In a previous note, I used Stata to simulate 2*2 tables of a one-off outcome. The simulation shows that odds ratios (ORs) are a much better estimate of the underlying causal effect or statistical association than relative rates are, given certain assumptions. One key assumption is that it is a one-off outcome, where it is reasonable to model the propensity for the event with a normal or logistic distribution. Where the outcome is the result of potentially repeated exposure to a risk (such as being ever married or ever infected with a particular pathogen) the resulting propensity is not likely to be normal. That is, if you are exposed to many opportunities to marry, saying yes once means you become ever-married for ever after, and even if the propensity to marry at a specific opportunity is normally distributed, the combined distribution of propensity to be ever-married after an unknown number of opportunities is likely not to be well-described as normal.

Continue reading Relative rates, odds ratios and the complementary log-log model