Biostatistics and Epidemiology by Sylvia Wassertheil-Smoller & Jordan Smoller

Author:Sylvia Wassertheil-Smoller & Jordan Smoller
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

If our observed RRyes,yes is significantly different from 3.0, we can reject the null hypothesis of no interaction and conclude that there is a multiplicative interaction.

To test this statistically, we would include a product term in our regression model, or Cox proportional hazards model (multiplying the value of variable B by the value of variable A for each person to get a new variable which is the product of A and B), and then calculate the following quantity:

This quantity squared is approximately distributed as chi-square with 1 degrees of freedom.

What we are really testing is whether the coefficient β is significantly different from 0. If it is, then this is equivalent to concluding that the RRyes,yes is significantly different from our expected value of 3.0

Note that if there is a significant interaction, we cannot interpret the main effects from that same model in the way we usually do. For example, if there were a significant interaction between smoking and hypertension, we would have to stratify on hypertension—i.e., look at the effects of smoking separately among hypertensives and non-hypertensives.

Suppose we wanted to see what kind of incidence figures might give rise to the table above. Remember, incidence is absolute risk, while relative risk is the absolute risk in one group relative to the absolute risk in the reference group. The two tables below both contain incidence figures that would give rise to the RR table above, so you can see it is possible to have different incidence rates or risks which have the same relative risk.Risk or incidence per 1,000

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