measure
                        NA
odds ratio with 95% C.I.  estimate     lower     upper
            Vaccinated   1.0000000        NA        NA
            Unvaccinated 0.2592593 0.1187428 0.5660582

$p.value
              NA
two-sided        midp.exact fisher.exact  chi.square
  Vaccinated             NA           NA          NA
  Unvaccinated 0.0004024082 0.0006504107 0.000406952

$correction
[1] FALSE

attr(,"method")
[1] "Unconditional MLE & normal approximation (Wald) CI"

# The odds ratio should be approximately 0.259
# This means vaccinated people have about 74% lower odds of getting flu
# (1 - 0.259 = 0.741 or 74.1% reduction)

Quick Takeaways

• Odds ratios measure association between two binary variables
• Use epitools::oddsratio() for easy calculation in R
• The function requires a 2x2 contingency table
• Choose the right method based on sample size:
  • Large samples: “wald”
  • Small samples: “fisher” or “midp”
• Always check confidence intervals for statistical significance
• OR > 1 means positive association, OR < 1 means negative association
• Wide confidence intervals indicate uncertainty (often due to small samples)

Conclusion

Calculating odds ratios in R using the epitools package is straightforward once you understand the basics. The oddsratio() function provides a powerful tool for analyzing binary relationships in your data.

Remember to:

• Structure your data as a 2x2 table
• Choose the appropriate estimation method
• Interpret both the odds ratio and its confidence interval
• Consider sample size when drawing conclusions

FAQs

Q1: What’s the difference between odds ratio and risk ratio? A: Odds ratios compare odds (probability of event/probability of no event), while risk ratios compare probabilities directly. Odds ratios are preferred in case-control studies where risk cannot be directly calculated.

Q2: When should I use Fisher’s method instead of Wald? A: Use Fisher’s method when you have small sample sizes (any cell count < 5) or sparse data. It provides exact p-values rather than approximations.

Q3: How do I handle tables larger than 2x2? A: The oddsratio() function only works with 2x2 tables. For larger tables, you’ll need to subset your data or use other functions like epitab() for more complex analyses.

Q4: What does it mean if my confidence interval is very wide? A: A wide confidence interval indicates high uncertainty in your estimate, usually due to small sample sizes. Consider collecting more data or using methods designed for small samples.

Q5: Can I use odds ratios for non-binary variables? A: No, odds ratios are specifically for binary (two-category) variables. For variables with more categories, consider other measures like relative risk ratios or multinomial logistic regression.

Found this guide helpful? Share it with fellow R programmers and let us know what topics you’d like us to cover next! Follow us for more R programming tutorials and statistical analysis guides.

References

1. https://cran.r-project.org/web/packages/epitools/index.html

2. https://www.statology.org/odds-ratio-in-r/

3. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6532386/

4. https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/

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odds Ratio in R

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