Statistical Analysis

Our dataset consisted of instantaneous values of several variables (ICP, CPP, Hb, FiO2) at time instances when measured values for both PbtO2 and PaO2 were available. Due to repeated simultaneous measurements of variables at different time points and for different subjects (longitudinal data), generalized estimating equations (an extension of generalized linear models) with a covariance matrix structured by an autoregressive model were employed (11). A p-value smaller than 0.05 was considered as statistically significant. All the analyses were conducted in Matlab R2017b (Mathworks, Natick, MA). Throughout this paper, the term “episode” refers to each simultaneous measurement of all variables. If PbtO2<Threshold for an episode, then that episode is referred as “an episode with compromised PbtO2” or “hypoxic.”

In our study, we conducted two analyses to further investigate the PbtO2 threshold: (A) We calculated the correlation of the percentage of hypoxic episodes (defined as Pbto2<Threshold) and the mortality outcome when Threshold value was changed from 7 to 40 mmHg. (B) We also obtained the odds ratio (OR) and its 95% confidence interval (CI) for mortality detection by applying generalized estimating equations when the compromised PbtO2 (dichotomized PbtO2<Threshold or PbtO2≥Threshold) were entered to the model as input, mortality outcome was considered as the response variable while adjusting for confounding factors such as ICP, CPP, age and gender by considering them as covariates (11).

Our goal was to determine whether PaO2/FiO2 can be used as a surrogate of PbtO2 and consequently as a predictor of hypoxia. For this purpose, PbtO2 was considered as the response variable. PaO2/FiO2 was entered into the model as continuous input variable while adjusting for confounding factors such as PaO2, CPP, and Hb by considering them as covariates in the model. To find an optimal threshold on PaO2/FiO2 value to indicate cerebral hypoxia, we plotted the mean and 95% CI of PaO2/FiO2 values over dichotomized group of episodes: those with compromised PbtO2 (PbtO2<Threshold), and those with normal PbtO2 values (PbtO2≥Threshold) when Threshold was changed over a range of 10–32 mmHg. We also calculated the probability of the two-sample t-test that the difference between average of compromised and normal PbtO2 episodes is significant.

We aimed to identify those variables (among PaO2, PbtO2, PbtO2/PaO2, PbtO2/FiO2, PaO2/FiO2) that were strong and independent predictors of mortality. For this purpose, we found the threshold value for each variable that can distinguish death from survival outcomes by calculating the percentage of episodes where the variable was smaller than the threshold value for each patient. The mean and 95% CI of these percentages were obtained and compared between patients who died and those who survived. Then the most predictive (optimal) threshold of mortality was identified as the threshold value where the difference between the death and survival plots are maximized in a statistically significant manner (when probability of t-test is smaller than 0.05). Each variable was then dichotomized using the obtained threshold value (variable< Threshold vs. variable ≥ Threshold) and entered into the model as input whereas the mortality outcome was considered as the response variable. The association of each dichotomized variable and mortality was also adjusted for confounding factors ICP, CPP, age, and gender.