Imagine that in a large observational study comparing people who regularly take =400 IU of vitamin D per day with people with no supplemental vitamin D intake, the crude incidence rate ratio of multiple sclerosis was 0.34. Smokers are less likely to take vitamin supplements and they are more likely to develop multiple sclerosis. If the authors of the observational study further adjust for smoking, the resulting adjusted incidence rate ratio may be

Question

Imagine that in a large observational study comparing people who regularly take >=400 IU of vitamin D per day with people with no supplemental vitamin D intake, the crude incidence rate ratio of multiple sclerosis was 0.34. Smokers are less likely to take vitamin supplements and they are more likely to develop multiple sclerosis. If the authors of the observational study further adjust for smoking, the resulting adjusted incidence rate ratio may be

BlackTom AI · Accepted Answer

Question restatement: In a large observational study comparing people taking ≥400 IU of vitamin D daily to those with no supplement, the crude incidence rate ratio (IRR) for multiple sclerosis (MS) is 0.34. Smoking is more common among non-supplement users and is also a risk factor for MS. After adjusting for smoking, what might the resulting adjusted IRR be?

Option-by-option analysis:
- Option a: 0.21
  This would indicate an even stronger protective association after adjustment. Given that smoking is a positive risk factor for MS and is less common among supplement users, adjusting for smoking typically reduces the magnitude of confounding that makes the exposure look more protective than it is. Therefore, it is unlikely that adjustment would push the IRR further away from 1 to become smaller than 0.34 (0.21) unless there was an extremely strong and specific interaction or unaccounted confounding. While not impossible, this is less plausible as a general expectation.
- Option b: 0.32
  This value is very close to the crude estimate (0.34). It would imply that adjusting for smoking almost entirely preserves the observed protective effect with only a tiny change. In practice, adjusting for a known confounder like smoking often attenuates the effect toward the null (toward 1) rather than keeping it nearly identical, unless smoking had almost no confounding impact. So this option is possible but not the most expected outcome.
- Option c: 0.85
  This value represents substantial attenuation toward the null, which fits the typical pattern when a confounder (smoking) is positively associated with the outcome (MS) and inversely associated with the exposure (vitamin D supplement use). By accounting for smoking, the observed protective effect could be weakened, moving the IRR from 0.34 toward 1.0, with 0.85 being a reasonable intermediate result.
- Option d: 1.23
  Here, the adjustment would not only attenuate the protective effect but reverse it, yielding a positive association where supplement use appears to increase MS risk after adjustment. This is less common but possible if smoking confounding was substantial and the true relationship is null or harmful once smoking is controlled. However, such a reversal would require a strong and specific confounding structure; it is not the typical expectation.
- Option e: a or b
  This choice asserts that the adjusted IRR could be either 0.21 or 0.32. Given the reasoning for a and b above, while 0.32 is plausible as a near-null effect, 0.21 is unusually low after adjustment unless there is unusual data aspects. Selecting both as possible without additional context is overly broad.
- Option f: c or d
  This option captures the idea that after adjusting for smoking, the adjusted IRR could plausibly be either 0.85 (attenuation toward null) or 1.23 (possible reversal or loss of protective effect) depending on the exact strength of confounding and data structure. Since smoking is a confounder that both moves exposure odds and MS risk in directions that could attenuate or even reverse the association, acknowledging both possibilities reflects theoretical and practical possibilities in observational adjustment.

Synthesis: The core concept is that confounding by smoking tends to move the crude estimate toward the null and can, in some scenarios, move it beyond 1 if residual or unmeasured confounding exists or if the direction of the association changes after adjustment. Therefore, the most comprehensive and defensible choice is that the adjusted IRR may be either 0.85 or 1.23, depending on how strongly smoking confounds the association in this dataset. This aligns with the idea that adjustments can both attenuate and potentially reverse observed associations in observational studies.

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