Walid Belazi

Salah- Eddine Ouldboukhitine

Alaa Chateauneuf

Abdelhamid Bouchair

Experimental and numerical study to evaluate the effect of thermostat settings on building energetic demands during the heating and transition seasons

Keywords: Thermostat setting points, Occupant behavior, Probabilistic model, Building energy performance simulation, Logistic regression. I. Introduction

Occupant behavior towards heating and cooling system setting is a very complex process that has been under investigation in the past years. As most of dynamic energy simulation tools consider energy consumption as fully deterministic with fixed and unrealistic schedules, the ability to predict properly the energy consumption is poor because of occupant interaction with indoor environment. In this study, the occupant in residential buildings is modeled as a probabilistic process. The occupant behavior related to thermostat settings is studied through experimental measurements collected in eleven buildings in France over a period of one year, by monitoring various parameters, including indoor air temperature, ambient temperature, indoor and outdoor relative humidity and indoor CO2. The occupant attitude was classified into three groups, active, normal and passive, according to the number of setting changes per year. The Logistic regression is adopted to calculate the probability of changing the thermostat setting by an occupant, in terms of different environment parameters. The results yield to a proposed model that can be implemented in simulation software, in order to take into account the occupant behavior in the assessment of realistic energy consumption.

Various activities have been modeled such as window opening, lighting and blind use [START_REF] Da Silva | Occupant's interaction with electric lighting and shading systems in real singleoccupied offices: Results from a monitoring campaign[END_REF][START_REF] Haldi | Interactions with window openings by office occupants[END_REF][START_REF] Andersen | Window opening behaviour modelled from measurements in Danish dwellings[END_REF][START_REF] Sutter | The use of shading systems in VDU task offices: A pilot study[END_REF]. These activities have shown to produce significant changes in energy use. In this study, a probabilistic model is developed to consider the effect of thermostat setting on energy consumption. Traditionally, the temperature regulation is typically modeled through deterministic scenarios in the dynamic thermal simulation tools, though this does not correspond to the real use of heating. For these reasons, several researchers proposed stochastic models to define the behavior patterns to be implemented in simulation software.

In the past decade, the probabilistic approach has been used to model the human behavior, as occupants have important influence on indoor environment. The institute of health watching (InVS) has found that occupants in France spend between 13.5 and 20 hours/day of their time at home [START_REF]Description du budget espace-temps et estimation de l'exposition de la population française dans son logement[END_REF]. Therefore, opening windows, switching lights and controlling HAVAC systems have important effects on energy consumption.

Recently, Shi and Zhao [START_REF] Shi | occupants' interactions with windows in 8 residential apartments in Beijing and Nanjing, China[END_REF] presented a stochastic model of occupant interactions with windows in 8 residential apartments in Beijing and Nanjing, relating the use of windows to many indoor and outdoor environmental factors, such as outdoor air temperature, outdoor relative humidity, outdoor wind speed, etc. They analyzed the influence of each parameter on the probability of window opening, using univariate and multivariate logistic regression. On the other hand, Haldi and Robinson [START_REF] Haldi | Interactions with window openings by office occupants[END_REF] proposed a model of window opening/closing by the occupants of the LESO building on the basis of 7 years of continuous measurements. Indoor air temperature and many environmental variables have been incorporated into the model. Several modeling approaches have been tested including logistic distributions, Markov chains and continuous time processes. The model has been validated and integrated in dynamic thermal simulation tools. Also, Fritsch et al. [START_REF] Fritsch | A stochastic model of user behaviour regarding ventilation[END_REF] proposed a model to predict the window opening angle in winter, on the basis of 8-months measurements taken every half hour in four office rooms facing the south in the LESO building. During the working hours, the transition probabilities between six possible opening angles over four orientations were defined.

In addition, several studies considered other occupant interactions such as blind and thermostat setting in building. Sutter et al. [START_REF] Sutter | The use of shading systems in VDU task offices: A pilot study[END_REF] studied the use of Venetian blinds in eight individual offices, every 15 min, over a period of 30 weeks. Their study showed that the number of use of manual systems is three times lower than that of automated systems. In addition, they concluded that when the screen quality is high in terms of emitted brightness level, the probability that the occupant accepts the high level of diffuse reflection increases, benefiting more from the available daylights. Furthermore, Andersen et al. [START_REF] Vinther Andersen | Modelling occupants' heating set-point prefferences[END_REF] studied the preferences in terms of temperature set, through a campaign of measurements on fifteen dwellings in Denmark in 2008. A linear regression was used to model the thermostatic valve positions of the radiators and the environmental variables (air temperature, relative humidity, wind speed and solar radiations). The results of this study indicate that the most influencing variables in the determination of the thermostatic valve positions are the outdoor temperature, relative humidity and wind speed.

Regarding uncertainties, Simona D'Oca et al. [START_REF] Simona | Effect of thermostat and window opening occupant behavior models on energy use in homes[END_REF] have modeled the occupant behavior in residential buildings by using probabilistic approaches developed to simulate both the effect of thermostat settings and window openings. The aim of this study was to compare mean values of the probabilistic distribution with a singular heating energy consumption value obtained by means of standard deterministic simulations. In order to highlight the effect of occupant behavior on energy consumption, simulations were performed for three different climate locations (Mediterranean, Continental and Nordic) and three comfort category conditions (Categories I, II, III). It can be noticed, that the deterministic approach (deterministic input) underestimated the heating consumption, when compared to probabilistic predictions taking into account the occupant behavior. As example, in Mediterranean climate and for Category of Comfort II, that the probabilistic distribution of heating loads ranges from 46 kWh/m²/year to 68 kWh/m²/year, with a maximum variation of 45%. Unlike, the heating load was 47 kWh/m²/year for the deterministic scenario. Whereas, the variation of the probabilistic distribution of heating loads in the Continental and the Nordic climates are 36% and 26% respectively for the same comfort category (Category II). Otherwise, the largest impact in delivered energy variation from deterministic to probabilistic simulations was observed for category III, with a maximum variation of 61%, 47% and 35% in Mediterranean,

Continental and Nordic climates respectively

In general, determinist scenarios are mostly applied to describe occupant activities in buildings. The occupant behavior is a complex and stochastic process [START_REF] Kashif | Simulating the dynamics of occupant behaviour for power management in residential buildings[END_REF]. Indeed, several parameters influence the occupant behavior and the energy consumption, such as gender, income, energy cost, health situation, clothing, activity level etc. [START_REF] Cohen | Energy requirements of households in Brazil[END_REF][START_REF] Gesche | The reality of English living rooms, A comparison of internal temperatures against common model assumptions[END_REF][START_REF] Karjalainen | Gender differences in thermal comfort and use of thermostats in everyday thermal environments[END_REF][START_REF] Lopes | Energy efficiency and energy savings in Japanese residential building-research methodology and surveyed results[END_REF]. These studies showed that the energy need is greatly affected by occupant behavior. Moreover, the probabilistic modeling presents a way to quantify the uncertainties and to provide an interval on possible outputs.

For example, Haldi and Robinson [START_REF] Haldi | Interactions with window openings by office occupants[END_REF] presented a mathematical method to model the occupant adaptive actions. This mathematical model, describing occupant behavior, needs to be implemented in simulation software. There is a need to consider the occupant interaction with indoor environment in order to decrease the gap between predicted and real energy use.

In the literature, heating profile is important parameter that influences the indoor temperature of residential buildings, with a large variation between different apartments [START_REF] Fabi | Influence of occupant's heating set-point preferences on indoor environmental quality and heating demand in n residential buildings[END_REF][START_REF] Huebner | The reality of English living rooms, A comparison of internal temperatures against common model assumptions[END_REF][START_REF] Firth | Targeting household energy efficiency measures using sensitivity analysis[END_REF][START_REF] Shipworth | Central heating thermostat settings and timing: building demographics[END_REF]. The occupant has strong influence due to his presence and activities in the building on one hand, and due to his control actions that aim to improve indoor environmental conditions, on the other hand [START_REF] Hoes | User behavior in whole building simulation[END_REF]. Xu et al. [START_REF] Baoping | Field investigation on consumer behavior and hydraulic performance of a district heating system in Tianj in China[END_REF] carried out investigations and field observations in China to study how occupants interact with thermostatic radiator valves (TRVs). They found that 26 % of the occupants never changed the set-point and 46 % of them rarely adjusted the TRV setting, which has remained unchanged for several months. The rest of the occupants modified the TRVs frequently. This study showed large variations in the use of thermostats and these differences are the results of occupant habits. Karjalainen [START_REF] Karjalainen | Gender differences in thermal comfort and use of thermostats in everyday thermal environments[END_REF] conducted a questionnaire survey in Finland in order to investigate gender effects on the adjustment of thermostat setting. The results have shown significant differences between the genders in terms of thermal comfort and use of thermostats. As a result, females are less satisfied with room temperatures than males and preferred a higher heating set-point than males, but males adjusted the thermostat setting more often than females did.

The studies mentioned above show that the set-point temperature is adjusted by occupants. Therefore, using a constant set-point temperature in the simulations will result in wrong estimations. Indeed, the designers calculate the energy consumption of a building by assuming that the heating set-point is always 19 °C and the cooling setpoint is always 26 °C [START_REF]Indoor environmental input parameters for design and assessment of energy performance of buildings addressing indoor[END_REF]. It is therefore mandatory to consider the variations in occupants' attitudes, preferences in indoor temperature and reactions with the indoor environment.

The development of behavioral models to predict occupant behavior inside buildings is a significant area of focus in the building sector. However, office buildings have been the objective of several surveys and behavior in residential building is not specifically treated. Furthermore, the most of the buildings monitored have been located in the UK, Switzerland and Asia, while France has been scarcely examined. In addition, in the literature, there is a lack of studies that evaluate the impact of thermostat changes in building energy consumption. As well, studies analyzing occupant behavior observed specificities in summer, but seasonal variations in behavior have yet to be taken into account. To answer the identified lacks, the present work provides new experimental results to show how the occupant behavior can impact the building energy use. In that case, models of the thermostat use, in residential buildings, were proposed to evaluate the impact of occupant behavior in building energy consumption when changing the thermostat. The description of the instrumented building is presented with statistical analysis of the obtained data. Afterward, the probabilistic analysis of the building energy performance is carried out to define the interaction patterns. The approach is constituted of two models: the univariate and multivariate logistic model of thermostat changes, as a function of indoor and outdoor environments and for different types of occupant behaviors (active, medium and passive) according to the seasons of the year (heating season and transition seasons). Finally, the study can be considered as a starting point defining the methodology of analysis and its advantages. It should be continued in the future with the purpose to not only show the importance of the probabilistic models of occupants' behavior but also to show how they can be coupled with building energy simulation software.

II. Data and methods

Experimental set-up

In this section, the building for which data have been collected is presented in order to provide the basis for the development model. The survey was performed on a collective social building (Figure 1) located at the city of "Cébazat" in France. It is a low energy building with 45.44 kWh/m²/year regarding the climate and geographical area.

The building has 18 apartments of type T2, T3 and T4 1 . It is divided into two sections separated by an expansion joint. Only the eleven apartments (T2 and T3) of the southern part were instrumented due to the limited budget. Table 1 lists the main features of the eleven monitored apartments.

The building is considered as independent building with an important mask at the north side (Figure 1). Built in 2010, the building has a concrete load-bearing structure. The eleven apartments are occupied by one to four people, as indicated in table 1.

Why considering this building

This building was chosen for several reasons: it is a low-energy building in the sense of the LEB-effinergie label. In addition being a social building, it was built to provide the maximum reduction of construction costs.

The orientation North-South, due to the land geometry, is the opposite of bioclimatic logic and monitoring of comfort will make it possible to survey problems of summer overheating. Finally, the owner wishes to make this building a showcase of its commitment to sustainable development and a prototype of his future constructions.

The envelope

The external envelope consists of the same type of wall found on most of the opaque vertical walls (Table 2).

The Reinforced concrete walls insulated with Xtherm Itex 32SE expanded polystyrene from Knauf, with thermal resistance R = 3.40 m².K/W. The walls of unheated area are insulated only from the inside. In several apartments, there are load-bearing walls which are used as partitions. The load-bearing walls are un-insulated and allow thermal transmission through the building. The roof is partially in wooden structure covered with Roman tiles insulated with 35 cm of cellulose wadding (R = 8 m².K/W). The remained roof is covered by green vegetation for which the insulation is provided by rigid polyurethane foam panels with composite facings, or expanded polystyrene (R = 5.15 m².K/W). The first floors are insulated to compensate any possible vacancy of shops in the ground Floor, the insulation is of type Unimat Sol Supra thickness 70 mm (R = 2.60 m².K/W).

Each intermediate floor is composed and insulated as follows:

• Concrete slab;

• 30 mm thick rock wool panels Isover Domisol LR30 on all surfaces;

• Extruded polystyrene foam panels of Isover Styrofoam 2000-A type on all surfaces, U = 0.29 W/ m².K, R = 2 .60m².K/ W; 1 T is used for type, which corresponds to a type of apartment with a number of main rooms (living room and bedrooms are the main rooms. While, the kitchen and bathrooms are considered as included in all the apartments). In the real estate sector in France, a T2, T3 or T4 is an expression used to designate a category of housing, which can be furnished or not. T2: Apartment 2 pieces including 1 bedroom and 1living room. T3: Apartment 3 pieces including 2 bedrooms and 1living room. T4: Apartment 4 pieces including 3 bedrooms and 1living room.

• Polyane film;

• 5 cm screed;

• Peripheral strip composed of 8 mm thick polyethylene foam.

Installed equipment

The ventilation is provided by a hygro-B single flow CMV 2 (controlled mechanical ventilation). The building is divided into two parts by an expansion joint. The apartments at the north of this joint are ventilated by a common extraction unit located on the roof. The southern part (the instrumented building) of the joint, the third floor is ventilated by two extraction groups. The heating is provided for each apartment by individual gas condensing boiler. The common areas are not heated. The T2 and T3 have combined boiler / DHW (domestic hot water) with micro accumulation of 23 kW. The building is uncooled. The domestic hot water (DHW) production is provided by individual gas boilers.

Data collection

A monitoring system was set up to record environmental parameters. The monitoring started on June 2011 and continues till now.

Table 3 presents the sensors and weather station characteristics. The time step used for data collection is one hour. The data is stored for a period of 21 days on the acquisition system located in the building's technical room.

The controllers are connected via Ethernet line to a server located in the local in owner's office, on which supervision software is installed. This software transmits by e-mails the raw data to be processed.

In each of the eleven instrumented apartments, the assessment of thermal comfort of occupants is carried out by measuring the indoor temperature Tint (°C), the indoor relative humidity RHint (%) and the CO2 concentration (ppm). The sensors are placed on the internal walls, about 1.5 m from the ground and at least 50 cm distant from the ceiling, the partition angles and any other dead zone. They are placed far from direct radiations, air streams, heat source and occupant proximity.

The layouts of the four apartments in the first-floor as well as the location of sensors in every measured room are specified in Figure 2. The plans of the two other floors and the sensors location are similar to those of the first floor. Each apartment has a central heating controller which transmits the set-point temperature. The heating season (winter) and the transition seasons (autumn and spring) corresponds to the period during which the central 2 A detailed explication on CMV is available in [START_REF] Evola | Controlled mechanical ventilation systems in residential buildings: Primary energy balances and financial issues[END_REF].

heating plant is operational, from September to May. One bedroom among the twelve apartments is equipped with carbon dioxide sensor. These sensors are used both to assess occupancy scenarios of the rooms where the measurements took place, in addition to indoor air quality.

To quantify the actual outdoor climate conditions applied to the building, a meteorological station is installed. This station allows the measurement of the following quantities:

-Dry bulb temperature (°C) and external relative humidity (%) -Diffuse and direct solar radiation on horizontal surface (W/m²).

-Wind speed (m/s).

-CO2 3 concentration of the outside air (ppm). This station is located on the roof of the building, away from solar masks as shown in Figure 3.

All the measurements were carried out in the living room and the bedroom of the apartments. The detail information relating to the location of the sensors of these apartments is shown in table 4. Moreover, occupant interactions with the set-point temperature were gathered by measurements of the most representative zones of the building. In this study, one thermostatic radiator valve (°C) in the living room is installed in each apartment.

III. Method 1. Statistical analysis

The objective of the study is to evaluate the influence on thermostat changing. The controls of the set-point temperature inside the apartments were monitored by the thermostat. Through these thermostat units, the occupants were permitted to change their set-points temperature for the rest of the day.

Figure 4 shows the distribution of heating consumption for each apartment during the heating season and the transition seasons. The heating consumption of the monitored apartments ranges from 441 kWh to 3157 kWh.

The ratio between the highest and the lowest consumptions is equal to 6 for type T2 and 7 for type T3. Moreover, regarding the season, important variation can be observed in the heating consumption of the 11 apartments, resulting in a ratio between highest and lowest heating consumption of 25, 25 and 17 in winter, spring and autumn respectively. Consequently, regarding the same apartments, a high variation is observed in heating consumption. These differences must be a result of differences in occupancy and differences in the occupants' behavior.

Large variations in occupant behaviors have been recorded. As shown in table 5 and Figure 5, the total number of thermostat changes strongly varies between apartments. The apartments were grouped according to the number of interactions with thermostat during the monitoring period. Three occupant profiles have been observed: Active, Passive and Medium. The probability of thermostat changes can be deduced for three different statistical models. It can be seen that the number of thermostat change is the highest in winter and spring and the lowest in autumn. It can also be noted that the apartment number twelve had the highest number of thermostat changes in winter, while the apartment number two and four had the lowest changes in autumn and spring.

A summary of indoor and outdoor parameters monitored during the survey is reported in Table 6. This gives the variation ranges for each parameter, as well as statistical analyses including the mean, max, min, and standard deviation values. Based on the results of the survey, the living room is considered to be occupied permanently in all the apartments. Apartment 04 had the highest indoor temperatures in winter and spring because of its orientation (East-facing), which provides direct solar radiation only in the morning. In contrarily, apartment 03 has the highest mean indoor temperature in spring (23.5 °C) owing to South-East its orientation which provides direct solar radiation all the day. Indoor humidity is very similar between the apartments, with a mean value of approximately 36% in winter, 42% in spring and 48% in autumn.

Figure 6 presents the distribution of the indoor temperatures during the heating season (winter) and transition seasons (autumn and spring). The median of indoor temperature fluctuate between 18 and 22°C, which indicates that the level of satisfaction in terms of comfort is very different between the apartments. This difference can be explained by household-specific attributes, such as age, income or social status. Contrary to expectations, the apartment orientation has shown low impact on the set-point temperature (table 1 and Figure 6). Moreover, the set temperature increases with the number of people in the apartment since the indoor temperature increase by 1°C to 3°C for identical apartments (same surface and orientation) with a larger number of occupants. Indeed, Kelly et al. [START_REF] Kelly | Do homes that are more efficient consume less energy?: a structural equation model of the English residential sector[END_REF][START_REF] Kelly | Predicting the diversity of internal temperatures from the English residential sector using panel methods[END_REF] showed that the number of occupants in a building have the largest effect on energy consumption. These results prove that for each extra person living in the building, the mean daily internal temperature increases by nearly 0.25 °C.

In addition, the apartment surface has no impact on the set temperature. The apartments of the intermediate floor have lower indoor temperature that in the other floors. Based on these measurements, a thermostat changes model is proposed. This model provides the probability to act on the thermostat of the living room.

Stochastic model of occupants interaction with thermostat in residential building

In this section, the model of occupant action is developed using logistic regression. In fact, the logistic regression models are very appropriate to predict probability p of a binary response variable when the explanatory variables x = (x1, x2,…, xn) are at particular values [START_REF] Haldi | Interactions with window openings by office occupants[END_REF].

In our study, the thermostat change is a binary response variable: the value of 1 indicates that the occupant changed the set-point temperature and 0 indicates that no change happened. The outdoor variables including Text, RHext, Vwind, CO2ext, F and indoor variable such as Tint-upper/lower and RHint are explanatory variables, as given in table [START_REF] Sutter | The use of shading systems in VDU task offices: A pilot study[END_REF]. The indoor temperature Tint-upper/lower represents the temperature of the upper and/lower apartment compared to the investigate apartment (Active, medium or passive).

The relationship between the set-point changes probability p of the response and each explanatory variable can be expressed by a univariate logistic regression as following:

= 1 - = 0 + (1)
where β0 is the intercept and β is the coefficient of the explanatory variable x. In the other hand, the relationship between the probability (p) of the binary response and multiple explanatory variables can be expressed by a multivariate logistic regression. Thus, in classical linear models, the probability can be assumed to take the form p(x) = β0 + β1x1 + … +βnxn where βn are the coefficients to be determined. However, this model would allow p to take values outside the interval [0 1]. It is then necessary to use a suitable transformation g of p(x) [START_REF] Haldi | Interactions with window openings by office occupants[END_REF].

The classical choice is the logistic transformation = log . The probability distribution is called logit distribution [START_REF] Haldi | Interactions with window openings by office occupants[END_REF]. The probability function is described by:

= 1, … , = exp 0 + 1 1 + ⋯ + 1 + exp 0 + 1 1 + ⋯ + ( 2
)
where p is the probability of an event, β0 is the intercept, β1+ … +βn are coefficients associated to each explanatory variable and x1+…+xn are the explanatory variables.

In our study, first the relationship between the probability of thermostat changing and single explanatory variable was analyzed using univariate logistic regression. Then, the multivariate logistic regression models were determined using the 'backward selection' procedure with the studied explanatory variables presented in table 7.

IV. Results

From the data collected over the seasons, the obtained univariate logistic regression parameters are given in table 8 and tables 9 to 10 (in appendix A). The regressions are presented in Figure 7 and the multivariate logistic regression parameters are listed in table 11. The statistical software R was used for all data analyses.

Univariate logistic model

Univariate logistic model allows as analyzing the relationship between the probability of thermostat changes and each single explanatory variable (table 7). The analysis of thermostat changes for the active occupant considers only the apartments where there is maximum action on the thermostat. The variables of the indoor and outdoor environment are considered in this evaluation.

Appendix C gives a summary of the possible criteria of goodness-of-fit for each of the models. Therefore, table 8 summarizes the regression parameters and the goodness-of-fit (GOF) estimators. The p-values are less than 0.001 for the outdoor temperature in autumn, winter and all the year, while they are higher for outdoor relative humidity, the solar flux and wind speed in the three seasons. Additionally, the indoor relative humidity and the indoor temperature of the upper/lower apartments had p-value < 0.001 in the different seasons and all the year. Although, the p-value of the CO2 concentration is less than 0.001 in autumn, spring and all the year only.

The above information indicates that the probability of thermostat changes has a significant correlation.

Indeed, a significant correlation is noticed in autumn with outdoor temperature, CO2 concentration, indoor relative humidity and the indoor temperature of the upper/lower apartment. Regarding winter, a correlation is noticed with outdoor temperature, indoor relative humidity and the indoor temperature of the upper/lower apartment. In spring, a correlation is noticed with outdoor CO2 concentration, indoor relative humidity and the indoor temperature of the upper/lower apartment. A correlation is noticed for all the year with the all explanatory variables except the wind speed. The probability of thermostat changes positively related to the outdoor relative humidity and negatively correlated with the rest of the explanatory variables.

In Figure 7 shows the observed probabilities and the corresponding logistic model during the all year (heating season and transition seasons), for the active occupant, for each explanatory variable. Thus, Figures 8 and9 in appendix B show the observed probabilities and the corresponding logistic model for the medium and passive occupants.

In general, the probability of thermostat changes decreases when the outdoor temperature increases. When the outdoor relative humidity is higher than 30%, the probability of thermostat changes tends to increase when the outdoor relative humidity increases. The probability of thermostat changes first increases as the wind speed increases. Then, when the wind speed becomes more than 9 m/s the probability decreases to 0 when the wind speed is kept increasing. The relationship between the solar flux, CO2 concentration and the probability of thermostat changes is less pronounced. As for the indoor relative humidity and indoor temperature for the upper/lower apartments, the probability related to the thermostat changes is monotonically decreasing function with respect to both variables.

Multivariate logistic model

The multivariate logistic regression is based on the assumption that the studied explanatory variables are independent. The explanatory variables in each multivariate logistic regression model were determined based on the forward and backward selection procedure using the Akaike information criterion [5, 6, and 29]. The purpose of this procedure is to create a model containing only explanatory variables that had a consistent effect on the probability. Rory et al. [START_REF] Jones | Stochastic behavioural models of occupants' main bedroom window operation for UK residential buildings[END_REF] presented the steps to be considered in practice.

The correlation between the explanatory variables for thermostat change models is assessed using the generalized variance inflation factor (GVIF). Table 12 shows the VIF and the GVIF analyses for thermostat change models. The GVIF 1/(2*Df) was used to assess all the thermostat changes models for the whole year and season in order to evaluate when the multicollinearity exists or not between the explanatory variables. A GVIF of 1 indicates that the explanatory variables are not correlated. As long as, a GVIF between 1and 5 indicates a moderate correlation between the explanatory variables, and more than 5 indicates a highly correlation [START_REF] Firth | Targeting household energy efficiency measures using sensitivity analysis[END_REF]. It can be seen that, the GVIF value of all the explanatory variables, are between 1 and 2, turned to be small (less than 5), therefore we can consider that there is no collinearity between the explanatory variables [START_REF] Jones | Stochastic behavioural models of occupants' main bedroom window operation for UK residential buildings[END_REF].

In order to compare the influence of the different explanatory variables, it is required to normalize these variables as following:

min Normal max min x-x x x -x = (3)
where xnormal is the normalized explanatory variable, x is the explanatory variable, xmax and xmin are respectively the maximum and the minimum observed values.

The multivariate logistic regression was carried out based on normalized explanatory variables and via backward and forward selection procedure. The parameters of the logistic model have been obtained using the 'step' in function R [START_REF] Vincent | R statistical software, one software to rule them all[END_REF]. Table 11 presents the coefficients of the explanatory variables included in the thermostat changes models.

For the active occupant, four multivariate thermostat models were obtained, according to seasons. Equations 4-7 show the most influential variables on thermostat changes behaviors in monitored apartments for the active occupant.

The multivariate logistic regression model of thermostat changes during the heating season is expressed in Equation 4. The Outdoor Temperature, Wind Speed, and Outdoor CO2 concentration are removed from the model because they do not have a consistent effect on the probability of the probability of thermostat changes.

The most influential factors are the outdoor relative humidity, the solar flux, the indoor temperature of the lower apartment and the indoor relative humidity. The regression coefficients of the indoor temperature of the lower apartment and indoor relative humidity are negative, indicating the negative correlation between thermostat changes and these two variables.

where p is the probability of thermostat changes in the living room, RHext is the outdoor relative humidity, F is the solar flux, RHint is the indoor relative humidity and Tint-lower is the indoor temperature of the lower apartment.

In transition seasons, the multivariate logistic regression model of thermostat changes behaviors is expressed by equation 5 which introduces the spring season and equation 6 which introduces the autumn season. During autumn, solar radiation and outdoor CO2 concentration variables are removed from the model because they do not have a consistent effect on the probability of a thermostat changes. The indoor temperature of the upper apartment is the most important factor. Wind speed is the least significant factor in the model, which varies from 0 to 2 m/s. The regression coefficient of the indoor relative humidity is positive, which indicates the overall increasing trend of indoor relative humidity with the increase of the thermostat change probability. On the other hand, during the spring season the variables of the outdoor temperature, the external and internal relative humidity, the solar radiation and the wind speed are eliminated from the model because they do not have a coherent effect on the probability of thermostat changes. The indoor temperature of the upper apartment is the least significant factor in the model. The regression coefficient of the outdoor CO2 concentration is negative, indicating the negative correlation between thermostat changes behaviors and this variable.

p T RH V p RH T • = - - - - + - (6)
where p is the probability of thermostat changes in the living room, RHext is the outdoor relative humidity, RHint is the indoor relative humidity, Text is the outdoor temperature, Vwind is the wind speed, CO2ext is the outdoor CO2 concentration and Tint-upper is the indoor temperature of the upper apartment.

In the all year model (heating season + transition seasons) expressed in Equation 7, solar radiation and relative indoor relative humidity are eliminated because they are insignificant. Instead of that, the thermostat changes behavior is more affected by the indoor temperature of the lower apartment and the outdoor temperature, followed by the wind speed, the outdoor relative humidity, and the outdoor CO2 concentration. The regression coefficient of the outdoor temperature is negative, which is similar to that of the autumn season. The external concentration of CO2 and the external relative humidity are the least significant factors in this model.

p T RH CO p V T - • = - - + + - + - ( 7
)
where p is the probability of thermostat changes in the living room, RHext is the outdoor relative humidity, Text is the outdoor temperature, Vwind is the wind speed, CO2ext is the outdoor CO2 concentration and Tint-lower is the indoor temperature of the lower apartment.

The indoor relative humidity, the indoor temperature of the upper/lower apartment as well as the outdoor relative humidity and the outside temperature contribute as a dominant factor in the majority of the proposed models. Solar radiation is significant only during the heating season (winter), which can be explained by the fact that the windows are toward North-East without direct sunlight coming in.

V. Implementation in Energy Models

The results obtained in the study provide the possibility of defining behavioral models of thermostat use to be implemented as a tool for energy simulation. Usually, the energy simulation software uses a deterministic scenario in nature, consequently it needs to interpret the probability of an action such as thermostat changes.

The implementation steps of the probabilistic models of thermostat changes to predict the effect on energy consumption are presented. Figure 10 shows a general scheme describing the implementation procedure for a dynamic simulation of thermostat changes for each time step. The first step consists of verifying the occupancy status. If the occupant is absent, the thermostat state is set as identical to its previous state. If the occupant is present, the logistic models are used to calculate the probability of thermostat changes according to the occupant profile (active occupant, medium occupant or passive occupant).

These probabilities are compared to random number in order to determine if the event takes place or not. The occupant changes the thermostat when the probability of the thermostat changes is more than the random number.

If the probability of thermostat changes is large than the random number, Predicted Mean Vote (PMV) is calculated. Indeed, the PMV is used to determine an index that allows knowing the percentage of dissatisfied.

Depending on the ranges of admissible PMV, three kinds of comfort zones can be considered [START_REF] Djongyang | Thermal comfort: a review paper[END_REF]. The PMV can be calculated using conventional parameters of the thermal environment (indoor temperature, indoor humidity), activity and clothing of occupant. In this work, the thermal comfort zone is usually spread between the sensation of light freshness (-1) and the sensation of slight heat (+1). If the PMV less than (-1), the occupant turns up the thermostat and if the PMV is higher than (+1) the occupant turn down the thermostat. Finally, the set-point was changed and the next time step starts.

VI. Discussion and limitation

In this study, it was noticed that the indoor conditions (indoor relative humidity and indoor temperature of the upper/lower apartments) impacts and describes thermostat changes action better than the outdoor conditions in the case of active occupant and univariate models. Moreover, the probability of thermostat changes given for multivariate models for active occupants tends to be always presented by the indoor environmental variables in all the cases (winter, spring, autumn and all the year). The main finding of this study underlines that the indoor environment of the upper/lower apartments is strictly interrelated to the thermostat changes.

The different probabilistic patterns of thermostat changes (active, medium and passive occupant for different seasons) are investigated. The behavior models could be considered as models of specific occupants.

Nevertheless, as the models were deducted from data of 11 different apartments including many residents, they could be considered as a representation of standard behavior patterns, enveloping the variation observed in the 11 apartments. For that, Haldi et al [START_REF] Haldi | A probabilistic model to predict building occupants' diversity towards their interactions with the building envelope[END_REF] discussed how different occupants could be assigned different model coefficients, to model the fact that different occupants will have different behavior patterns.

The present study is focused on developing thermostat changing models based on indoor and outdoor environment variables. However, other variables such as the psychological, social and economic behaviors should be considered. Gill et al. [START_REF] Gill | Low-energy dwellings: the contribution of behaviours to actual performance[END_REF] show that the behavioral and social factors account for 51%, 37%, and 11% of the variance in heat, electricity and water consumption respectively. So, future research should try to collect larger dataset.

In this study, the weather data for the all monitored apartments are specific only for one city. Hence, this study ignored the spatial difference of weather data. So, for the future analysis of occupant's interaction with thermostat, it is better to take on a large interval of meteorological data in order to have an international model and improve the accuracy of the research. Additionally, the behavior due to psychological and many social factors which were not evaluated in this study need to be studied as they may have stronger relationship with the thermostat changing.

VII. Conclusion

This study investigated occupant behavior in residential building during the heating period. Occupant interaction with thermostat was evaluated. The adaptive actions executed on thermostat changes have been correlated with the different season as well as the indoor and outdoor environmental variables. Hence, behavioral models have been suggested. The aim of this study is to assess whether thermostat changes are driven by the outdoor variables and/or the indoor variables.

Based on one year of observations of thermostat changes and indoor/outdoor variables in eleven apartments, and regarding the results, three occupant behaviors; active, medium and passive were noticed.

A model has been established for occupant interaction with thermostat and indoor/outdoor environmental variables. The indoor environment variables and the outdoor temperature are the most important variables in determining the univariate logistic regression models of thermostat changing. In this context, four multivariate regression logistic models of thermostat changes were proposed in this study. The results of multivariate logistic regression based on normalized explanatory variables illustrate that the thermostat changes is mainly affected by: indoor relative humidity and temperature of the lower apartment in winter, and by the outdoor CO2 concentration in the other seasons.

These models can be used in building performance simulation software to predict the energy consumption of residential buildings. The results of this study, recommended that when analyzing and modeling occupant behaviors in building, other variables, than just indoor/outdoor, should be taken into account. Ongoing studies have been initiated to take into account the psychological, social and economic factors on energy building simulation for a better energy use prediction. 2)

Null n M Nagel ke n M LL LL R LL - -- = -- (8) 2 1
M M cF adden null LL R LL = - (9)
where the null model is the logistic model with just the constant and the M model contains all the predictors in the model, based on n observations. The McFadden and Nagelkerke R² are the easiest to understand: when the regression is useless, the explanatory variables explain nothing, the indicator is 0; when the regression is perfect, the indicator is 1

List of Figures

  int_

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 123456 Fig.1. External view of monitored building Fig.2. View plan of the first-floor apartments with sensor locations

Fig. 7 .

 7 Fig.7. Thermostat change probabilities in terms of explanatory variables for the active occupant: univariate model

Fig. 8 .

 8 Fig.8. Thermostat change probabilities in terms of explanatory variables for Medium occupant: univariate model

Fig. 9 .Fig. 10 .

 910 Fig.9. Thermostat change probabilities in terms of explanatory variables for Passive occupant: univariate model

Fig. 1 .Fig. 2 .

 12 Fig.1.External view of monitored building

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 3456 Fig.3. Weather station

Fig. 7 .

 7 Fig.7. Thermostat change probabilities in terms of explanatory variables for the active occupant: univariate model

  autumn, the univariate logistic regression model with CO2 concentration, indoor relative humidity and indoor temperature of the upper/lower apartment had the highest values of Nagelkerke's R², McFadden's R² and AUC. This indicates that the univariate logistic regression model with these variables had the best predictive capability. Hence, the lowest values of the goodness-of-fit indicate the poor predictive capabilities of the model.

In winter, the univariate logistic regression model with the outdoor temperature, indoor relative humidity and the indoor temperature of the upper/lower apartments had the highest values of Nagelkerke's R², McFadden's R² and AUC. In the other hand, the CO2 concentration and indoor relative humidity had the higher values of Nagelkerke's R², McFadden's R² and AUC for the univariate logistic regression model in spring. Finally, the goodness-of-fit estimators indicate that the outdoor temperature, the indoor relative humidity and indoor temperature of the upper/lower apartment are the principal driver for the univariate logistic regression model for all the year.

Table 6

 6 Summary of measured settings

		Variable		Max			Min			Mean			St. Dev
			W *	S*	Au*	W*	S*	Au*	W*	S*	Au*	W*	S*	Au*
		Temperature (°C)	17.2	32.8	28	-13.4	0.1	0	4.12	11.89	13.67	5.84	5.42	5.73
		Solar flux (w/m²)	589.4	915.6	672	0	0	0	46.39	121.8	25.10	105.12 204.17 95.50
	Outdoor	Outdoor RH (%)	98.9	98.4	98	28.4	7	24	73.77	63.72	71.35	12.43	16.88	16.26
		CO2 concentration (ppm)	3020	770	2180 190	330	840 709.12 579.56 1169.93 241.45 64.31 202.77
		Wind speed (m/s)	17.73	11.94	2	0	0	0	1.42	1.52	0.014	1.67	1.62	0.17
	Apartment 01	Indoor temperature (°C)	21.6	23.4	24	18.75 12.5	20	19.6	19.17	21.32	0.34	1.26	1.3
		Indoor RH (%)	82.6	81.7	71	32.4	32.6	44	48.62	55.79	57.79	5.93	7.06	5.36
	Apartment 02	Indoor temperature (°C)	22.15	25.35	25	11.05 12.95 18	17.07	20.6	21.20	2.65	1.71	1.57
		Indoor RH (%)	79.1	88.3	72	16.4	25.7	31	35.87	42.06	49.31	8.41	8.55	7.67
	Apartment 03	Indoor temperature (°C)	23.85	26.8	28	15.5	16	20	20.82	21.88	23.25	0.75	1.54	1.61
		Indoor RH (%)	54.9	67.3	60	14.9	16.1	30	30.85	38.19	43.78	7.04	7.45	7.38
	Apartment 04	Indoor temperature (°C)	23.65	25.4	27	19.1 19.55 20	21.4	22.22	22.7	0.88	0.89	1.21
		Indoor RH (%)	51.5	66.1	62	19.8	26.2	38	36.03	40.74	47.21	5.3	6.72	5.48
	Apartment 08	Indoor temperature (°C)	21	22.6	24	18.3	16.8	19	19.65	19.6	20.95	0.48	1.22	1.37
		Indoor RH (%)	53.9	64.2	71	18.4	27.9	36	39.22	43.61	50.65	5.96	5.63	7.24
	Apartment 09	Indoor temperature (°C)	22.3	25.85	27	12.55 11.85 19	17.74	19.43	21.91	1.27	1.43	1.9
		Indoor RH (%)	56	77.6	69	17.4	24.4	31	35.07	41.70	47	7.08	9.07	7.33
	Apartment 10	Indoor temperature (°C)	24.75	26.25	26	11.35 10.6	18	17.19	19.14	22.33	1.71	2.27	1.8
		Indoor RH (%)	56	83.4	63	16.8	24.3	29	35.11	41.83	45.29	7.59	9.82	6.88
	Apartment 11	Indoor temperature (°C)	22.35	25.65	26	17.55 18.85 20	20	21.33	22.18	0.65	1.36	1.55
		Indoor RH (%)	58.4	64.9	67	23.7	28.3	33	37.15	40.40	47.17	6	6.68	6.65
	Apartment 15	Indoor temperature (°C)	22.2	23.9	24	15.45 15.4	18	21.14	20.27	21.77	0.53	0.98	1.62

*: winter, S*: spring, Au*: autumn

Acknowledgements

• The data analyzed in this paper is drawn from Cerema (Center of Studies and Expertise on Risks, Environment, Mobility and Development) of Clermont-Ferrand. The authors would like to thank Mr. Cédric Besairie, Mr. Olivier Bonneau, Mr. Laurent Selve and Mr. Nicolas Laveissiere for their contribution in creating and managing the data set.

• The Conseil Général de l'Alier -France, is grateful to have provided financial support for this study.

Appendix C. Statistical tests for logistic models 1. p-value for models

The p-value is the probability under a specified statistical model that a statistical summary of the data would be equal to or more extreme than its observed value. The p-value for a model determines the significance of the model compared with the null model. So the p-value for the model indicates if there is a significant relationship described by the model. A p-value provides one approach to summarizing the incompatibility between a particular set of data and a proposed model for the data. The most common context is a model, constructed under a set of assumptions, together with a so called "null hypothesis." Often the null hypothesis postulates the absence of an effect, such as no difference between two groups, or the absence of a relationship between a factor and an outcome. Smaller pvalues do not necessarily imply the presence of larger or more important effects, and larger p-values do not imply a lack of importance or even lack of effect. Any effect, no matter how tiny, can produce a small p-value if the sample size or measurement precision is high enough, and large effects may produce unimpressive p-values if the sample size is small or measurements are imprecise. Similarly, identical estimated effects will have different pvalues if the precision of the estimates differs [START_REF] Wasserstein | The ASA's statement on p-values: context, process, and purpose[END_REF][START_REF]Perturbations on the uniform distribution of p-values can lead to misleading inferences from null-hypothesis testing[END_REF].

Area under ROC curve

In this study, the area under ROC curve is called the AUC index. It is a direct measure of the discriminating power of a given model. The AUC of the logistic model have been obtained using the software R. The area under the ROC (Receiver Operating Characteristic) curve range from zero to one and provides a measure of the model's ability to discriminate between those subjects who experience the outcome of interest versus those who do not.

ROC curves plot sensitivity as a function of specificity for different values of the cutpoint between 0 and 1. A higher value of sensitivity for a given value of specificity indicates better performance [START_REF] Haldi | Interactions with window openings by office occupants[END_REF][START_REF] Hosmer | Applied logistic regression[END_REF].

As a general rule:

: this suggests no discrimination. • If 0.6 ≤ AUC < 0.8 : this is considered acceptable discrimination.

• If 0.8 ≤ AUC < 0.9 : this is considered acceptable discrimination.

• If AUC ≥ 0.9 :this is considered outstanding discrimination.

The Nagelkerke R² and the McFadden R²

The Nagelkerke R² or the McFadden R², called the coefficient of determination and generalized R², measures the proportion of explained deviance in a model and are defined as [START_REF] Rakotomalala | Pratique de la Régression Logistique[END_REF]:

List of Tables


MD Rody El Nawar

MD, PhD Bertrand Lapergue

MD, PhD Michel Piotin

MD, PhD Benjamin Gory

MD, MSc Raphael Blanc

MD Arturo Consoli

MD, PhD Georges Rodesch

MD, PhD Mikael Mazighi

MD Frederic Bourdain

BST Maéva Kyheng

BST Julien Labreuche

MD Fernando Pico
email: fpico@ch-versailles.fr

Higher Annual Operator Volume is Associated with Better Reperfusion Rates in Stroke Patients Treated by Mechanical Thrombectomy in the ETIS Registry

Keywords: Mechanical thrombectomy, Acute Ischemic Stroke, Operator Volume, ETIS register

Background: Mechanical thrombectomy (MT) is a level IA treatment in acute ischemic stroke (AIS) patients. The operator's effect has been found to be an independent predictor for clinical outcome and technical performance in interventional cardiology. Purpose: The aim of this study was to determine if individual operator characteristics have an impact on reperfusion and procedural complication rates. Methods:From the ETIS (Endovascular Treatment in Ischemic Stroke) study, a prospective, multicenter, observational real world MT registry, we included allAIS patients consecutively treated by MT between January 2012 and March 2017 in 3 high volume comprehensive stroke centers by 19 operators. We assessed the effect of individual operator characteristics on successful reperfusion, defined as modified Thrombolysis In Cerebral Infarction 2b/3 at the end of MT, and procedural complications using a multivariable hierarchical logistic regression models. Results: A total of 1541 anterior and posterior AIS patients were enrolled (mean age 67 years; median NIHSS 16). There was a significant operator effect on successful reperfusion, with an intraclass correlation coefficient (ICC) of 0.036 (P=0.046), but not on complications (ICC=0). There was a dose response relationship between annual operator volume and successful reperfusion rate (P=0.003) with an adjusted Odds Ratio for successful reperfusion equal to 2.52 (95% CI, 1.37-4.64) for patients treated by an operator with annual volume ≥40 MT/year compared to those treated by operator with less than 14 MT per year (first tertile). Nevertheless, this result did not translate to better clinical outcomes. Conclusions: Our data suggest that operator volume of MT per year have a positive impact in AIS patients on successful reperfusion but not on clinical outcomes nor on complication rate. Further studies are warranted to investigate threshold procedure numbers associated with better outcomes.

INTRODUCTION

Endovascular mechanical thrombectomy (MT) is considered a class I, level of evidence A, recommendation for immediate revascularization of proximal intracranial arterial occlusion of the anterior circulation [START_REF] Berkhemer | A randomized trial of intraarterial treatment for acute ischemic stroke[END_REF][START_REF] Goyal | Randomized assessment of rapid endovascular treatment of ischemic stroke[END_REF][START_REF] Campbell | Endovascular therapy for ischemic stroke with perfusionimaging selection[END_REF][START_REF] Saver | Stent-retriever thrombectomy after intravenous t-PA vs. t-PA alone in stroke[END_REF][START_REF] Jovin | Thrombectomy within 8 hours after symptom onset in ischemic stroke[END_REF][START_REF] Powers | American Heart Association Stroke Council. 2015 American Heart Association/American Stroke Association focused update of the 2013 guidelines for the early management of patients with acute ischemic stroke regarding endovascular treatment: a guideline for healthcare professionals from the American Heart Association/American Stroke Association[END_REF]. According to the Joint Commission in the collaboration with the American Heart Association/American Stroke Association, stroke centers must present precise standards and advanced stroke certification to be considered as a MT-capable stroke centers.

Moreover, the Joint Commission propose a minimum volume of 12 MT procedures per year or 24 over the past 2 years accomplished by 2 to 3 experienced operators [START_REF]Proposed requirements for the new thrombectomy-capable stroke center certification program[END_REF]. Nevertheless, these thresholds arenot supported by strong evidence. There is a need for studies assessing therelationship between operator experience, operator volume, success reperfusion, and complications rates.

Robust data support the association of higher complications rate with low operator's experience in several cardiological interventions such as percutaneous coronary intervention (PCI), coronary stent placement, and Percutaneous Left Atrial Appendage Closure (PLAAC) [START_REF] Klein | Does low individual operator coronary interventional procedural volume correlate with worse institutional procedural outcome?[END_REF][START_REF] Kastrati | Operator volume and outcome of patients undergoing coronary stent placement[END_REF][START_REF] Reddy | Safety of Percutaneous Left Atrial Appendage Closure: Results from the Watchman Left Atrial Appendage System for Embolic Protection in Patients With AF (PROTECT AF) Clinical Trial and the Continued Access Registry Circulation[END_REF]. The main purpose of our study was to analyse the impact of the individual operator characteristics on reperfusion and complication rates at the end of MT procedure.

METHODS

Patient population

The study population wasselected from the prospective observational multicenter ETIS (Endovascular Treatment in Ischemic Stroke) registry referred to three large comprehensive stroke centers in France. All patients were identified from ETIS between January 2012 and March 2017 [START_REF] Desilles | Successful reperfusion with mechanical thrombectomy is associated with reduced disability and mortality in patients with pretreatment diffusionweighted imaging-alberta stroke program early computed tomography score≤ 6[END_REF]. The number of operators in this registry was 19. Patients enrolled in this study presented an acute ischemic stroke (AIS) with occlusion of the internal carotid artery or the middle cerebral artery (M1 and M2 segments) or vertebro-basilar arteries and were treated with MT by either contact aspiration or stent retrievers. A more detailed description of the technique has been published previously [START_REF] Desilles | Successful reperfusion with mechanical thrombectomy is associated with reduced disability and mortality in patients with pretreatment diffusionweighted imaging-alberta stroke program early computed tomography score≤ 6[END_REF].A local ethics committee and the French Data Protection Agency approved the use of patient data for this research protocol. In accordance with the French legislation, informed consent was not needed from patients because this study used analysis of anonymized data collected prospectively as a part of routine clinical care.

Patient's characteristics

The following clinical characteristics of each patient were analyzed: age, gender, vascular risk factors, treatments before the procedure, vital signs before treatment, the severity of the acute ischemic stroke using the National Institutes of Health Stroke Scale (NIHSS) score at admission and 24 hours after the initiation of treatment assessed by a certified medical professional or by a stroke neurologist implicated in the acute management of patient post MT, and the degree of disability or dependence in the daily activities using themodified Rankin Scale at day 90. Furthermore, the following radiological imaging characteristics were identified: 1) DWI-ASPECT score and CT brain ASPECT scoreeach ASPECTS region was scored 0 if abnormal and 1 if normal, 2)site of occlusion in the middle cerebral artery M1 or M2, 3) mTICI score, 4) imaging results 24 hours after MT to evaluate the presence of a hemorrhagic transformation.

Concerning treatment and procedure, we assessed: 1) time from symptom onset to initiation of intravenous thrombolysis, to groin puncture, and to final reperfusion, 2) the use of general or local anaesthesia during the MT.

Operator's experience characteristics

Operator characteristics were defined according to the number of MT performed per year during the study and according to the year of the first MT. The name of the operator was checked on signed interventional report. The experience of operator was estimated by the year of first MT. Operator were divided in 2 groups (≤ 2010 or > 2010), according to the median year of first MT in this sample.

Outcome

The primary study outcome was the angiographic success rate defined by a reperfusion of the occluded artery evaluated by the modified Thrombolysis In Cerebral Ischemia (mTICI) scores of 2b/3 (considered as restoration of flow to more than 50% of the involved brain territory at the end of the MT procedure). Secondary outcomes include the favourable outcome and procedural complications. Favourable outcome was evaluated by the modified Rankin Scale (mRS) at 90 days post MT, during face-to-face interviews or via telephone conversations with the patient, their relatives, or their general practitioner.

The procedural complications during and post MT collected from register were: intracranial hemorrhage (ICH), subarachnoid hemorrhage (SAH), groin complication (formation of a groin hematoma, retroperitoneal hematoma, femoral artery pseudo-aneurysm), distal limb artery occlusion by migrated emboli, recurrent AIS, vessel perforation or dissection, vasospasm, device fracture, infection, death. We grouped ICH according to the classification of the European Cooperative Acute Stroke Study (ECASS) 1criteria: parenchymal hematoma type 1 and 2, hemorrhage infarction type 1 and 2 [START_REF] Fiorelli | Hemorrhagic transformation within 36 hours of a cerebral infarct[END_REF]. Symptomatic ICH was considered in patients presenting within 24 hours an increase of 4 or more points in their NIHSS score caused by the hemorrhage.

Statistical Analysis

Continuous variables are expressed as means (standard deviation) in the case of normal distribution or medians (interquartile range) otherwise. Categorical variables are expressed as numbers (percentage). Normality of distributions was assessed using histograms and the Shapiro-Wilk test. Main patient's level characteristics were compared between patients with and without successful reperfusion, with and without a favourable outcome, and between patients with and without procedure complications using Student t test (or Mann-Whitney U test) for continuous variables and Chi-Square test for categorical variables.

To assess the effect of operators on each outcome (successful reperfusion, favourable outcome and procedural complications), we used a multivariable mixed (hierarchical) logistic regression model including all patient-level characteristics associated with outcome in bivariate analyses (P<0.20) as fixed effects and operators as a random effect. We derived from this model the intraclass correlation coefficient (ICC) which represents the outcome variability attributable to individual operator. We further investigate the association of the two main operator characteristics (annual volume categorized into 3 levels and operator experience categorized in two levels using date of January 2010) with each outcome by including theannualoperatorvolume as covariate into the previous multivariable hierarchical logistic regression model. Odds ratios (OR) for middle and upper relative to lowest tertile of annual operator volume were calculated as effect size.Statistical testing was conducted at the two-tailed -level of 0.05. Data were analyzed using the SAS software version 9.4 (SAS Institute, Cary, NC).

RESULTS

From January 2012 to March 2017, 1541 AIS patients treated by MT in 3 French comprehensive stroke centers. During the study period, a total of 19 operators performed MT with a median number of MT per year of 27 (range from 5 to 69MT per operator per year). Patient's characteristics are reported for overall study population.

Successful Reperfusion and Clinical Outcome

The overall rate of successful reperfusion was 76.6% (n=1175; 95%CI, 74.5-78.7). As shown in Table 1, intravenous thrombolysis, local anaesthesia, diabetes and higher ASPECTS score were significantly associated with successful reperfusion in univariate analyses. In multivariable hierarchical logistic regression model controlling for all patient-level characteristics associated with successful reperfusion(P<0.20), the effect of operator on successful reperfusion was significant (P=0.046), with an ICC of 0.037 meaning that 3.7% of the successful reperfusion variability was due to interoperator variation.

When annual operator annual volume was included in multivariable hierarchical logistic regression model as covariate, we found a dose response relationship between annual operator volume and successful reperfusion (P=0.003 associated with one-level increase) (Table 2A).

Compared with patients treated by operator with annual volume less than 14 MT, the patientlevel characteristic adjusted OR of successful reperfusion was 1.75 (95%CI, 1.02-2.99) for patients treated by an operator with annual volume between 14 and 39 and was 2.52 (95%CI, 1.37-4.64) for patients treated by an operator with annual volume equal or greater than 40 MT.

No association was found between the year of the first MT(≤ 2010 or > 2010), taken as a marker of operator experience, and the rate of successful reperfusion (P=0.85).

Clinical favourable outcome was achieved in 44.1% (n=680; 95%CI, 41.7-46.6). In multivariable hierarchical logistic regression model controlling for all patient-level characteristics associated with clinical favourable outcome (P<0.20), the effect of operator on successful reperfusion was not significant (P=0.13), with an ICC of 1.5%. In addition, operator characteristics had no effect on clinical favourable outcome rate (Table 2B).

Procedural Complications

Two hundred and forty seven patients (16.4%, 95%CI, 14.5-18.2) presented at least one procedural complication. Embolization in new territory (n=102) was the most frequent complication followed by arterial perforation (n=67), arterial dissection (n=63) and spasm (n=24). As shown in Table 3, higher rate of procedural complications was associated with no prior history of antiplatelet medication, higher admission NIHSS score, lower ASPECTS score, and less often M1 middle cerebral artery occlusion. In multivariable hierarchical logistic regression model controlling for patient-levels characteristics associated with procedure complications (P<0.20), we found no effect of operator (ICC=0). In addition, when annual operator volume was included in multivariable hierarchical regression model, we found no change in odds ratio of procedural complication with increasing annual operator volume (P=0.67, Table 4) nor with the year of first MT (P=0.91). Of note, none of the MT complications neededan urgent neurosurgical intervention directly related to the procedure.

DISCUSSION

Our large multicenter real-world MT cohort, including 1541 consecutive anterior and posterior AIS patients documented the correlation between higher operator's volume and successful reperfusion rate with an intraclass correlation coefficient of 0.037 (P=0.046), but not on complications. We observed dose response relationship between annual operator volume and successful reperfusion (P=0.003). This finding is in line with previous studies in other interventions. For example, characteristics of operators such as volume of procedures per year and number of years of practice, have been found to be an independent clinical and radiological outcome predictorin interventional cardiology for myocardial infarction syndromes in several studies [START_REF] Klein | Does low individual operator coronary interventional procedural volume correlate with worse institutional procedural outcome?[END_REF][START_REF] Kastrati | Operator volume and outcome of patients undergoing coronary stent placement[END_REF][START_REF] Hannan | Incomplete revascularization for percutaneous coronary interventions: Variation among operators, and association with operator and hospital characteristics[END_REF][START_REF] Xu | Impact of operator experience and volume on outcomes after left main coronary artery percutaneous coronary intervention[END_REF]. Moreover, several studies, such as CAPTURE 2, analyzing the association of the physician variables and outcomes in CAS, showed that one of the most important determinants of perioperative carotid artery stenting outcomes was the operator carotid stenting volume [START_REF] Gray | Influence of site and operator characteristics on carotid artery stent outcomes: analysis of the CAPTURE 2 (Carotid ACCULINK/ACCUNET Post Approval Trial to Uncover Rare Events) clinical study[END_REF].However, this annual volume operator effect on successful reperfusion rates was not found to have an impact on mRS≤2 at 90 days in our study. We can hypothesize that our study was underpowered to observe an effect on clinical outcome, as the 90-day mRS scores integrate other factors that the sole success of MT such as individual and environmental factors [START_REF] Goyal | Poor clinical outcome despite successful arterial recanalization. What went wrong? How can we do better?[END_REF].

To date, only one study performed on the MR CLEAN registry based on 313 patients showed no significant relation between the level of experience, neurological adverse events and poor outcomes in operators with less than 50 MT procedures [START_REF] Beumer | The relationship between interventionists' experience and clinical and radiological outcome in intra-arterial treatment for acute ischemic stroke. A MR CLEAN pretrial survey[END_REF].

In our study, two hundred and forty seven patients had complications. The most common one was embolization in a new territory (7%). The overall rate of complications was not statistically significant between the operators' experience and volume. There was no significant operator variation for complications. This finding is somewhat controversial in the literature for other interventions. In therandomized CREST trial, there was no association between operator's volume and rate of complicationsin carotid revascularization [START_REF] Hopkins | The Carotid Revascularization Endarterectomy versus Stenting Trial: credentialing of interventionalists and final results of lead-in phase[END_REF]. In contrast, experience and high volume had better prognosis on many procedures such as carotid artery stenting, coronary stenting, and percutaneous left atrial appendage closure [START_REF] Kastrati | Operator volume and outcome of patients undergoing coronary stent placement[END_REF][START_REF] Reddy | Safety of Percutaneous Left Atrial Appendage Closure: Results from the Watchman Left Atrial Appendage System for Embolic Protection in Patients With AF (PROTECT AF) Clinical Trial and the Continued Access Registry Circulation[END_REF][START_REF] Shishehbor | Experience and outcomes with carotid artery stenting: an analysis of the CHOICE study (Carotid Stenting for High Surgical-Risk Patients; Evaluating Outcomes Through the Collection of Clinical Evidence)[END_REF][START_REF] Carrafiello | Carotid artery stenting: Influence of experience and cerebrovascular risk factors on outcome[END_REF][START_REF] Kimmel | The relationship between coronary angioplasty procedure volume and major complications[END_REF][START_REF] Levine | ACCF/AHA/SCAI guideline for percutaneous coronary intervention: executive summary: a report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines and the Society for Cardiovascular Angiography and Interventions[END_REF].

Our analysis also demonstrated a better reperfusion rate associated with female gender, patients on antiplatelet therapy, high ASPECT score before MT and M1 segment of the middle cerebral artery occlusion as previously reported [START_REF] Nogueira | Predictors of good clinical outcomes, mortality, and successful revascularization in patients with acute ischemic stroke undergoing thrombectomy: pooled analysis of the Mechanical Embolus Removal in Cerebral Ischemia (MERCI) and Multi MERCI Trials[END_REF][START_REF] Tsivgoulis | Association of Pretreatment ASPECTS Scores with tPA-Induced Arterial Recanalization in Acute Middle Cerebral Artery Occlusion[END_REF][START_REF] Luo | Factors Associated with 90-Day Outcomes of Patients with Acute Posterior Circulation Stroke Treated By Mechanical Thrombectomy[END_REF][START_REF] Raymond | Patient selection for mechanical thrombectomy in posterior circulation emergent large-vessel occlusion[END_REF][START_REF] Yoon | Predictors of good outcome after stent-retriever thrombectomy in acute basilar artery occlusion[END_REF].

Our findings should not be taken asa guideline, but we noted that a volume of at least 40 MT procedures per operator per year,that is less than one per week,was associated with better reperfusion rate. Currently, the Joint Commission has suggested a minimum of 12 MT during the previous year, or 24 MT over the past 2 years to certificate a thrombectomy-capable stroke center [START_REF] Fargen | Practice makes perfect: establishing reasonable minimum thrombectomy volume requirements for stroke centers[END_REF]. Based on the minimum number of 75 coronary interventions/operator/year required to obtain formal certification in coronary interventional procedures, it is important to establish a minimal number of procedures/operator/year to accredited each operator and MT-capable stroke centers [START_REF] Levine | ACCF/AHA/SCAI guideline for percutaneous coronary intervention: executive summary: a report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines and the Society for Cardiovascular Angiography and Interventions[END_REF]. Our results didn't allow to establish a threshold volume for accreditation but added valuable data on this topic.

Our study has several limitations. First, it was done in 3 large volume stroke centers. It will be interesting to compare in the future our results with other stroke centers with a lesser volume of MT per year. Secondly, the majority of ourpatients enrolled in this study were treated during the first 6 hours. Several studies such as DAWN and DEFUSE 3 studies showed the benefit of MT beyond 6 hours of last seen well [START_REF] Nogueira | Thrombectomy 6 to 24 hours after stroke with a mismatch between deficit and infarct[END_REF][START_REF] Albers | Thrombectomy for stroke at 6 to 16 hours with selection by perfusion imaging[END_REF]. It will be interesting to compare in the future, the operator volume effect on reperfusion and complication rate between 6 and 24 hour after AIS onset. Thirdly, in our study, we analyzed only the volume of mechanical thrombectomy and not all kind of interventions on brain vessels such as embolization of intracranial aneurysm or AVM. This issue could be assessed in further studies in particular if the volume of all intervention on brain vessel have and added value on better outcomes that the sole volume of mechanical thrombectomy. Lastly, no formal sample size was calculated for the present study's objectives. We calculated that with 1500 patients, we have a precision greater than 2.55% to estimate the primary outcome rate (successful reperfusion).

CONCLUSIONS

Our data suggest that successful reperfusion in AIS patients treated with MT is dependent on the operator volume of MT per year. We did not find any relation between operator volume and complication rates, and the better procedure outcome did not translate into better clinical outcomes. Further studies are warranted to confirm these findings and investigate threshold procedure numbers associated with better outcomes."

ACKNOWLEDGEMENT

We thank Mary Osborne-Pellegrin for her help in editing the final draft of the article.