How do I use many highly correlated continuous variables in a logistic regression?

Question

Low Blood Pressure (BP), below a threshold, say 90 mmHg, is associated with worse outcomes in surgery. The depth (how low the BP gets) and the time spent at that depth are both associated with worse outcomes. The association between BP and outcome is also non-linear. I have time spent at each BP value < 90 for each patient, however, they are highly correlated and they are more highly correlated with the numbers above it then below it. A patient with a BP = 60 usually also has BPs of 58, 59, 61, and 62. If I include all BPs in the model, I get odds ratios (OR) results like

• BP OR
• 60 1.2
• 59 1.4
• 58 0.6
• 57 1.5

Binning the BPs (e.g., 51-55, 56-60, ...) produces the same pattern - every several values there is one BP or one BP bin that is way out of whack from its neighbors. I don't want to combine the BPs into a summary statistic (e.g., time spent below 90 or area under the 90 curve). any help on how to analyze this would be greatly appreciated. Thank you.

Answer 1

There are various variable-interrelatedness measures and data reduction techniques discussed here. But I suggest you spend more time with the quantification of the phenomenon. The amount of time below a blood pressure of 90 is very useful, and the extent to which it is < 90 is also useful, but you may be able to capture more information by computing an integrated measure of BP in various zones, e.g. the area under the BP curve when it is below 90, treating BP > 90 as BP = 90.

Answer 2

It sounds like you have a curve as the predictor of the surgical outcome, that is, you have the pattern of blood pressure over time and want to use that to predict the surgical outcome.

This sounds like the exact case for which functional-data-analysis is intended.