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 a 10 year increment in age and death within three years after adjusting for educational attainment?

Question

BlackTom AI · Accepted Answer

To tackle this question, I will parse the table and extract the relevant coefficient and its interpretation.
Option by option evaluation:
- First, identify the reported coefficient for age. The table shows a Coef. for age equal to 0.0609695 with a standard error of 0.0046032. In logistic regression, the coefficient for a predictor is the log odds ratio associated with a one-unit increase in that predictor.
- Interpreting per-year effect: The odds ratio for a 1-year increase in age is exp(0.0609695). Calculating this gives roughly exp(0.061) ≈ 1.063. This means each additional year of age increases the odds of death by about 6.3% when adjusting for education.
- Now scale to a 10-year increment: a 10-year increase corresponds to 10 times the per-year log-odds change, i.e., 10 * 0.0609695 = 0.609695. The odds ratio for a 10-year increment is exp(0.609695) ≈ 1.84.
- Compare with the provided options:
  • 13.24 would imply a much larger log-odds increase (roughly exp(2.586) ≈ 13.24), which is not consistent with the per-year coefficient shown.
  • 1.84 matches the computed OR for a 10-year increment (exp(0.609695) ≈ 1.84).
  • 1.06 would correspond to a very small per-year increase (roughly exp(0.06) ≈ 1.06) if interpreted as the yearly OR, but the question asks for a 10-year increment, not a single year.
  • 0.06 would be a near-zero odds ratio, which would be misinterpreting the coefficient entirely (it resembles the log-odds or a mis-scaled value, not an OR).
- Therefore, the correct interpretation requires converting the 1-year log-odds to a 10-year odds ratio by multiplying the coefficient by 10 and exponentiating, yielding approximately 1.84.
- In summary, the key concept is that the coefficient for age represents the log-odds change per year, and exponentiating 10 times that coefficient gives the odds ratio for a 10-year increase. The other options either misapply the per-year interpretation or fail to convert to a 10-year increment correctly.

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