The table below shows the output from a logistic regression model evaluating the relationship between age (in years), educational attainment (less than high school, completed high school, or at least some college) and the outcome of death over a 3-year follow-up period. Based on this output, what is the odds ratio for the association between having at least some college education and death within three years after adjusting for age at entry into the cohort?

Question

BlackTom AI · Accepted Answer

First, restating the question and options to anchor what we're evaluating: the question asks for the odds ratio for the association between having at least some college education (i.e., education category '> High School') and death within three years, adjusting for age at entry into the cohort, based on the logistic regression output provided. The answer choices are: a. -0.53, b. 0.53, c. 0.59, d. -0.59.

Now, examine the logistic regression output for the education variable. The table shows two education categories beyond the reference: 'High School' and '> High School'. The coefficient (Coef.) for '> High School' is -0.530652. In logistic regression, the exponentiated coefficient exp(beta) gives the odds ratio for the corresponding category relative to the reference group.

Option A: -0.53 is a coefficient, not an odds ratio. Since the question asks for an odds ratio, this numeric value cannot be the correct odds ratio without exponentiation. Therefore this option is conceptually incorrect.

Option B: 0.53 is the magnitude of the exponentiated value only if the coefficient were approximately -0.63 (since exp(-0.63) ≈ 0.53). The actual coefficient is -0.530652, and exp(-0.530652) must be computed to obtain the OR. Without exponentiation, this numeric form is not directly the odds ratio, making this option suspect.

Option C: 0.59. This matches the odds ratio you obtain by exponentiating the coefficient for '> High School': exp(-0.530652) ≈ 0.588, which rounds to 0.59. This represents the odds of death within three years for individuals with at least some college education compared to those with less than high school, after adjusting for age.

Option D: -0.59 is also a coefficient-like value and negative; as with option A, odds ratios are obtained by exponentiating coefficients, which yields a positive number. Therefore this cannot be the odds ratio.

Putting it together, the only option that correctly reflects the odds ratio after exponentiating the education coefficient is the value around 0.59. The negative coefficients in the table are log-odds, not odds ratios themselves, so they must be transformed via the exponential function to interpret them as odds ratios.

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