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?


1 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.
  • $\begingroup$ However time is represented, a spline function of time could be used to represent eventual nonlinearity. $\endgroup$ Feb 20, 2018 at 20:14
  • $\begingroup$ @kjetilbhalvorsen yes that is an advantage of splines: they would predict similar trends whether sequence-order or date strata were used. A limitation is that the estimated trend is sensitive to the specification of splines, sparseness and poor behavior in the tails could be unflexible, and they do not summarize the first order trend (is there a general increase/decrease in the frequency of the outcome). $\endgroup$
    – AdamO
    Feb 20, 2018 at 20:52
  • $\begingroup$ @AdamO thank you for the informative response. Your assumption about ordering from 1-600 is true for my sequence order. I was planning on using a logistic regression (the outcome is a simple, was there a surgical complication or not) and then follow up with multivariate to control for a host of factors as you indicated. Would you suggest using the Cochran-Armitage test instead? I was planning on interpreting significance based on the p value of the logistic regression models. Again, thank you for your expert insight. $\endgroup$
    – Alsie
    Feb 21, 2018 at 19:02
  • $\begingroup$ @Alsie you can in fact call the model you are fitting a Cochran-Armitage Trend Test. It is asymptotically equivalent (gives basically the same answer in decently large samples) to a logistic regression. If you adjust for other things, it is a stratified CATT. $\endgroup$
    – AdamO
    Feb 21, 2018 at 19:06
  • $\begingroup$ @AdamO it appears that if I run the Cochran-Armitage trend test using my sequence order, each procedure is in its own bin and I have low cell counts (It looks like a chi square output) . Should I collapse procedures into 1 year bins, or similar? Or just stick with the logistic regression and call it Cochran-Armitage? $\endgroup$
    – Alsie
    Feb 21, 2018 at 19:09

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