Case-control analysis with Haskell

Performing case-control analysis in Haskell can be done using a combination of built-in functions and libraries like statistics and hmatrix. However, due to Haskell’s functional nature, the process might not be as straightforward as in other programming languages. Here’s how to go about it in Haskell:

Step 1: Set Up Your Data

Assume you have the following 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.

In Haskell, we can represent these values as variables.

 -- Define case-control data
 exposedCases :: Double
 exposedCases = 50
 
 notExposedCases :: Double
 notExposedCases = 30
 
 exposedControls :: Double
 exposedControls = 20
 
 notExposedControls :: Double
 notExposedControls = 100

Step 2: Calculate the Odds Ratio

The odds ratio (OR) can be calculated using the formula:

$$ \text{OR} = \frac{(\text{exposedCases} \times \text{notExposedControls})}{(\text{notExposedCases} \times \text{exposedControls})} $$

 -- Calculate the odds ratio
 oddsRatio :: Double
 oddsRatio = (exposedCases * notExposedControls) / (notExposedCases * exposedControls)
 
 main :: IO ()
 main = putStrLn $ "Odds Ratio: " ++ show oddsRatio

Step 3: Calculate Confidence Interval for the Odds Ratio

To compute a 95% confidence interval for the odds ratio, we use the formula:

$$ \ln(\text{OR}) \pm Z \times \sqrt{\frac{1}{\text{exposedCases}} + \frac{1}{\text{notExposedCases}} + \frac{1}{\text{exposedControls}} + \frac{1}{\text{notExposedControls}}} $$

where ( $Z \approx 1.96$ ) for a 95% confidence level. The statistics package can be used for this computation.

 import Statistics.Distribution.Normal (normalDistr, quantile)
 
 -- Z-score for 95% confidence interval
 z :: Double
 z = quantile (normalDistr 0 1) 0.975  -- 1.96 for a two-tailed 95% CI
 
 -- Logarithmic Odds Ratio and Standard Error
 lnOR :: Double
 lnOR = log oddsRatio
 
 seLnOR :: Double
 seLnOR = sqrt (1/exposedCases + 1/notExposedCases + 1/exposedControls + 1/notExposedControls)
 
 -- Confidence Interval for Odds Ratio
 ciLower, ciUpper :: Double
 ciLower = exp (lnOR - z * seLnOR)
 ciUpper = exp (lnOR + z * seLnOR)
 
 main :: IO ()
 main = do
     putStrLn $ "Odds Ratio: " ++ show oddsRatio
     putStrLn $ "95% Confidence Interval: [" ++ show ciLower ++ ", " ++ show ciUpper ++ "]"

Step 4: Perform a Chi-Square Test

A chi-square test can be done using the Statistics.Test.ChiSquared module in the statistics package. This will help determine if there is a statistically significant association between exposure and outcome.