Logistic Regression in Case–Control Studies

Logistic Regression in Case–Control Studies

1. Two groups of subjects

   • Cases
     • subjects newly diagnosed with the disease of interest
   • Controls
     • subjects without the disease of interest
   • The most cost-effective analytical epidemiological study design and is recommended when the incidence of the disease or condition of interest is low
     • Objetives
       • Define the concepts of crude and adjusted odds ratios (ORs) to assess the magnitude of the association between an exposure and a specific disease using a logistic regression model.
         • Definition of the Odds Ratio
           • Odds of exposure among cases
           • Odds of exposure among controls
           • Exposure odds ratio
             • cases-controls
       • Assess confounding and effect modification using the results of the logistic regression model.
         • it is necessary to compare the point estimate of the crude odds ratio (ORcrude) and the point estimate of the adjusted odds ratio (ORadjusted).
         • Effect modification
           • There is no homogeneity among the ORs
           • When the magnitude of the association between the exposure and disease does not behave the same way across the levels of a third variable
           • Mantel–Haenszel method

2. Unconditional Logistic Regression Model

3. Types of Logistic Regression Models

   • Binary Case
     • The random variable under study (Y) is collected as dichotomous (0,1). For example, assume that Y defines the type of subject (case or control).
   • Binomial Case
     • In the binomial case, the random variable under study (Y) is collected as the number of sick people from the total number observed persons.
     • data are grouped
   • Computing Adjusted OR
     • Odds of disease in exposed group: E=1
     • Odds of unexposed group: E=0

4. crude odds ratio

   • Adjusted ORs
     • especially if the number of confounders is small, and the results can be compared

5. Inference of OR

   • The exposure factor is a dichotomous in the factor there are two possible results (presence vs absence) that are encoded by 0 and 1
   • The exposure factor is quantitative, specific values will be compared (subjects who smoke 20 cigarettes daily vs those who smoke 5 cigarettes daily)
   • The exposure factor is categorical with different levels, where the comparison is between one category (k) and a reference category (assuming it is the one with the lowest code).

6. propensity score

   • Improve the matching procedure using the logistic regression model to estimate the probability of being exposed given a set of predictors

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