Catherine Gabaude

Bruno Baracat

Christophe Jallais

Marion Bonniaud

Alexandra Fort

Cognitive load measurement while driving

Driving is a complex activity requiring good management of attentional resources, efficient cognitive control and decision-making. Numerous studies have sought to understand dual task interference, and in particular whether drivers have enough spare capacity to take on an additional task or whether the mental effort that demands results in driving task alteration. This study aims to analyse the relationship between mental effort and driving performance and to identify mental effort indicators from three different measurements recorded on a car simulator: cardiac activity, driving performance, and subjective data (DALI, Driving Activity Load Index). Three conditions have been designed to vary the driver's mental effort: driving as the sole task (control situation), driving while solving two different cognitive tasks, resolution of verbal or visuo-spatial enigmas. Preliminary results show that although heart rate variability does not seem sensitive enough to reflect the mental effort in car simulator studies the HF/LF ratio could be used as an indicator of the participant's investment in the task. In addition, the DALI seems useful for identifying the mental effort variation between the verbal and the visuospatial added tasks. Finally, the detection of mental effort from lane position variability seems encouraging.

Introduction

Driving is a complex activity carried out under time constraints and requiring dynamic adjustment of cognitive control to the driving context. Given that human behavior is active and adaptive, drivers seek to keep an acceptable level of performance at a comfortable level of effort (or energetical state) and achieve such an adaptation by means of a cognitive compromise to maintain an acceptable task load level [START_REF] Hoc | Cognitive control dynamics for reaching satisficing performance in complex dynamic situations[END_REF]. As they drive, the task demand fluctuates according to the situations they encounter (e.g. monotonous driving vs. merging into a flow of traffic). Basically, the task load level is low when processes are automatic and high when processes are controlled and/or when several controlled tasks interfere. As pointed out by De [START_REF] De Rivecourt | Cardiovascular and eye activity measures as indices for momentary changes in mental effort during simulated flight[END_REF], the mental workload concept is often used to indicate to what extent task demand affects a driver's information processing capacity. It is important to avoid confusing three notionsmental or cognitive resources, cognitive capacity and cognitive workload. According to [START_REF] Barrouillet | Ressources, capacités cognitives et mémoire de travail : postulats, métaphores et modèles[END_REF], cognitive resources correspond to the maximum energy available, cognitive capacities to the maximum resources available at a given time and cognitive workload to the resources required. Unlike the other two notions, cognitive workload is not an individual property, depending instead on the characteristics of the task to be performed. The consequence of this for the driver is that his/her mental effort varies according to the difference between the information processing system resources available and required for performing a given task.

Both overload and underload can have an impact on drivers' performance. When the resources required exceed those available, human error can occur, but performance may also go down when the resources available exceed those required (e.g. even in complex situations drivers can act in an unconscious mode of activity, investing minimal resources in the present, by virtue of past and future actions, or, more frequently, in private objects that have nothing to do with the driving activity, see Hoc & Amalberti 2007 for a review). To guarantee optimum performance, the resources required should match the resources available to the driver. For example, it was demonstrated recently that mind wandering while driving may jeopardize the driver's ability to take account of information from the environment, thereby threatening road safety (Galéra et al, 2012). Intense mind wandering was associated in the study with being responsible for a crash: 17% [responsible] vs. 9% [not responsible], adjusted OR [95% CI]=2. 12 [1.37-3.28]. As well as on-board safety monitoring systems dedicated to avoiding driver distraction caused by multi-tasking at the wheel, research to develop systems that can detect periods of driving vulnerability as a result of inattention due to mind-wandering or mental effort should be supported owing to the potential it offers for further improving safety.

Experimental research can be really helpful in this context. Different types of data (subjective, driving performance, and physiological data) can be collected to evaluate drivers' mental effort. The difficulty with subjective measures is that it is hard to distinguish the task demands from the invested effort, and so the use of complementary physiological measures is a good alternative. Several physiological measures (like heart rate and heart rate variability in two frequency bands) have been shown to be sensitive to mental effort [START_REF] Boutcher | Cardiovascular response to Stroop: Effect of verbal response and task difficulty[END_REF][START_REF] Causse | Emotion and uncertainty favor risky decision-making in pilots: evidence from cardiovascular and oculometric measurements[END_REF][START_REF] Jorna | Spectral analysis of heart rate and psychological state: a review of its validity as a workload index[END_REF][START_REF] Wilson | Physiological measures of workload in multi-task environments[END_REF]. Low frequency bands (LF) are most consistently related to mental effort [START_REF] Mulder | Attention, effort and sinus arrhythmia: how far are we?[END_REF], but high frequency bands (HF) have also proved to be sensitive to mental effort [START_REF] Wilson | Air-to-Ground Training Missions -a Psychophysiological Workload Analysis[END_REF]. In general, Heart Rate (HR) increases and overall Heart Rate Variability (HRV) decreases when mental effort increases. This could be the result of orthosympathetic dominance over parasympathetic [START_REF] Backs | Going beyond heart rate: autonomic space and cardiovascular assessment of mental workload[END_REF][START_REF] Bernston | Cardiovascular psychophysiology[END_REF]Task Force, 1996). Even though spectral measures appear to be sensitive to task-rest differences but less so to difficulty levels within the same type of task, the use of physiological measures is promising for capturing mental workload and especially for simulator driving studies [START_REF] Brookhuis | Monitoring drivers' mental workload in driving simulators using physiological measures[END_REF]. For laboratory studies involving short tasks (between 30 s to 300 s) requiring demanding mental operations in working memory, the general cardiac response pattern in mental effort studies is similar. With these variables, it now seems possible to explore some important questions with the help of spectral analysis of heart rate measures collected while driving a simulator. Is it possible to measure mental effort variation while driving? What are the methodological problems to be solved? Does the measure of mental effort vary according to the type of cognitive tasks performed by drivers? What are the best indicators of cognitive load variation?

Using empirical research, this study seeks to understand how drivers manage their mental effort while driving a simulator. Drivers' mental effort measurement is investigated by manipulating road type and the performance of two extra tasks (using a dual-task paradigm, i.e. where drivers have to solve verbal and visuo-spatial enigmas). Mental effort in this case is used as an indirect measure of operator capacity. As pointed out by [START_REF] Veltman | A comparative study of psycho physiological reactions during simulator and real flight[END_REF], it is possible that participants' motivation when performing the added task differs, with some participants willing to make an effort when performing the task and others not). To gain a better understanding of how drivers regulate their mental effort, an in-depth activity analysis will be conducted for each driving scenario.

It is expected that an increase in mental effort as a result of participants performing an additional task will be reflected by both subjective and objective measures. HRV is an objective index of mental effort that should be sensitive even if used during driving. A lower HRV is expected when mental effort is higher. In addition, the cognitive load should be higher for the visuo-spatial task because similar visuospatial abilities are required so it shares the same cognitive resources as driving. In our experiment, indicators of drivers' mental effort will also be investigated with a specific driving index (lane position).

Materials and method

Participants

Twenty-one individuals were included in this experiment. All of them had their driving licence for at least 5 years, had normal or corrected-to-normal vision and were naive to the purpose of the experiment. They were recruited via a newspaper advertisement. Participants were asked to avoid energy drinks for 3 days prior to the experiment (and drink less than 2 coffees per day); smokers of more than 5 cigarettes a day were excluded. The CPP Sud-Est Lyon II Ethics Committee approved the experiment, and all procedures were carried out in accordance with the relevant laws and ethical guidelines. All participants were required to read and sign an informed consent form. In return for taking part in the experiment, participants received 45 euros. 4 participants yielded data that could not be used (due to bad cardiac signal, failure of sensors or experimental errors). The mean age of the remaining 17 participants (12 men, 5 women) was 33 years (± 3,5).

Material

The study was carried out in an instrumented full-cab fixed-base simulator developed at IFSTTAR. The simulator is also equipped with virtual reality-based visual and audio systems, a computer program for vehicle motion simulation, and a host computer system for simulating the driving environment. Driving performance data were captured at 60 Hz from the original equipment manufacturer brake, accelerator and steering wheel. A front projection screen provided an approximate 180° horizontal and 40° vertical view of the virtual environment. Force feedback was provided through the steering wheel, and auditory feedback was delivered in the form of engine noise. Audio tasks and instructions were also communicated via the vehicle sound system. A microphone located inside the cab recorded participants' responses to the additional tasks.

Cardiac activity was recorded on lead II according to Einthoven's triangle, with three disposable electrodes (Ag-Cl). This signal was sent to a MP150 unit via a Bionomadix wireless device. AcqKnowledge 4.1 (running on a PC computer) was used for 1000 Hz acquisition with a 0.05 -35 Hz band pass filter.

Procedure

After a training session with the driving simulator, participants had to respect the Highway Code. They drove on both motorways and secondary roads (with the same driving tasks in each scenario: direction following, speed regulation, overtaking). The experimental plan required them to drive with and without two types of additional cognitive task (verbal or visuo-spatial). Heart rate data were recorded during each experimental session.

-In the verbal task condition (VT), three words were communicated, and the driver had to find a 4th word associated with the other three (e.g.: "Sugar"; "Bees"; "Moon" plus "Honey" as a possible 4 th word). After 30 s, if a participant did not find a solution, the three words were repeated once. After a further 30 s, a new enigma was communicated.

-In the visuo-spatial task condition (VST), before driving participants had to learn a 3x3 object grid containing nine different objects. Then, while driving, they were told to listen to a displacement instruction (up, down, left or right) and given 30 s to find and remember the name of the object in the target case. Every four instructions, they had to name the object aloud.

These tasks require only the utterance of a single word, interfering moderately with the HRV indices. The two additional cognitive tasks both required participants to remain focused on the enigmas throughout the driving scenarios. Each driving scenario lasted 7 to 10 minutes. All the conditions were counterbalanced between participants. After each driving scenario, participants used the Driving Activity Load Index (DALI) to assess their (subjective) mental effort.

Measures and analysis

Cardiac data

Before analysis, the cardiac signal was cleaned with digital filtering and/or template correlation and/or manual corrections until a clean tachogram was obtained. HRV was then calculated from a 5-minute recording in the LF (0.04 to 0.15 Hz) and HF (0.15 to 0.40 Hz) bands via FFT transformation and Power spectral density computation (expressed in sec 2 .Hz -1 ). LF and HF HRV as well as the LF/HF ratio in HRV were retained. All these computations were performed with AcqKnowledge 4.1. Five variables were used to describe cardiac activity: mean heart rate (HR), total heart rate variability (HRV), LF HRV, HF HRV and the LF/HF ratio in HRV.

Subjective data

Participants filled out the Driving Activity Load Index (DALI), a revised version of the NASA-TLX questionnaire adapted to the driving task [START_REF] Pauzié | A method to assess the driver mental workload: the driving activity load index (DALI)[END_REF]. It assesses various dimensions including effort of attention, temporal demand, situational stress, and interference. Participants have to answer each question using a 6 point scale (0 = low, 5 = high). The total score is the sum of the four dimensions.

Driving data

In the search for a real-time indicator of drivers' low attentional status, we also analysed driving performance by studying lateral control during nominal driving. Lane position (the distance between the middle of the road and the vehicle's center of gravity) was analyzed with wavelet transforms. We extracted the wavelet coefficients at 10 Hz (best frequency defined after data visualisation). An individual baseline was set at the 70th percentile of the wavelet coefficients (arbitrary expertise-based value). Lane position variability was defined as the wavelet percentage below the baseline.

Regulation strategies

To gain a better understanding of how each driver coped with the mental effort, we analysed video data to obtain an in-depth activity analysis for each driving scenario. It was decided to assign penalty points whenever a driver was not able to perform the driving task or cognitive task in a manner deemed efficient. A penalty point was assigned every time a participant asked the experimenter for help, with the same procedure used for both driving errors and secondary task errors. An extra penalty point was given whenever the experimenter observed any signs of stress (breathing, mimics, scratching). It was thereby possible to define a workload regulation score: a low value indicated that the driver used the best regulation strategy (i.e. driving performance remained at a high level), and a high value indicated a worsening of driving performance in the two secondary task conditions. The penalty scores are shown in Figure 1 (min = 0 to max = 16.5). With a score of 0 to 8 points the workload regulation strategy was considered focused (9 participants were in the focused group; they were motivated by the driving task). With a score of 9 to 16.5 it was considered distracted (8 participants were in the distracted group; it was also noticed that they were often stressed by the experimental settings).

Statistical analysis

Cardiac and subjective data were tested with a univariate repeated measures analysis of variance. Two independent variables were used: road type (motorway vs secondary road) and task type (driving alone, driving while solving verbal enigmas, driving while solving visuo-spatial enigmas). Standard post-hoc tests were used to compare all driving conditions. In addition, as two mental load regulation strategies were identified (more focused on the driving task vs distracted by the additional task), a between-subject factor was added (group type). To analyse the effects of participants' workload regulation strategies on the cardiac data, an exploratory analysis was conducted including type of road and type of task as within-subject variable and group type as betweensubject variable. This group analysis was performed on the HF power and LF/HF power ratio in order to test for differences in subjects' investment in the tasks. Finally, correlation coefficients were calculated between workload regulation scores and lane position variability.

Results

Subjective data for the mental effort measurement

For technical reasons, five participants failed to fill in the DALI questionnaire properly and were excluded from the analyses. No main effect of road type was found, but a main effect was observed for the driving task condition (F(2,22)=5.24, p=0.029, η²=0.32). The subjective mental efforts as measured with the DALI differ, with post-hoc comparisons indicating that scores were lower in the control condition than in the other two conditions (verbal task and visuo-spatial task) (Figure 2). No significant interaction was observed between road type and driving task condition. The total score for the Driving Activity Load Index incorporating four dimensions (effort of attention, temporal demand, situational stress and interference) would appear to be sensitive to our experimental manipulation. Objective data for the mental effort measurement A unique significant effect was observed with the ANOVAS conducted on the five cardiac variables (HR, HRV, LF HRV, HF HRV, LF:HF ratio in HRV). A main effect was observed for the driving task condition for the HRV (F(2,32)=3.99, p=0.033, η²=0.20). As illustrated in Figure 3 and confirmed by post-hoc analysis, HRV is higher in the verbal task condition than in the two other conditions (control and visuo-spatial). No significant interaction was observed between road type and driving task conditions. The traditional correlation between HR and HRV is observed for the VST condition (r=-0.702, p=0.002), with HR increasing as HRV decreases.

Exploratory analysis according to the workload regulation strategies

These preliminary results must be interpreted with caution because of the small number of participants in each group. Many more participants will be included in the coming months to improve the statistical power of the results.

To understand the workload regulation strategies of the two participant groups, the LF/HF ratios in HRV (Figures 4 and6) were analyzed in parallel to the HF HRV values (Figures 5 and7). Based on these preliminary results, a significant interaction effect is expected between road type and group type for the LH/HF ratio and the HF HRV values (F(1,15)=3.78, p=0.07, η²=0.20 and F(1,15)=4.26, p=0.06, η²=0.22 respectively) as more participants will be included. As the HF HRV values for the distracted group did not change according to road type (Figure 5), it would seem participants still invest in completing the secondary task, even on secondary roads in the case of greater driving task complexity (the cognitive load in this situation also increases slightly as the LF/HF ratio increases, cf. Figure 4. For the focused group the HF HRV value is higher on secondary roads. Participants seem to invest less in the additional tasks on secondary roads; it would appear that they retire from the secondary task more easily.

As shown in Figures 6 &7, presented by task type, the two groups adopt different workload regulation strategies, especially for the verbal task. An interaction effect between task type and group type reaches significance for the LF/HF ratio and marginal significance for HF variability (respectively, F(2,30)=3.43, p=0.05, η²=0.19 and F(2,30)=3.02, p=0.07, η²=0.17). The only significant effect at this stage is a shift in the LF/HF ratio for the focused group in the VT task (see Fig 6)

Correlations between lateral control and workload regulation scores

To explore the influence of an extra task on driving performance, we studied lateral control during nominal driving by analysing lane position in the driving simulator.

With reference to an individual baseline performance, we observed that, for both additional tasks, the workload regulation score was correlated with lane position variability at 10 Hz (VST: r = 0.66, p = 0.005; VT: r = 0.75, p = 0.001): the higher the penalty score, the higher the lane position variability. When a mental effort is made, lane position at this specific frequency seems amplified.

Discussion

Through an experimental approach using a dual-task paradigm, subjective, cardiovascular, task performance and driving indices were measured in a driving simulator in order to analyse the relationship between mental effort and driving performance and in an attempt to identify mental effort indicators. The subjective and objective data results indicate that the drivers made an extra mental effort to solve a number of enigmas. Consequently, at the subjective level, the mental effort measured in the DALI is higher for the two additional tasks than for the control situation.

Regarding the cardiac data, the results were less clear-cut. As overall HRV was lower for the control and VST conditions, the mental effort measured with the cardiac data seemed higher for these two conditions. What is surprising is that HRV was also low for this control situation, whereas it was supposed to be the lowest in mental workload. It seems that even when the participants were driving without an additional cognitive task the mental effort invested by them was higher when they were only driving the simulator than when they were driving while solving the verbal enigmas. Further analysis will be conducted in an attempt to explain the low HRV obtained in the control condition. Contrary to our expectations, cardiac activity as measured through the overall HRV index is not the right one for discriminating the control condition (only driving) from the other two conditions (driving while performing an additional cognitive task).

For the Verbal condition, it was expected that HRV would be lower than for the control task, but, surprisingly, it was higher. This result can be discussed in terms of the mental effort invested in carrying out the extra task. It is assumed that an increase in task demands is linked to an increase in mental effort [START_REF] Cnossen | Adaptive strategy changes as a function of task demands: a study of car drivers[END_REF][START_REF] Vicente | Spectral analysis of sinus arrhythmia: a measure of mental effort[END_REF]. Accordingly, we hypothesized that a more demanding task would require greater mental effort in order for it to be adequately completed. We noticed, however, that the complexity of the verbal task was not constant throughout the period studied, insofar as the difficulty to find a solution varied depending the different three-word sets. For some sets, the solution was sometimes obvious (found fairly automatically without any mental effort required). For the more difficult enigmas, it is possible some of the participants failed to spend the entire minute with their attention focused on finding the solution, withdrawing instead from solving the task. Because of their successive failures, the motivation for these participants to complete this task may also have been lower and their mental effort not constant [START_REF] Veltman | A comparative study of psycho physiological reactions during simulator and real flight[END_REF]. Further experiments are currently being conducted on this specific issue [START_REF] Baracat | Assessment of cognitive load induced by a dual task using cardiac and GSR measures[END_REF] in order to test this hypothesis.

For the Visuo-Spatial condition, the traditional correlation was observed between HR and HRV (e.g. [START_REF] Mulder | Measurement and analysis methods of heart rate and respiration for use in applied environments[END_REF][START_REF] Jorna | Spectral analysis of heart rate and psychological state: a review of its validity as a workload index[END_REF], in other words HR increases as HRV goes down. In this particular condition, the mental effort seemed greater than in the verbal condition. This result can be interpreted as strong investment on the part of the participants for the whole 5-minute period. The difference observed between the two additional tasks is also consistent with our hypothesis that the visuo-spatial task should be more disruptive than the verbal one as it shares some visuo-spatial characteristics in common with the driving activity.

The general cardiac response pattern in mental effort studies is characterized by an increase in heart rate and a decrease in heart rate variability (HRV) when mental effort increases, and vice versa. The same pattern of results is also found in field studies and simulator studies [START_REF] Brookhuis | Monitoring drivers' mental workload in driving simulators using physiological measures[END_REF][START_REF] Jorna | Heart rate and workload variations in actual and simulated flight[END_REF][START_REF] Mulder | Measurement and analysis methods of heart rate and respiration for use in applied environments[END_REF], such that cardiac activity and especially HRV has long been used to gauge mental effort (i.e. [START_REF] Boutcher | Cardiovascular response to Stroop: Effect of verbal response and task difficulty[END_REF][START_REF] Causse | Emotion and uncertainty favor risky decision-making in pilots: evidence from cardiovascular and oculometric measurements[END_REF][START_REF] Jorna | Spectral analysis of heart rate and psychological state: a review of its validity as a workload index[END_REF][START_REF] Wilson | Physiological measures of workload in multi-task environments[END_REF]. However, this pattern of variations could be obtained in different ways at the autonomic level. Generally a rehearsal in sympathetic activity is observed, coupled with a reduction in parasympathetic activity. Nevertheless, this is not systematically the case, and the same kind of variations in HR and HRV could be obtained with a different mode of autonomic regulation (Berntson et al., 1991;Berntson et al., 1993). An interesting issue here is the evaluation of a subject's investment in the tasks as attested by a shift in orthosympathetic activity, independently of parasympathetic variations. The LF/HF ratio can be analysed in this context, but, unfortunately, at the autonomic level there is only one unambiguous measure namely the power in the HF band which is related solely to the parasympathetic activity. For its part, the power in the LF band is a mixture of parasympathetic and orthosympathetic influences. Consequently, an orthosympathetic shift can be asserted only when the LF/HF ratio changes without any change in HF. Thanks to the workload regulation strategies approach, the group comparison to be conducted in future with more participants in each group could provide a possible explanation regarding dual task management or investment in carrying out additional tasks.

It is possible that this study has a methodological limitation relating to the width of one frequency band chosen. As recommended by the Task Force (1996), HRV was calculated in the 0.04 to 0.15 Hz Low Frequency band. As mentioned in De Rivecourt et al. ( 2008), the HRV in the 0.02 to 0.06 Hz band is mostly to do with the regulation of body temperature and gradual change in task characteristics. As changes in temperature regulation functions often arise with simulator sickness [START_REF] Casali | Manifestation of visual/vestibular disruption in simulators: Severity and empirical measurement of symptomatology[END_REF], this may have had an influence on the mental effort measurement conducted in this experiment. We shall be studying the HRV in the two different bands (0.04 to 0.07 Hz and 0.07 to 0.14 Hz) to clarify this issue.

A major restriction to the use of ECG-based measures is the effect speech has on blood pressure, and therefore on the 0.10 Hz component of heart rate variability [START_REF] Mulder | Assessment of cardiovascular reactivity by means of spectral analysis[END_REF][START_REF] Sirevaag | Assessment of pilot performance and mental workload in rotary wing aircraft[END_REF]. In our experiment, verbalization was not a predominant aspect of operator performance. The answers to the enigmas were really short and infrequent (about one word per minute). As [START_REF] Porges | Research methods for measurement of heart rate and respiration[END_REF] recommend no corrective action in cases where the verbalization duration is short (less than 10 s) or if speech is relatively infrequent (one to five times per minute), we thought we could use ECG-based measures to evaluate drivers' mental effort with these two cognitive tasks.

Other methodological approaches regarding mental effort assessment could be envisaged. For example, the development of short-erm analysis techniques seems promising. First, the possibility to analyse Evoked Cardiac Response (ECR) associated or not with galvanic skin response (GSR) is being examined [START_REF] Baracat | Assessment of cognitive load induced by a dual task using cardiac and GSR measures[END_REF]. Another study also indicated that a short-segment averaging approach is well suited for obtaining spectral power estimates of short data segments even with varying length [START_REF] De Rivecourt | Cardiovascular and eye activity measures as indices for momentary changes in mental effort during simulated flight[END_REF]. Finally, realtime detection of workload changes with heart rate variability using sub-Gaussian fitting could be used [START_REF] Hoover | Real-time detection of workload changes using heart rate variability[END_REF].

Moreover, to take this type of studies furthers, an in-depth analysis of driving behaviour is also necessary. In a road safety perspective, it is important to increase our knowledge about attentional failures during driving. With this kind of experimental procedure associated with a driving activity analysis, a classification of attentional failures could be considered and could allow us to gain a better understanding of how driving performance is impaired (for example, distraction errors leading to a failure of routines could be dissociated from failures in motor control or interruption errors and discrimination errors).

This study aimed to explore the influence of cognitive task completion on driving activity taking into account the cardiac signal. In the near future, the complementarity between this technique and electrophysiological techniques already used in driving simulator studies [START_REF] Bueno | An electrophysiological study of the impact of a forward collision warning system in a simulator driving task[END_REF][START_REF] Fort | Attentional demand and processing of relevant visual information during simulated driving: A MEG study[END_REF][START_REF] Fort | Impact of totally and partially predictive alert in distracted and undistracted subjects: an event related potential study[END_REF] will be investigated. Better understanding of drivers' cognitive workload regulation should be sought in order to identify avenues worth exploring regarding awareness campaigns and the design of driving assistance. To that end, driver monitoring with the help of computational techniques have the capability to determine optimal sensor fusion and automated data analysis for the recognition of mental effort and stress manifestation. In this regard, the result regarding lateral control of the vehicle, identifying a possible indicator of the impairment of driving performance when the driving activity is monotonous (nominal driving) is encouraging.

The experimental approach developed in this study with physiological, behavioural and subjective data, combined with the methodological development suggested is a promising approach towards better identification of driving performance degradation, a necessary step to improving road safety.

Figure 1 :

 1 Figure 1: Workload regulation scores for all participants

Figure 2 :

 2 Figure 2: Total DALI scores for the three driving conditions

Figure 3 :

 3 Figure 3: Total heart rate variability for the three driving conditions

Acknowledgements

The research was supported by an ANR (French National Research Agency) grant (ANR-09-VTT-04).


Florent CHATELAIN Thanh Trung Le

Christophe Berenguer

Hidden Markov Models for diagnostics and prognostics of systems under multiple deterioration modes

Multi-state systems have recently attracted a great deal of interest with regards to reliability and maintenance. Since most mechanical equipment operates under some sorts of stress or load, it tends to degrade over time, thus possibly resulting in discrete degradation states (damage degrees), ranging from perfect functioning to complete failure. Over recent years, Hidden Markov Models (HMMs) have been applied to model these discrete degradation states for diagnostic and prognostic purposes. However, most of the reported researches on HMMs for multi-state equipment in the literature consider only one degradation mechanism of degradation processes. The present paper proposes a novel model called multi-branch HMM (MB-HMM) to deal with deterioration processes modeling under multiple competing modes. To illustrate the proposed approach, a numerical study is given.

INTRODUCTION

Condition-based Maintenance (CBM) plays nowadays an important role in the maintenance of engineering systems since it has the ability to recommend in advance proper maintenance actions by basing on the information collected from condition monitoring [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing conditionbased maintenance[END_REF]. Within a CBM program, diagnostics and prognostics are two important aspects where the former deals with fault detection, isolation and identification when it occurs and the latter helps to assess the current health state of the system and predict the remaining time before a failure occurs. An accurate prediction of the remaining useful life (RUL) could provide ample time for maintenance engineers to schedule a repair, and to acquire replacement components before they actually fail [START_REF] Zhang | An integrated approach to bearing fault diagnostics and prognostics[END_REF]. Due to the stochastic nature of the deterioration, stochastic processes have been adapted to model the deterioration processes and have shown the promising results within the CBM framework [START_REF] Van Noortwijk | A survey of the application of gamma processes in maintenance[END_REF][START_REF] Le Son | Remaining useful life estimation based on stochastic deterioration models: A comparative study[END_REF][START_REF] Wang | Chmm for tool condition monitoring and remaining useful life prediction[END_REF].

As a stochastic process, Hidden Markov Model (HMM) has been successfully applied in many domains, such as Speech recognition, genes and Deoxyribonucleic acid (DNA) analysis [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] thanks to its strong mathematical basis. In the CBM context, HMMs can divide equipment conditions into several meaningful states, such as "good", "minor defect", "maintenance required" and "failure" and therefore easy to understand [START_REF] Si | Remaining useful life estimation-a review on the statistical data driven approaches[END_REF]. They can also characterize the stochastic relationship between the features extracted from condition monitoring data and the actual health states of the equipment. For these reasons, HMMs, in the recent year, are being more and more investigated to be used as an efficient tool for the deterioration modeling and the RUL estimation [START_REF] Wang | Chmm for tool condition monitoring and remaining useful life prediction[END_REF]. For example, Baruah et al. employed HMMs for carrying out both the diagnostics and the prognostics for metal cutting tools [START_REF] Baruah | Hmms for diagnostics and prognostics in machining processes[END_REF]. In [START_REF] Zhang | An integrated approach to bearing fault diagnostics and prognostics[END_REF], the authors used the HMMs to construct a health/degradation index representing the current system health status. This index was then fed into an adaptive prognostic scheme in order to estimate the RUL of a bearing. In order to better represent the real degradation mechanism, several extensions of HMMs have being adopted in the literature, such as Mixture of Gaussian HMM [START_REF] Tobon-Mejia | A data-driven failure prognostics method based on mixture of gaussians hidden markov models[END_REF], age-based HMM [START_REF] Peng | A prognosis method using age-dependent hidden semi-markov model for equipment health prediction[END_REF], segmented HMM [START_REF] Geramifard | A physically segmented hidden markov model approach for continuous tool condition monitoring: Diagnostics and prognostics[END_REF], segmented Hidden Semi-Markov Model [START_REF] Dong | A segmental hidden semi-markov model (hsmm)-based diagnostics and prognostics framework and methodology[END_REF], etc.

To our best knowledge, almost all of the HMMbased frameworks in the literature consider only the mono-mode case, meaning that there is only one degradation mode occurring at one time. In practice, however, multiple degradation modes could exist in competition. In this paper, we propose a new HMM-based structure called multi-branch Hidden Markov Model (MB-HMM) to deal with this problem. In order to evaluate the effectiveness of the proposed model with respect to a traditional monobranch HMM, a simulation study is implemented.

The remainder of the paper is organized as follows. Section 2 is devoted to review some basic theories of HMMs. Section 3 describes the extension to MB-HMM and its application for diagnostics and prognostics. To illustrate the methodology, a comparative study is introduced in the section 4. Conclusion follows in Section 5.

METHODOLOGY

Basic theory of Hidden Markov Model

Hidden Markov Model is an extension of the Markov chain in which the state process are latent and can be only revealed through an observation process. This is where the word "hidden" comes from. In the deterioration modeling framework, the hidden state process represents the health states of the equipment, while the observations can be measurable signals such as the vibration signals or the features extracted from condition monitoring data. The relation between these two processes is represented by a probabilistic model. Mathematically, the complete specification of an HMM consists of the following elements [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] • N, the number of states in the model • M, the number of distinct observation symbols per state, i.e., the discrete alphabet size

• A finite set of hidden states, i.e., S = {S 1 , S 2 , ..., S N }

• A state transition probability distribution, i.e., A = {a ij }, where a ij = P (q t+1 = S j | q t = S i )

• An observation symbol probability distribution, i.e., B = {b j (k)} where b j (k

) = P (Y k | q t = S j ), 1 ≤ k ≤ M
• An initial state probability distribution, i.e., π = {π i } where

π i = P {q t = S i }, 1 ≤ i ≤ N
For convenience, in this study, an HMM is represented by a compact notation λ = (A, B, π).

HMM topology selection

In order to apply the HMM model for the deterioration modeling framework, one question is naturally raised: Given the observations, how one can choose/select a proper topology of the model. For instance, how can we choose the type of the model, how many states should be used or which observation probability distribution is suitable? These questions will be answered in this sub-section.

HMM type selection

There are several types of HMMs existing in the literature, such as the ergodic HMM or the left-right (Bakis) model [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF]). Since the deterioration processes are often irreversible in reality, components cannot come back from a bad health state to a better one as time progresses. For this reason, the left-right HMM model is chosen to be investigated. More precisely, the used left-right model in this study has the characteristic that the state index can either stay the same or increase by one. In other words, the components can only stay in the current health state or move to the next one. In this case, the coefficients of the transition matrix of the model satisfy the following properties:

a ij = 0, j < i a ji = 0, j > i + 1 a N N = 1, a N i = 0, i < N
The state S N is considered as the final (failure) state.

Observation model selection

The observations are usually considered as discrete symbols, hence discrete probability densities are used to model the observation probabilities. However, in the framework of machine condition monitoring, the observations obtained are typically continuous signals [START_REF] Tobon-Mejia | A data-driven failure prognostics method based on mixture of gaussians hidden markov models[END_REF]. In this case, the continuous HMM possessing a continuous probability density function (pdf) to model the emission probabilities could give a better accuracy in diagnostics, compared to the discrete HMM [START_REF] Wang | Chmm for tool condition monitoring and remaining useful life prediction[END_REF]. However, to ensure that the parameters of the HMM can be estimated in a convenient way, the observation pdf should be elliptically symmetric densities or mixtures of elliptically symmetric pdf [START_REF] Rabiner | Some properties of continuous hidden markov model representations[END_REF]. For this reason, the Gaussian pdf is used in this study as the observation model:

b j (O) = N (O, µ j , Σ j ) , 1 ≤ j ≤ N
where µ j and Σ j are the mean vector and covariance matrix in state S j .

Number of states selection

Selecting the number of states in an HMM model is always an interesting but difficult question. It exists several methods as well as criteria for this selection purpose, such as Akaike information criterion (AIC), Bayes information criterion (BIC), Cross-validation, etc. [START_REF] Knoblauch | Data driven number-of-states selection in hmm topologies[END_REF]. In this study, we investigate the use of BIC for selecting the number of state N.

The Bayes information criterion (BIC) is defined as follow

BIC = -2L + klogN (1)
where L is the log-likelihood function; k is the number of free parameters to be estimated and N is the number of data points in observation sequences O. The chosen model will be the one having the minimum BIC value.

EXTENSION TO MULTI-BRANCH HIDDEN MARKOV MODEL

General principles

The idea of the multi-branch HMM have been appeared in the literature and have mainly been applied for the applications of handwriting recognition [START_REF] Lee | Data-driven design of hmm topology for online handwriting recognition[END_REF][START_REF] Wang | Multi-branch and two-pass hmm modeling approaches for off-line cursive handwriting recognition[END_REF]. In this section, we will present the general principle of MB-HMM for modeling degradation processes under different modes. An example of a two-branch HMM is presented in the figure 2. Such a multi-branch model is suitable to model the equipment deterioration process which could follow different modes due to different changes of the operating condition. Considering the propagation of the crack appearing in a bearing. In a normal condition, the bearing operates normally. However, when more stress is applied on it, the crack could initiate and then propagate with different rates. The more stress applied, the more quickly the crack propagates. In the MB-HMM model, each constituent branch is dedicated to model a different deterioration mode. It is worth noting that the observations emitted from the corresponding states in different constituent branches could be similar (e.g. having the same probability distributions). The only thing that distinguishes the branches is the rate of deterioration which is represented by the transition probabilities.

There are some important assumptions that must be made in constructing the model. Firstly, once the equipment has degraded following one mode, it will follow that mode until it reaches the end of its life. There is hence no connection between the branches. The second assumption is that, the normal condition can last very long with no special characteristics in the measurement. We are interested in the deterioration process, with the purpose of assessing the deterioration level of equipment as well as predict its residual lifetime when it has suffered a problem. For this reason, the initial state can be assumed as a dummy state with no emission of observation. Each branch can therefore be seen as a single model and is assigned an a priori probability π k as shown in the figure 2. These a priori probabilities satisfy:

π k = P (λ k ) = K k /K, M k=1 π k = 1 (2)
where λ k denotes the constituent HMM for branch k, K k is the number of training data sequences corresponding to mode k, K is the total number of training data sequences and M is the total number of branches of the MB-HMM.

MB-HMM for diagnostics and prognostics

The application of MB-HMM for diagnostics and prognostics can be implemented in two phases, as shown in figure 3.

In the off-line phase, the training data is classified into M different groups and then, each constituent HMM model is trained individually with the data in the corresponding group. At this step, the well-known Baum-Welch algorithm can be used without any modifications. In the next step, the number of data in each group is used to assign the a priori probabilities for each model (c.f equation ( 2)). Finally, a trained MB-HMM model is obtained.

In the online phase, the diagnostics involves two sessions. In the first session, the mode that the equipment is following must to be identified . This goal can be achieved by using the decision theory. For instance, the model that has the maximum a posterior probability, given the data, can be chosen in order to minimize the misclassification rate, [START_REF] Bishop | Pattern recognition and machine learning[END_REF]. That is:

k = arg max k P (λ k | O) (3)
Note that, using Bayes' theorem, these a posteriori probabilities can be calculated as follows: After having identified the deterioration mode, the next stage of the diagnostics is to recognize the actual health state of the equipment. This is carried out in two steps consisting of finding the single state sequence (path) which is the most probable one representing the given test data, and considering the final state as the actual health state. The first step is done thanks to the well-known Viterbi algorithm. Let q t denote the equipment state at time t and Q = (q 1 , q 2 , . . . , q t ) denote a path till the current time. Given the estimated mode, the most probable path is the one that gives the maximum joint probability of the path and the observation:

P (λ k | O) = P (O | λ k ) P (λ k ) M k=1 P (O | λ k ) P (λ k ) (4)
Q * = arg max Q k P (O, Q k | λ k) (5)
where Q i represents a possible path within the mode i. The actual health state of the equipment is the final one of the path Q * .

RUL calculation

Given the deterioration mode and the current health state estimated from the diagnostic stage, the RUL estimation can be conducted the same as in a single HMM case and is straightforward. In the MB-HMM framework, this estimation, however, strongly depends on the mode detection. Indeed, a wrong deterioration mode detection may result in a large bias in the RUL estimation. For example, if a crack propagates with a high rate, the detection of a low rate mode may lead to an extremely larger value of the RUL than the actual one. This phenomenon often occurs at the beginning of a defect propagation since the observations are insufficient to show an obvious deterioration trend. In this study, the Bayesian Model Averaging (BMA) technique [START_REF] Hoeting | Bayesian model averaging: a tutorial[END_REF]) is implemented to tackle this problem. The RUL distribution is calculated as an average of the posterior distributions under each constituent model, weighted by their posterior model probability:

P (RUL | O) = M k=1 P (RUL | λ k , O) P (λ k | O) (6)
where P (λ k | O) is calculated from the equation (4).

The RUL estimation now turns to the estimation of the individual RULs under each constituent HMM, which is straightforward and can be computed in a recursive way as follows. Given the test data, the health state of equipment is identified thanks to the Viterbi algorithm. The RUL can be defined as the necessary time steps to reach for the first time the final state S N from the current state S i (i < N):

RUL = min {n ≥ 0 : q t+n = S N | q t = S i } (7)
where q t denote the health state at the time t. By this definition, the RUL can be seen as a discrete variable and its probability mass function is given by

P (RUL = n | q t = S i ) = P (q t+n = S N , q t+n-1 = S N , . . . , q t+1 = S N | q t = S i ) (8) Denote h (n) i = P (RUL = n | q t = S i ).
Since the model is strictly one-order left-right topology HMM, the RUL can be calculated by the following backward recursive equations:

At state S N -1 :

h (1) N -1 = a (N -1)N (9) h (n) N -1 = a (N -1)(N -1) h (n-1) N -1 (10)
At state S N -2 :

h (1) N -2 = a (N -2)N (11) h (n) N -2 = a (N -2)(N -2) h (n-1) N -2 + a (N -2)(N -1) h (n-1) N -1 (12) • • • • • • At state S i h (1) i = a iN (13) h (n) i = a ii h (n-1) i + a i(i+1) h (n-1) i+1 (14)
where a ij is the transition probability from state S i to state S j and is obtained from the transition matrix A.

After calculating all the individual components, the RUL estimation under the MB-HMM can be accomplished by the equation ( 6).

NUMERICAL EXAMPLES

Fatigue Crack Growth model for data generation

To evaluate the proposed MB-HMM-based diagnostic and prognostic framework performance, it is necessary to have the data which represent several different deterioration modes. In this section, the Fatigue Crack Growth (FCG) model is used to model the crack appearing and propagating within a bearing and to generate both the training as well as the testing data. The FCG is chosen since it has been widely used to describe the crack propagation in the literature [START_REF] Huynh | Adaptive condition-based maintenance decision framework for deteriorating systems operating under variable environment and uncertain condition monitoring[END_REF][START_REF] Myotyri | Application of stochastic filtering for lifetime prediction[END_REF]). The bearing is supposed to operate under different operation conditions so that the crack will propagate with different rates which represent different deterioration modes for our purpose.

Fatigue Crack Model

The FCG model is constructed based on the popular Paris-Erdogan equation to express the crack growth rate:

dx dt = C (∆K) n ( 15
)
where x is the crack depth, t is the time, ∆K is the stress intensity amplitude and C and n are constant depending on the material property. It is shown that ∆K is roughly proportional to square root of crack depth x by a factor β: ∆K = β √ x [START_REF] Myotyri | Application of stochastic filtering for lifetime prediction[END_REF].

To take into account the stochastic aspect of the crack propagation, equation ( 15) could be discretized and then randomized by adding a multiplicative factor following a log-normal distribution as follows:

x t i = x t i-1 + e wt i C βe √ x t i-1 n ∆t (16)
where w t i are independent and identically distributed according to a Normal distribution N (0, σ 2 w ), 0 < x t i-1 < x t i < ∞. This discretized and randomized model allows us to determine recursively the crack depth x t i at time t i given the previous depth x t i-1 and the model parameters. By this way, the deterioration data can be generated.

For modeling different deterioration modes, the factor β is considered to be a function β(e) of the operating environment state e as below [START_REF] Huynh | Adaptive condition-based maintenance decision framework for deteriorating systems operating under variable environment and uncertain condition monitoring[END_REF]:

β (e) = β b • e γe (17)
where β b is the base stress level of system, the values γ e ≥ 0, e = 1, 2, . . . , M determine the level of extra stress linking with the state e of the environment. Obviously, from the equations ( 16) and ( 17), the propagation rate is directly proportional to the parameters γ e : the greater the value of γ e is, the more quickly the crack propagates.

Observation model

The actual crack depth is difficult to be directly and accurately measured because of several different reasons [START_REF] Huynh | Adaptive condition-based maintenance decision framework for deteriorating systems operating under variable environment and uncertain condition monitoring[END_REF]). Hence, we need an observation model to represent the relationship between these actual values and the measure ones. In this study, the measurement is assumed to be the sum of the actual crack depth and a zero-mean Gaussian noise. Let X denote the crack depth and Y denote the corresponding measurement, the observation model is:

Y = X + ξ (18)
where ξ ∼ N 0, σ 2 ξ is the measurement error.

Application of MB-HMM for FCG data

In this section, the bearing is supposed to operate under two different environments and therefore the crack propagates in two different rates. A two-branch HMM is chosen to represent these two deterioration modes. The following parameters of the FCG model are chosen:

C = 0.005, n = 1.3, β b = 1, σ w = 1.7, ∆t = 1, γ e = [0 0.75] T , σ 2 ξ = [5 10] T
where the subscript T denotes the transpose of a vector. The different variance values of σ 2 ξ mean that the measurement error may depend slightly on the operating condition.

The bearing is supposed to be failed once the crack depth reaches a critical level d = 100. 100 data curves have been generated by using the FCG model with the above parameters and used as the training data. Figure 4 illustrates this training data set.

In this study, the number of deterioration modes is assumed to be known beforehand. Therefore, "kmeans" tool is used to classify the failure times into 2 "clusters". Based on this, the training data can be In order to train each constituent model, it is necessary to determine the number of states of each model. This task is done by using the BIC criterion. Figure 5 illustrates the BIC values with respect to different state numbers for a branch of the MB-HMM. Since the crack propagation herein is a continuous process, the increase in the states number N will obviously reduce the BIC value. To avoid the overfitting situation, it is sufficient to take the "knee" point on the BIC curve. The value N statesmode1 = 10 is hence chosen for this example.

After having determined the number of states, each model is trained thanks to the Baum-Welch algorithm. The next step is to assign the a priori probability for each branch (c.f. equation ( 2)) and the result are: π 1 = 0.41 and π 2 = 0.59. An MB-HMM is obtained and the offline phase is terminated.

We now move to the on-line phase. One data curve representing the propagation of the crack depth from the beginning to the end of bearing life is also generated by the FCG model. This curve serves as the test data and is shown in the figure 6 (upper sub-figure). Only the red part till the actual time t act = 100h are assumed to be observable. The estimated RUL pdf is illustrated in the lower sub-figure of the figure 6.

To simulate the on-line RUL estimation problem, the actual time t act is gradually replaced by 30h towards the failure. After each replacement, more information about the deterioration is achieved and the diagnostic and prognostic procedures are reimplemented. Figure 7 represents the mean value of the estimated RUL associated with the 95% confidence interval. It can be realized that, at the early instances, the lack of information due to the limited observations results in the bias and large variance in the RUL estimation. However, the actual values always lie within the 95% confidence interval. As the time passes, the length of the confidence interval significantly decreases and the estimated RUL converges to the real value. This demonstrates demonstrates the accuracy of the proposed RUL estimation method.

MB-HMM vs average HMM

Investigating the advantage of the proposed approach naturally raises a question: given the same data set, which method between the one using the proposed MB-HMM and the one using only an "average" HMM will give the better performance in RUL prediction. To answer such question, a comparative study is given in this section with 100 test data curves. The prognostic performance of each method is characterized by the root mean squared error (RMSE) metric.

For notation convenience, we denote the average HMM by AVG-HMM. In the training phase, the training data set in the previous section is not grouped and is used as a whole to train only one AVG-HMM. This model is then used in the on-line phase to estimate the RUL. At t act = 100h, we obtain RMSE AVG-HMM = 74.4. Compared to the corresponding result of the MB-HMM: RMSE M B-HM M = 52.5, it can be concluded that the MB-HMM give a better performance in RUL estimation compared with the AVG-HMM for this case.

Another interesting question raised in evaluating the advantages of the proposed MB-HMM is: does the above conclusion still hold in case that the two propagation rates are not quite different, or in case that there are two obvious trends in the training data? To answer this question, it is necessary to define a "distance" between two deterioration modes. In this study, the "mode distance" is defined by the gap between the two propagation rates and can be changed through the parameter γ e of the FCG model. Indeed, as indicated in the section 4.1.1, the propagation rate of a crack is directly proportional to γ e . The greater the value of γ e is, the more quickly the crack propagates. Therefore, by fixing γ 1 and do varying γ 2 , the mode distance is changed. Figure 8 shows that, when the distance between modes increases, the RMSE given by MB-HMM approach decreases while with AVG-HMM, the RUL prediction error increases. It can be concluded that the larger the distance between deterioration modes is, the better performance in RUL estimation it is given by the proposed MB-HMM approach, in comparison to an "average" HMM.

CONCLUSION

The present paper proposes a novel model called multi-branch Hidden Markov Model (MB-HMM) to deal with the deterioration modeling problem in case that there are several competing modes existing in deterioration mechanism of equipment. A diagnostic and prognostic framework based on the proposed model is also given. The actual health state recognition and the RUL estimation can be implemented in the same way as the traditional HMM. However, by using different HMM models for different modes, together with the a priori probabilities of each model, the MB-HMM shows a very promising result in dealing with the multi-mode deterioration mechanism.

Future research will be focused on the extension of the MB-HMM to a multi-branch Hidden semi-Markov Model (MB-HSMM) due to the fact that the state sojourn time of an HMM follows an exponential distribution, which may not be hold in practice. Another possible extension of the model is the ability of transition between the states of the different branches. The proposed model and the extension should also be validated on the data of real systems.

Figure 1 :

 1 Figure 1: A five state left-right HMM

Figure 2 :

 2 Figure 2: Example of a two-branch HMM

Figure 3 :

 3 Figure 3: Proposed MB-HMM framework for diagnostics and prognostics

Figure 4 :

 4 Figure 4: Two-mode training data

Figure 5 :

 5 Figure 5: BIC for number of state selection

Figure 6 :

 6 Figure 6: Observations and RUL estimation at t act = 100h

Figure 7 :

 7 Figure 7: RUL estimation at different time instances

Figure 8 :

 8 Figure 8: Prediction RMSE vs γ 2

ACKNOWLEDGEMENT

This work is a part of the Ph.D research work of Thanh Trung LE in the framework of SUPREME ("SUstainable PREdictive Maintenance for manufacturing Equipment") project, funded by the European Comission in FP7 Programme, under the Factories of the Future PPP.


Philippe Corsenac

Emmanuel Lagarde

Blandine Gadegbeku

Bernard Delorme

Aurore Tricotel

Anne Castot

Nicholas Moore

Pierre Philip

Bernard Laumon

Ludivine Orriols
email: ludivineorriols@isped.u-bordeaux2.fr

Road traffic crashes and prescribed methadone and buprenorphine: A french registry-based case-control study

Keywords: methadone, buprenorphine, road traffic crashes

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Opioids have been shown to impair psychomotor and cognitive functioning in healthy volunteers with no history of opioid abuse. [START_REF] Zacny | A review of the effects of opioids on psychomotor and cognitive functioning in humans[END_REF][START_REF] Zacny | Should people taking opioids for medical reasons be allowed to work and drive?[END_REF] Clinical doses of buprenorphine impair reaction time, muscle coordination, attention and short-term memory [START_REF] Macdonald | Psychomotor effects of ketorolac in comparison with buprenorphine and diclofenac[END_REF][START_REF] Saarialho-Kere | Psychomotor, respiratory and neuroendocrinological effects of buprenorphine and amitriptyline in healthy volunteers[END_REF] Likewise, single oral dose of methadone have been shown to increase reaction time and to impair ocular coordination. [START_REF] Gordon | Reaction-times of methadone treated ex-heroin addicts[END_REF][START_REF] Lombardo | Cognitive functioning under moderate and low dosage methadone maintenance[END_REF] Opioids used as a substitution maintenance therapy (buprenorphine and methadone) are prescribed in relatively stable doses over a long period of time (usually more than six months). The effects of long-term use of opioids on driving skills have been reviewed by [START_REF] Fishbain | Are opioiddependent/tolerant patients impaired in driving-related skills? A structured evidence-based review[END_REF] with little evidence of any association [START_REF] Fishbain | Are opioiddependent/tolerant patients impaired in driving-related skills? A structured evidence-based review[END_REF]. Available studies were conducted in the 70's in the United States and focused on methadone maintenance [START_REF] Babst | Driving records of methadone maintenance patients in New York State[END_REF][START_REF] Blomberg | Narcotic use and driving behavior[END_REF][START_REF] Maddux | Driving records before and during methadone maintenance[END_REF]. Three more recent studies found no differences in traffic-relevant performances between patients maintained on buprenorphine or methadone and healthy controls. [START_REF] Baewert | Influence of peak and trough levels of opioid maintenance therapy on driving aptitude[END_REF][START_REF] Schindler | Maintenance therapy with synthetic opioids and driving aptitude[END_REF][START_REF] Shmygalev | The impact of long-term maintenance treatment with buprenorphine on complex psychomotor and cognitive function[END_REF] As far as opioids used as analgesics are concerned, the crash risk has been found to be increased by two-fold in two studies using prescription databases [START_REF] Engeland | Risk of road traffic accidents associated with the prescription of drugs: a registry-based cohort study[END_REF][START_REF] Leveille | Psychoactive medications and injurious motor vehicle collisions involving older drivers[END_REF]. These results may be partly explained by an irregular use of analgesic opioids as opposed to steady doses for long periods that are prescribed in the treatment of opioid dependence. Other studies used blood and/or urine samples to detect the presence of opioids in drivers involved in a crash. [START_REF] Drummer | The involvement of drugs in drivers of motor vehicles killed in Australian road traffic crashes[END_REF][START_REF] Movig | Psychoactive substance use and the risk of motor vehicle accidents[END_REF][START_REF] Mura | Comparison of the prevalence of alcohol, cannabis and other drugs between 900 injured drivers and 900 control subjects: results of a French collaborative study[END_REF] Only one of these studies found an association between morphine and the risk of crash (OR=8.2, 95% CI: 2.5-27.3). [START_REF] Mura | Comparison of the prevalence of alcohol, cannabis and other drugs between 900 injured drivers and 900 control subjects: results of a French collaborative study[END_REF] These studies are however unable to distinguish between legal and illegal use of opioids. Most of the available epidemiological studies concerned opioids used as analgesics and the few others that focused on substitution maintenance therapy are relatively old and limited to the study of methadone effects on the risk of crash. The aim of our study was to investigate the association between the risk of being responsible for a road traffic crash and the use of buprenorphine and methadone within the general driving population.

METHODS

The study consisted of extracting and matching data from three French nationwide databases.

The national health care number (national ID) of drivers involved in injurious crashes was extracted from the police report database. These reports were matched with data from the national police database of injurious crashes to provide details on the crash. National IDs extracted from police reports were sent to the national health care insurance database to collect data on medicine exposure. [START_REF] Orriols | On behalf of the CESIR research group. Prescribed medicines and the risk of road traffic crashes: a French registry-based study[END_REF] This study was approved by the French Data Protection Authority.

Crash data

Police reports. French police forces are required to fill out a police report for each injurious crash defined as a crash resulting in injury for at least one individual involved occurring in the country (about 70 000 reports each year). Police reports are scanned and stored as image files.

For some of the drivers involved in these injurious road traffic crashes, the national ID is recorded in the police report. This national ID was extracted from image file. All 210,818 available police reports available over the study period (from July 2005 to May 2008) were compiled. The exact number of drivers registered in police reports is unknown as it is not feasible to read manually all police reports. However, this figure may be estimated from the number of drivers registered in the national police database of injurious crashes.

National police database of injurious crashes.

Police forces also collect details on the same injurious crash events which are stored in the national police database of injurious crashes. This standardized database contains descriptive variables on the crash characteristics, the vehicles and the people involved in the crash. Police forces also conduct additional investigations regarding injury severity from hospital records and categorize the people involved into four groups: unhurt, slightly injured, seriously injured (hospitalized more than 24 hours) or killed (in the 30 days following the crash). All drivers involved in an injurious road traffic crash are supposed to be tested for the presence of alcohol using a breath test. If this test is positive (corresponding to a blood alcohol concentration above the French legal limit of 0.5 g/L), if the driver refuses to take the test or the severity of the crash makes the test impossible, then the blood alcohol concentration is measured. If the breath test is negative then the driver is registered as not being under the influence of alcohol.

National ID extraction and matching procedures. The first step of the study was extracting and matching data from the comprehensive French nationwide databases described above.

Drivers were included through their national ID, gender, and date of birth, as extracted from police reports. An application, based on optical character recognition, was developed to automatically extract, from the image files, the date of the crash, an individual's national ID, gender, and date of birth. The extraction procedure was validated on a subsample of 293 police reports, which were printed and manually coded. A procedure was implemented to match each individual whose ID was extracted from police reports with the corresponding record from the national police database of injurious crashes. Two records were considered matched if six descriptive variables were in agreement. If a pair had three or more discordant variables, it was considered unmatched. For pairs with concordance for fewer than six variables and more than three variables, a probabilistic linkage method was developed [START_REF] Jaro | Probabilistic linkage of large public health data files[END_REF]. When a decision could not be made automatically, pairs were reviewed by hand. Data on reimbursed medicines dispensed within 6 months before the crash were obtained by linking included drivers to the national health care insurance database using their national ID, gender, and date of birth. Confidentiality was ensured by using the personal information anonymization function of the national health care insurance system. [START_REF] Trouessin | FOIN: a nominative information occultation function[END_REF] Medicine exposure data Health care insurance database. The national health care insurance system database covers the entire French population (in 2008, 64,000,000) and includes data on reimbursed prescription medicines. A record is entered into the database each time a prescription medicine is dispensed to an outpatient at the pharmacy, including the national ID, the date of dispensing and the seven-digit code assigned to the medicine at the time of its marketing authorization. Data on long-term chronic diseases are also registered in this database, with the International Classification of Diseases 10 th edition (ICD-10) code, start and end dates of disease.

Exposure periods. Exposure was considered starting on the day following dispensing. To ensure that medicines were not prescribed as a consequence of the crash, medicines dispensed on the crash day were not considered.

Methadone and buprenorphine.

French legislation imposes a strict framework for the prescription and dispensation of these medicines [START_REF] Augé-Caumon | L'accès à la méthadone en France. Bilan et recommandations: rapport au ministre de la santé[END_REF]. The first prescription of methadone must be filled in by a medical doctor in a specialized care center for drug addicts or in a health care center. Buprenorphine treatment may be initiated in specialized centers but also and mostly in community pharmacies. Methadone is prescribed for no more than 14 days, and on a special form which is non automatically renewable.

Buprenorphine is also prescribed on a specific non automatically renewable form, and for a maximum of 28 days. Usually, pharmacists are allowed to dispense one to seven days' worth of treatment with methadone or buprenorphine except if the practitioner mentioned, "to dispense at once".

The exposure period was estimated from our database as the most frequently observed delay between two dispensations. This delay proved to be seven days for the two medicines, which corresponds to the French legislation.

Concomitant exposure. In France, a four-level risk classification system of medicines affecting driving abilities has been established, ranging from level 0 (no or negligible risk) to level 3 (major risk) (Afssaps, 2009). Comparisons were adjusted for the use of other medicines as classified in the highest levels of risk (levels 2 and 3), including antiepileptics, psycholeptics, all benzodiazepines and derivatives. While the effect of level 2 medicines depends both on phamacodynamics and on individual susceptibility, with level 3 medicines, the pharmacodynamic effect is predominant so all users are advised not to drive. Exposure data was available for all classes of medicines in our database.

Analysis

Subject inclusion.

Drivers were censored at their first involvement in a road traffic crash in order to mitigate the impact of previous crashes on medicine exposure. All drivers with a national ID recorded in the police report were included. Subjects whose police reports did not contain their national ID were not included. There are several possible reasons for noninclusion of drivers: the police reports did not contain the driver's national ID (national ID recording is not mandatory), the extraction procedure failed, or the linkage with the corresponding record in the national police database of injurious crashes did not succeed. We compared, by logistic regression, age, gender, injury severity, vehicle type, crash location, type of police forces filling the police report, alcohol level and responsibility between included and non included drivers.

Descriptive analysis.

Frequencies of exposures to methadone or buprenorphine were compared according to individual and crash characteristics. All variables significantly associated with exposure in the bivariate analysis were included in the multivariate analysis, performed by logistic regression.

Responsibility analysis. The purpose of responsibility analysis is to compare exposure probabilities on the day of crash between responsible drivers (cases) and non-responsible drivers (controls). Responsibility levels in the crash were determined by a standardized method adapted from Robertson and Drummer [START_REF] Robertson | Responsibility analysis: a methodology to study the effects of drugs in driving[END_REF]. This method, recently validated in France using data from the national police database of fatal crashes [START_REF] Laumon | Cannabis intoxication and fatal road crashes in France: population based case-control study[END_REF], takes into consideration the different factors likely to reduce driver responsibility: road, vehicle and driving conditions, type of accident, traffic rule obedience and difficulty of the task involved. A score is assigned to each driver for each of these factors from 1 (favourable to driving) to 4 (not favourable to driving). Drivers were further grouped into two levels of crash responsibility: responsible (score < 15) or nonresponsible (score ≥ 15).

Statistical analyses were conducted using logistic regression. The association between responsibility and age, gender, socioeconomic category, time of crash, season, region of France where the crash occurred (North or South of France), location (urban or non urban), vehicle type, injury severity, blood alcohol concentration (BAC), concomitant treatments (using the four-level French classification system) and chronic long-term disorders were initially investigated using bivariate analysis; these variables were included in the multivariate model as their p-value was less than 20% (Chi-squared test).

Data were analyzed using the SAS statistical software package, version 9.1 (SAS Institute Inc, Cary, NC, USA).

RESULTS

The validation study conducted on 293 police reports showed that the national ID was recorded for 140 of the 455 drivers involved (28%). The automatic OCR software extracted 110 of these 140 national IDs (extraction rate=79%). Matching with the police national database of injurious crashes was possible for 90% of the IDs. The driver inclusion rate was thus expected to be around 20%.

Results of the overall extraction and matching procedures are illustrated in Figure 1. We extracted 109,078 national IDs/gender/date of birth, from 210,818 police reports available from July 2005 to May 2008, corresponding to any individual involved in an injurious road traffic crash. Ninety percent of these individuals were matched with a corresponding record in the police national database of injurious crashes (72.8% fitted on all variables, 14.0% were matched by the probabilistic linkage method and 3.1% manually). The linkage failed for 10% of the individuals, because the ID corresponded either to a driver involved in the crash but not captured in the police national database or to an individual not involved in the crash (e.g. a witness, the owner of a vehicle involved).

The procedure led to the inclusion of 72,685 drivers (34,896 responsible and 37,789 nonresponsible drivers), i.e.18.5% of the 392,169 drivers registered in the police national database of injurious crashes.

Injury severity was the main factor associated with the probability of being part of the study (34% of seriously injured drivers included), thus explaining higher rates of inclusion for bicycle and scooter drivers (27% and 23% respectively) and drivers involved in non-urban accidents (25%), all of whom have been consistently documented in literature to be more seriously injured. The inclusion rate was approximately the same for responsible and nonresponsible drivers (respectively, 18.8% and 18.3%).

Exposure to buprenorphine or methadone was higher among men and young drivers (29-38 years old) and drivers using level 2 and level 3 medicines. (Table 1) Forty nine drivers (25% of the 196 buprenorphine or methadone users) were exposed to one or more level 3 medicines and 76 drivers (39% of the 196 buprenorphine or methadone users) were exposed to one or more level 2 medicines on the day of crash, all belonging to the nervous system class of the WHO Collaborating Center for Drug Statistics Methodology ATC (Anatomical Therapeutic Chemical) classification. These other medicines used concomitantly to buprenorphine and methadone were mainly anxiolytics, hypnotics, antipsychotics and antidepressants. (Table 2) Adjusted responsibility analysis showed a two-fold increased risk associated with the use of buprenorphine or methadone (OR=2.02, 95% CI: 1.40-2.91). The analysis conducted on the effect of each of these two medicines separately showed an increased risk of being responsible for a crash for buprenorphine users and no significant association was found for methadone users (Table 3).

The same analysis, performed for the 387 drivers who received at least one dispensation of buprenorphine or methadone in the six month preceding their crash, showed an increased responsibility risk for these drivers (OR=1.70, 95% CI: 1.36-2.14). The odd ratio was 1.52, 95% CI: 1.14-2.03 when excluding the 159 drivers who had a dispensation in the eight days before the crash from the analysis. DISCUSSION 72,685 drivers involved in an injurious road traffic crash in France, over a three-year period, were included in the study. We evidenced an increased risk of being responsible for a crash among patients under buprenorphine or methadone (OR= 2.02, 95% CI: 1.40-2.91), as compared to non users. When considering each substance individually, buprenorphine was associated with responsibility risk while there was no association for methadone, probably because of the small number of drivers exposed to this medicine; an effect of methadone can thus not be excluded.

The responsibility analysis is a real strength of the study as it allows for the comparisons of cases and controls that share the same characteristic of being drivers. In a previous study on the impact of illegal drug consumption, using the same police national database but limited to fatal crashes [START_REF] Laumon | Cannabis intoxication and fatal road crashes in France: population based case-control study[END_REF], the same method used to determine responsibility was approved by an independent expert evaluation of responsibility. Furthermore, because the responsibility analysis relies on the assumption that non responsible drivers are representative of the driving population, the authors of the previous study validated the comparison of a subset of the non responsible subjects with the driving population in France [START_REF] Laumon | Cannabis intoxication and fatal road crashes in France: population based case-control study[END_REF]. Finally, the strong dose-effect relationship found in our study between alcohol level and responsibility is a further indirect validation of the method. Importantly, responsibility levels were computed independently of alcohol and illicit drug use because of their potential interactions with medicine use.

A study conducted in 2004, focusing on fatal crashes did not find an association between opiates and driver responsibility. [START_REF] Drummer | The involvement of drugs in drivers of motor vehicles killed in Australian road traffic crashes[END_REF] In this study, using toxicological testing, methadone was only one of the tested substances among other licit and illicit opioids making difficult the comparison with our results. Moreover, the authors highlighted the lack of power to address the issue.

The results showed that injury severity was associated with the probability of being part of the study. Thus severely injured drivers were more likely to be included than slightly injured drivers. Killed drivers and uninjured drivers still had lower inclusion rates. This finding can be explained by the fact that injured drivers were more likely to be admitted to hospital so their healthcare number was more frequently noted in the police report. Thus, our study sample slightly over-represented drivers injured in more severe crashes.

Medicine exposure was ascertained from computerized records of reimbursed prescriptions filled at the pharmacy. These data were not subject to underreporting, a major problem encountered when medicine exposure data is self-reported [START_REF] Honkanen | Role of drugs in traffic accidents[END_REF]. However, we did not know whether the medicines were actually ingested or not. Non-compliance, which we were not able to check, would therefore result in exposure misclassification.

Another study showed that the French healthcare insurance data are reliable indicators of actual exposure for medicines used over a long time frame [START_REF] Noize | Comparison of health insurance claims and patient interviews in assessing drug use: data from the Three-City (3C) Study[END_REF], which is the case for substitution maintenance treatments.

The first prescription of methadone must be filled in by a medical doctor in a specialized care center for drug addicts or in a health care center. Consequently, our study was unable to consider the very first prescription of methadone. This initiation period might be critical regarding the risk of crash. Buprenorphine treatment may be initiated in specialized centers but also and mostly in community pharmacies. Moreover, some patients will never have any dispensation in community pharmacies and will be only followed in these centers during their whole treatment course. While this loss of information is unlikely to have biased association measures, it has consequences in exposure prevalence estimates which are therefore underestimated.

Prescription of takeaway doses of methadone results in diversion for illicit use by those not in treatment [START_REF] Mattick | Buprenorphine maintenance versus placebo or methadone maintenance for opioid dependence[END_REF] Buprenorphine is even more easily accessible than methadone due to less restrictive policies and some patients may consult several practitioners to acquire more prescriptions [START_REF] Thirion | Buprenorphine prescription by general practitioners in a French region[END_REF]. Health care insurance data showed that in 2005-2006, 25% of buprenorphine dispensations were for the benefit of 5% of the patients, leading to concern about contraband networks. [START_REF] Chast | Opiate replacement therapy in France: assessment of the public policies[END_REF] Misuse and accidents have also been reported (intravenous drug use, fatal overdoses…). [START_REF] Chast | Opiate replacement therapy in France: assessment of the public policies[END_REF] While it has been shown that buprenorphine is one of the medicines that are the most frequently reported in suspicious prescriptions (8.8% of the suspect prescriptions between 2001 and 2004) [START_REF] Boeuf | Survey of forged prescriptions to investigate risk of psychoactive medications abuse in France: results of OSIAP survey[END_REF], the part of substitution maintenance prescriptions that are diverted from therapeutic remains impossible to estimate.

Codeine is used to reduce withdrawal symptoms or to substitute for other opioid dependence.

Because several medicines containing codeine are available without a prescription, these consumptions could not be estimated from the health care insurance database. Néocodion® is a codeine preparation, available without prescription, and also known to be misused by opiate addicts. [START_REF] Armand | Neocodion misuse: evolution between 1992 and 2002[END_REF][START_REF] Olivier | Use of codeine and non-codeine cough suppressant. A survey among a French network of community pharmacists[END_REF] A study conducted in 2002 in France estimated that 21% of Néocodion® users were concomitant methadone or buprenorphine users. [START_REF] Armand | Neocodion misuse: evolution between 1992 and 2002[END_REF] We observed however that buprenorphine or methadone users had very few concomitantly prescription of opioid analgesic level 2 medicines (as defined in the French classification system) on the day of their crash.

Finally, consumption of illicit products is commonplace in maintained patients. Heroin was reported to be used in 22% to 59% of the patients during their treatment. [START_REF] Amato | An overview of systematic reviews of the effectiveness of opiate maintenance therapies: available evidence to inform clinical practice and research[END_REF] Other drugs such as cannabis, cocaine, amphetamines are also frequently reported. In France, the detection of drugs is mandatory in fatal road crashes only and is missing for 95% of drivers involved in injurious crashes.

In our study, 48% of the buprenorphine or methadone users were estimated to be exposed to another nervous system medicine on the day of crash; most of these medicines were benzodiazepines and/or benzodiazepine-related medicines. Interestingly, patients were found with very old generation of hypnotics like flunitrazepam which are known to have a strong addictive component. [START_REF] Sec | Misuse of psychotropic medications in a population of subjects held for custody in the city of Paris[END_REF] A literature review concluded that during substitution treatment, about 30% of patients are affected by dependence on alcohol and benzodiazepines. [START_REF] Laqueille | Abuse of alcohol and benzodiazepine during substitution therapy in heroin addicts: a review of the literature[END_REF] Seventeen percent of drivers under buprenorphine or methadone had a blood alcohol concentration above the legal limit as opposed to 5.6% among other drivers who were not under such treatment. Blood alcohol is however not consistently tested in drivers involved in crashes resulting in slight injury (defined as resulting in a less than 24 hours hospital stay).

In a previous study, using the same database, the odds ratios for prescribed medicines that may have a deleterious effect on driving performances (level 2 and level 3 according to the French classification) were OR=1.31, 95% CI: 1.24-1.40 and OR=1.25, 95% CI: 1.12-1.40, respectively. These risk levels mainly include hypnotics, anxiolytics and antidepressants, known to be associated with an increased risk of crash [START_REF] Barbone | Association of road-traffic accidents with benzodiazepine use[END_REF][START_REF] Bramness | Minor Increase in Risk of Road Traffic Accidents After Prescriptions of Antidepressants: A Study of Population Registry Data in Norway[END_REF][START_REF] Engeland | Risk of road traffic accidents associated with the prescription of drugs: a registry-based cohort study[END_REF][START_REF] Gustavsen | Road traffic accident risk related to prescriptions of the hypnotics zopiclone, zolpidem, flunitrazepam and nitrazepam[END_REF][START_REF] Leveille | Psychoactive medications and injurious motor vehicle collisions involving older drivers[END_REF][START_REF] Neutel | Risk of traffic accident injury after a prescription for a benzodiazepine[END_REF][START_REF] Neutel | Benzodiazepine-related traffic accidents in young and elderly drivers[END_REF][START_REF] Orriols | Benzodiazepine-like hypnotics and the associated risk of road traffic accidents[END_REF][START_REF] Ray | Psychoactive drugs and the risk of injurious motor vehicle crashes in elderly drivers[END_REF].

It is therefore very unlikely that the OR of 2 found here for buprenorphine and methadone would be solely explained by their pharmacological action. This is an indirect argument in favour of the impact of risky behaviour in this population. A recent study conducted in the same database found a similar risk estimate for drivers with zolpidem misuse (very high consumtion level) (OR=2.38, 95% CI: 1.61-3.52) [START_REF] Orriols | Benzodiazepine-like hypnotics and the associated risk of road traffic accidents[END_REF], showing that drivers with a profile of abusers may be more likely to have an increased risk of causing a crash. On the other hand, when considering all drivers who received at least one dispensation of buprenorphine or methadone in the six month preceding their crash, the odds ratio was 1.70, 95% CI: 1.36-2.14. When drivers receiving a dispensation in the eight days just before the crash were excluded from this analysis, the odds ratio was even lower (1.52, 95% CI: 1.14-2.03). This indicates that an effect of the treatments can not be excluded. A literature review of experimental studies suggested however that there was no impairment of psychomotor abilities immediately after the administration of opioids to opioid-maintained patients. This review also showed no impairment of psychomotor abilities as measured in laboratory tests and in driving simulators. [START_REF] Fishbain | Are opioiddependent/tolerant patients impaired in driving-related skills? A structured evidence-based review[END_REF] The absence of a relevant impact on driving abilities has also been shown recently in clinical studies [START_REF] Baewert | Influence of peak and trough levels of opioid maintenance therapy on driving aptitude[END_REF][START_REF] Schindler | Maintenance therapy with synthetic opioids and driving aptitude[END_REF][START_REF] Shmygalev | The impact of long-term maintenance treatment with buprenorphine on complex psychomotor and cognitive function[END_REF]. However, in such studies, drivers may not behave as in reallife driving conditions. One of the studies underlined the difficulty to generalize the findings due to major problems in this specific patients group (illicit drugs consumption and lack of social reliability) [START_REF] Shmygalev | The impact of long-term maintenance treatment with buprenorphine on complex psychomotor and cognitive function[END_REF].

Further work is therefore needed to disentangle the effect of treatments and the characteristics of the particular population using methadone or buprenorphine. * The discrepancy between the number of police reports and the number of records in the national police database of injurious crashes is explained by the fact that a small proportion of unavailable reports were being used for on-going further legal investigations. Reference group = drivers not exposed to the medicines considered † Crude odds ratios ‡ Model computed for 62,766 drivers without missing values for the adjustment variables § Odds ratios adjusted for age, gender, socioeconomic category, region, location, time of day, month, vehicle type, alcohol level, injury severity, concomitant level 2 and 3 medicine exposure and long-term chronic diseases ║ 2 drivers were estimated as exposed to both medicines on the day of crash

Figure 1 .

 1 Figure 1. Flowchart of the inclusion procedure.

Table 1 . Exposure to buprenorphine or methadone on the crash day according to driver and crash characteristics, France, 2005-2008

 1 Reference group=not exposed to the medicine considered * The total number of drivers is not equal to 72,685 because of missing values ‡ Multivariate analysis, logistic regression, model computed for 61,567 drivers without missing values (2-sided test)

Table 2 . Level 2 and 3 medicines used concomitantly on the day of crash, France, 2005-2008

 2

* Some drivers were exposed to several of these medicines

Table 3 . Odds ratios for responsible road traffic crashes in users of buprenorphine or methadone, France, 2005-2008

 3 p<0.05, ** p <0.001 (2-sided tests)

*