Supplemental methods (1) and supplemental Table 1
Variable Definitions
This core set of intraoperative predictors was used to derive additional predictors. Multiple exponential moving average (EMA) and exponential moving variance (EMV) series were calculated for each continuous vital sign and volatile anesthetic end-tidal concentration. A 5- minute half-life and a 15-minute half-life was used for the EMA/EMV weights. The EMA is calculated from a time series for times t = 1, 2, 3, … by initializing and computing subsequent values recursively as:
( )
where . At a given time t, all values are given a non-zero weight in the average, but the weight decreases the older the value is. Except for the first value, , the data points are given weight ( ) for . EMV is also calculated recursively, after initializing , as:
( ) ( ) ( )
The weighting parameter was calculated as ⁄ , which leads to the value half-life minutes in the past (5 or 15 minutes for this study) having half the weight as the most
recent value in the average. The EMA series indicated the typical level of the vital sign over a shorter (5-minute) or longer (15-minute) period of time, which smoothed out the minute-to- minute readings. The EMV series indicate the volatility of the vital sign over the two time frames.
The EMA/EMV weights decay so that more recent values have more weight in the averages than more remote values. Fluid volumes, medication types, and medication doses administered at each minute were calculated. Table 2 lists the fluid and medication types that were included.
Bolus medications and continuous infusions were combined at this step. A bolus dose was
considered to have been administered entirely within a single minute while the infusion rate was used to calculate the dose administered within a minute. These per-minute doses were then filtered to provide cumulative values with exponential decay. Two decay rates were used: a 5- minute half-life to provide a short-term memory of fluids and medications administered and a 60- minute half-life to provide a long-term memory. Specifically, the series of doses administered during each minute, , was transformed to a cumulative dose with decay, , by convolving with an exponentially decaying impulse response function ,
∑
⁄
This approach to deriving additional predictors based on vital signs and medications
accumulated over different time scales is similar to an approach used to predict intraoperative hypoxemia24.
Data Cleaning and Handling of Missing data
Prior to analysis, the intraoperative time series of vital signs and volatile anesthetics was screened for invalid or artifactual values. Any such values identified were excluded and treated as missing data, as described below. Artifacts were detected in multiples ways. First individual values were compared to specified upper and lower limits. Second, rates of change were compared to specified limits. Lastly, for the blood pressure series specifically, MAP, SBP, and DBP were compared to confirm whether SBP exceeded MAP and MAP exceeded DBP, each by at least 5 mmHg. If any condition was not met, all three blood pressure values were treated as artifactual. The limits used to detect artifacts are shown below in supplementary Table 1below.
Supplementary Table 1
Ranges of valid values for intraoperative vital signs used to detect artifacts Limits
Vital sign Lower Upper Max Rate of Change
MAP 30 mmHg 180 mmHg 20 mmHg•minute-1
SBP 50 mmHg 220 mmHg 20 mmHg•minute-1
DBP 10 mmHg 150 mmHg 20 mmHg•minute-1
End-tidal CO2 10% 70% 10%•minute-1
Heart rate 10 bpm* 150 bpm* 20 bpm*•minute-1
FiO2 1% 100% -
SaO2 50% 100% 15%•minute-1
Respiratory rate 3 bpm** 30 bpm** 5 bpm**•minute-1 Peak end-expiratory pressure 0 cmH2O 15 cmH2O -
Peak inspiratory pressure 0 cmH2O 50 cmH2O -
Tidal volume 0 mL 1500 mL -
End-tidal sevoflurane 0% 6% 1%•minute-1
End-tidal isoflurane 0% 4% 1%•minute-1
Temperature 33⁰C 42⁰C 3⁰C•minute-1
*beats per minute; **breaths per minute
The intraoperative MAP time series had occasional missing values. To maximize the outcome data available, linear interpolation was used to impute MAP values for the purposes of outcome determination only. Imputation was performed only if the sequence being imputed was <10 minutes long. Remaining minutes missing MAP were excluded. For the purpose of determining episodes of hypotension (≥5 consecutive minutes of MAP < 60 mmHg as described earlier), missing values of MAP were treated as breaks in the sequence. Therefore, no MAP values within designated hypotensive episodes were missing by definition. These imputations only applied to the MAP series used to define the outcome of hypotension. The original MAP series used as a predictor was imputed again in another way, described below, consistent with all other predictors. Note, the outcome being predicted is hypotension 5 minutes in the future, so the same values are not being used as predictor and outcome at the same time.
Missing data among the intraoperative vital sign and volatile anesthetic series used as
predictors, including MAP, was handled in multiple ways. The first step was to replace missing
values with the most recently observed value (last observation carried forward). Interpolation was not used for predictors because future values of the series would be required which would not be available in real time. The resulting time series was supplemented by two parallel time series: one which counted the number of minutes since the most recently observed value (non- imputed) and an indicator of whether the vital sign measurements had started. The latter series was to handle cases where the vital sign was not being sampled immediately at the beginning of the procedure, in which case there was not a value to carry forward. These two additional series per vital sign were included as predictors to the machine learning algorithms as they provide information related to the reliability of the current vital sign value at each moment in time.
