Logistic regression with a dummy variable for time

Question

New to the site. I would like to evaluate whether rates of a binary outcome (yes/no) changed over the course of 10 years and 600 operations. I was thinking of doing a logistic regression and just ordering the procedures according to date, so the dummy variable would be 1-600. What would you all suggest as an alternative? or does this work?

Answer 1

Logistic regression does not account for any serial order between observations. I'm assuming in the trend-test you describe, you are actually adjusting for an ordinal time-index, 1 for the first observation, 600 for the 600-th observation. As a note, this is not a dummy variable. You can call it a sequence order. We have to assume further that the binomial probability model is appropriate for the outcome. When these hold, the logistic model you describe, as your intuition suggests, measures some type of trend, for which you can conduct a test of statistical significance. It is very related to the Cochran-Armitage trend test.

A couple limitations to note:

• It's unclear what you believe are the underlying determinants of the procedure chosen. The calendar time could instead be the contributor to the likelihood of procedural election; The time of the procedure, as a number of years since the start of the 10 year span, would be the right regressor in the logistic model. This accounts for a likely imbalance in timing of procedures, and the notion that two consecutive procedures happening merely days apart are more likely to be similar than two consecutive procedures months or years apart.
• It's important that the observations are indeed conditionally independent. Large volumes of patients contribute to provider fatigue, delayed operations, and adverse patient outcome (like not having the procedure at all, and presenting later with greater complications), adjusting for patient-level risk factors like insurance, severity, age, sex, etc. is important, you can also adjust for surgeon-level factors with random effects if there are multiple surgeons performing the procedure at your site(s).
• The odds ratio is difficult to interpret. An additive risk model (binomial probability model with identity link) summarized an actual difference in risk as a percentage point across time strata. Robust, sandwich, standard errors can account for non-linearities, small sources of dependence, and so on to provide valid inference under a variety of scenarios which invalidate the usual inference.