We acknowledge that the term “hypoxia” may not fully represent the exposures in these cardiac surgery patients and note that most patients are exposed to relatively high PaO2 levels during surgery. Thus, “relative hypoxia” may more accurately represent the exposures to those individuals with lower PaO2 levels; our analysis in quartiles emphasizes this relative comparison. We also agree that average PaO2 does represent a secondary exposure, with stroke as the outcome in both analyses.
Regarding the concern about temporal proximity between PaO2 level and stroke, stroke events were identified prospectively and entered into a database. All included strokes took place within 10 days after surgery, with the majority occurring (or being identified) within the first 5 days; we also excluded individuals experiencing strokes within the first 24 hours to ensure, as much as possible, that the exposure occurred before the stroke.
Drs Charchaflieh and Zafar also suggest that a linear association is inappropriate to describe the relationship between PaO2 and stroke, given the nonlinear relationship between PaO2 and arterial hemoglobin saturation (and thus cerebral oxygen delivery). We thank them for pointing out this important fact. As described in the Methods, but not included in the final article due to space limitations, we did evaluate several other nonlinear relationships but did not find (1) that the model fit was any better using these other modeling approaches or (2) that the results changed substantively when analyzed with these approaches. Thus, we present results modeling PaO2 in a linear manner. It is quite possible that the estimates we describe only apply to a relatively narrow range of PaO2 values (those observed in this study) and may not reflect nonlinear relationships that occur at different PaO2 levels.
Finally, the issue of unmeasured confounding is brought up in the letter. Although it is impossible to completely eliminate potential confounding in an observational study of this nature and particularly in a case–control study, we attempted to address it with a primary analysis adjusting for a number of known and potential confounders, in addition to a generalized propensity score in a sensitivity analysis. These results are available in an online-only supplement.
We believe that observational data demonstrating a possible association are an important part of research3 despite the limitations described in the letter, in this response, and in the article itself. Observational studies can be used to test preliminary hypotheses before applying them to either a larger cohort or ultimately a clinical trial. As stated in our article, we feel that our results, demonstrating an association in our cohort between PaO2 and stroke after cardiac surgery, should be replicated in an independent cohort and that further studies are needed before clinical management is modified on the basis of these findings.