In Julia, case-control analysis can be conducted similarly to other statistical software by calculating odds ratios, confidence intervals, and conducting hypothesis tests like the chi-square test. Julia has packages like DataFrames for data manipulation, StatsBase for basic statistical functions, and GLM for logistic regression.
Assume we have two groups — "cases" (with the outcome) and "controls" (without the outcome) — and a binary exposure variable.
Example data:
exposed_cases: Number of cases who were exposed.not_exposed_cases: Number of cases who were not exposed.exposed_controls: Number of controls who were exposed.not_exposed_controls: Number of controls who were not exposed. # Define case-control data
exposed_cases = 50
not_exposed_cases = 30
exposed_controls = 20
not_exposed_controls = 100
A contingency table helps structure the data for further analysis.
using DataFrames
# Create a 2x2 contingency table
data = DataFrame(Exposure = ["Exposed", "Not Exposed"],
Cases = [exposed_cases, not_exposed_cases],
Controls = [exposed_controls, not_exposed_controls])
println(data)
The odds ratio (OR) quantifies the association between exposure and outcome, and is calculated as:
$$ \text{OR} = \frac{(\text{exposed\_cases} \times \text{not\_exposed\_controls})}{(\text{not\_exposed\_cases} \times \text{exposed\_controls})} $$
# Calculate odds ratio
odds_ratio = (exposed_cases * not_exposed_controls) / (not_exposed_cases * exposed_controls)
println("Odds Ratio: ", odds_ratio)
To calculate the 95% confidence interval for the OR, we use the formula:
$$ \ln(\text{OR}) \pm Z \times \sqrt{\frac{1}{\text{exposed\_cases}} + \frac{1}{\text{not\_exposed\_cases}} + \frac{1}{\text{exposed\_controls}} + \frac{1}{\text{not\_exposed\_controls}}} $$
where ( $Z \approx 1.96$ ) for a 95% confidence level.