Appendix 2 – Statistical Methods
We summarized the profile of log(τE) over volume segment with a polynomial function that
included a linear and a squared term. To assess the effect of injury and respiratory gas
composition on both τE,TOT and τE,RS, linear mixed-effects regression models were used to assess
group differences in the average profile and variability of the change of log(τE) over volume
segment. All equations were fitted using restricted maximum likelihood methods and with the
assumption of normality for the error term, and log transformation was used to reduce.
Experimental condition (type of gas), volume segment (1 to 5, treated as continuous) and volume
segment squared were included as fixed effects and group-specific intercepts and slopes were
employed. Random effects included condition-specific intercepts and slopes for volume segment.
A random effect of volume segment squared was not needed. The model used can be specified
as:
𝑙𝑜𝑔 ( 𝑡𝑎𝑢𝑗𝑘(𝑖) ) = 𝛽0𝑖 + 𝛽1𝑖 𝑉𝑆𝑗 + 𝛽2𝑖 𝑉𝑆𝑗2 + 𝑏0𝑘(𝑖) + 𝑏1𝑘(𝑖) 𝑉𝑆𝑗 + 𝜀𝑗𝑘(𝑖)
where log(𝑡𝑎𝑢𝑗𝑘(𝑖) ) represents the natural log of tau for the kth pig in the ith group at volume
segment j. . The model is presented graphically in Supplementary Figure A for He pre injury.
There is an average curve (thick grey line) for the group of animals, which is represented by the
fixed effects:
𝑙𝑜𝑔 ( 𝑡𝑎𝑢𝑗𝑘(𝑖) ) = 𝛽0𝑖 + 𝛽1𝑖 𝑉𝑆𝑗 + 𝛽2𝑖 𝑉𝑆𝑗2
about which the individual animals are allowed to vary (thin grey lines). For example, the curve
for the first pig would be:
𝑙𝑜𝑔 ( 𝑡𝑎𝑢𝑗1(𝑖) ) = (𝛽0𝑖 + 𝑏01(𝑖) ) + (𝛽1𝑖 + 𝑏11(𝑖) )𝑉𝑆𝑗 + 𝛽2𝑖 𝑉𝑆𝑗2 + 𝜀𝑗1(𝑖)
The animal-specific regression parameters (i.e. the random effects) b0k and b1k reflect the natural
heterogeneity in the animals.
Supplementary Figure A – Demonstrating the relationship between individual animals (thin
grey lines) and the group (think grey line) in the model.
Comparison of the fixed effects between groups was achieved by comparing the average curves.
Comparison of the random effects was achieved by comparing the variability estimates. For
example, comparing the intercepts β0.HE and β0.N2, compared the average starting level of the two
groups He and N2. Comparing the coefficient “sets” (β1.HE, β2.HE) and (β1.N2, β2.N2) compares the
evolution over volume segment of the groups (i.e., the combined linear and quadratic trends
Differences in the average response profiles of the three groups can be assessed by pair-wise
comparisons of 𝛽0𝐻 , 𝛽0𝑁 , 𝛽0𝑠 and (𝛽1𝐻 , 𝛽2𝐻 ), (𝛽1𝑁 , 𝛽2𝑁 ), (𝛽1𝑠 , 𝛽2𝑠 ); the latter assessing the rate
of change in log(tau). Differences in the variability of the response about their respective average
curves can be assessed from the random effects.
The profile of log(τE) over volume segment was summarized with a polynomial function that
included a linear and a squared term. We used the logarithmic transformation to reduce the
heteroscedasticity (increasing variance with increasing mean). Comparing the average profiles
between gases or between injury states allows for a more parsimonious comparison than
comparing groups at each volume segment value.