Validating and extending the three process model of alertness in airline operations

Abstract

Sleepiness and fatigue are important risk factors in the transport sector and bio-mathematical sleepiness, sleep and fatigue modeling is increasingly becoming a valuable tool for assessing safety of work schedules and rosters in Fatigue Risk Management Systems (FRMS). The present study sought to validate the inner workings of one such model, Three Process Model (TPM), on aircrews and extend the model with functions to model jetlag and to directly assess the risk of any sleepiness level in any shift schedule or roster with and without knowledge of sleep timings. We collected sleep and sleepiness data from 136 aircrews in a real life situation by means of an application running on a handheld touch screen computer device (iPhone, iPod or iPad) and used the TPM to predict sleepiness with varying level of complexity of model equations and data. The results based on multilevel linear and non-linear mixed effects models showed that the TPM predictions correlated with observed ratings of sleepiness, but explorative analyses suggest that the default model can be improved and reduced to include only two-processes (S+C), with adjusted phases of the circadian process based on a single question of circadian type. We also extended the model with a function to model jetlag acclimatization and with estimates of individual differences including reference limits accounting for 50%, 75% and 90% of the population as well as functions for predicting the probability of any level of sleepiness for ecological assessment of absolute and relative risk of sleepiness in shift systems for safety applications.

Figure 1. Observed ratings of subjective sleepiness on the Karolinska Sleepiness Scale (KSS) plotted against time of day (at home base) with a LOWESS line indicating approximate means for home base time zone (left) and other time zones (middle) with the overall distribution of time zones for all ratings (right).

KSS ratings have had a random jitter applied to better illustrate the distribution at different levels.

Figure 2. Observed sleep probability across time of day for the home base time zone and westward time zone shifts (left) and eastward time zone shifts (right).

Figure 3. Residuals (observed ratings-predicted sleepiness) plotted against predicted KSS (left), time awake (middle) and time of day (right) for the best model with assumed default phase of C (model 5c, top) and circadian type adjusted phases of C_T (model 6d, bottom) with a LOWESS line indicating potential systematic bias in predictions.

Figure 4. Observed, predicted and generated sleep.

The top panel shows the proportion of observed 5 minute segments (n = 577969 for 118 subjects with sleep data) with observed duty, observed sleep, sleep generated by the TPM (with default thresholds) and predicted sleep based on the fixed part of a multilevel mixed effects logistic regression (equation 15) with observed sleep as the dependent variable and generated sleep as the predictor. The middle panel shows observed sleep for different circadian types. The bottom panel shows the output from three different sleep generators. The default sleep generator used a fixed phase of C (p = 16.8) for all subjects and threshold of S+C+U at 8.38 for falling asleep and 11.38 for waking up. Default sleep generator with adjusted phase use individually adjusted phases (p = 14.61 h, 15.28 h, 15.95 h, 16.62 h) depending on rated circadian type (morning type – extreme evening type). The new sleep generator use adjusted phases of C_T with a threshold for falling asleep of S+C<8 and waking up S+C>13.

Figure 5. Predicted probabilities as a function of alertness score (S_B+C+U) based on equation 17.

Left panel shows probabilities for specific outcomes (KSS = 6–9) and right panel shows probabilities for severe sleepiness (KSS≥7) with reference limits accounting for 75% and 90% of subjects (below the line) in addition to the average subject (i.e. 50% reference limit).

Figure 6. Empirical Bayes’ estimates of all subjects circadian phase based on equation 13.