Senior Member, IEEE Jean-François Brudny

Tifany Szkudlapski

Fabrice Morganti

Member, IEEE Jean-Philippe Lecointe

Method for Controlling the PWM Switching: Application to Magnetic Noise Reduction

Keywords: Alternating current (ac) variable-speed drives, noise of magnetic origin, pulsewidth modulation (PWM) supply, switching harmonic control

This paper presents an analytical method that makes it possible to define the pulsewidth modulation (PWM) supply output voltage spectral content, particularly the harmonic phase sequences, without switching instant determination. The results obtained from these developments lead to define a PWM control strategy that allows deleting some switching harmonics in order to reduce undesirable effects. Numerical studies and experiments confirm the theoretical approach and this harmonic control strategy.

I. INTRODUCTION

T HE inverters supplying alternating-current electrical ro- tating machines are commonly used for many industrial applications [START_REF] Marian | High-performance motor drives[END_REF]. If the sinus-triangle pulsewidth modulation (PWM) is still widely used [START_REF] Holmes | Pulse Width Modulation for Power Converters-Principles and Practice[END_REF], new techniques, such as space vector PWM (SVPWM), have been developed [START_REF] Da Silva | Pulsewidth modulation strategies[END_REF]. However, the use of such converters generates some undesirable effects tied to the switching three-phase harmonic (STPH) systems. Some of them concern additional losses [START_REF] Khomfoi | Influence of PWM characteristics on the core losses due to harmonic voltages in PWM fed induction motors[END_REF], the acoustic noise of magnetic origin [START_REF] Iida | Study on magnetic noise caused by harmonics in output voltages of PWM inverter[END_REF], [START_REF] Pellerey | Active reduction of electrical machines magnetic noise by the control of low frequency current harmonics[END_REF], and the overvoltages induced in the windings, leading to the premature aging of the electrical insulation system [START_REF] Mihaila | A simulation method to predict the turn-to-turn voltage spikes in a PWM fed motor winding[END_REF]. To get away from these effects, the simplest solution consists of adding a filter at the inverter outputs. However, because of their cost and their dimensions, they are not always compatible with the industrial constraints. That is why the inverter output signals can be directly modified with multilevel converters, for example [START_REF] Malinowski | A survey on cascaded multilevel inverters[END_REF].

The magnetic noise is mainly generated by Maxwell's forces, which result from the square of the air-gap flux density wave, composed of the fundamental and harmonic components due to the toothing and the switching. The double products, which combine the fundamental with the harmonics, are at the origin of phenomenon vibration, leading to acoustic effects that are particularly annoying if the force frequencies are close to the natural resonances of the stator. There are many studies [START_REF] Da Silva | Pulsewidth modulation strategies[END_REF] about the reduction of this noise, with appropriate PWM strategies [START_REF] Besnerais | Characterization and reduction of audible magnetic noise due to PWM supply in induction machines[END_REF], [START_REF] Kim | A Study on the design process of noise reduction in induction motors[END_REF]. Some of them increase the switching frequency [START_REF] Hashemi | Acoustic noise reduction for an inverter-fed three-phase induction motor[END_REF] or use random PWM techniques [START_REF] Habetler | Acoustic noise reduction in sinusoidal PWM drives using a randomly modulated carrier[END_REF]- [START_REF] Lai | Prediction of noise radiation from induction motors[END_REF]. Leleu et al. [START_REF] Leleu | Reduction of vibrations in an induction machine supplied by high power PWM inverter[END_REF] compared the generalized discontinuous PWM, the homopolar 3 PWM, and the SVPWM in order to obtain the more silent machine. A technique called harmonic injection PWM-frequency-modulated triangular carrier to act on the reference and the carrier is given in [START_REF] Ruiz-Gonzalez | Reducing acoustic noise radiated by inverter-fed induction motors controlled by a new PWM strategy[END_REF]. It is also possible to adapt the machine to the switching effects [START_REF] Brudny | Rotor design for reducing the switching magnetic noise of AC electrical machine variable-speed drives[END_REF] or to modify the mechanical structure response [START_REF] Tischmacher | Sound optimisation of a converterfed drive system using an acoustic camera in combination with modal analysis[END_REF]. In [START_REF] Ojeda | An active piezoelectric absorber for vibration control of electrical machine[END_REF], piezoelectric actuators are controlled to generate effects opposed the stator external vibrations. A new magnetic circuit structure presented in [START_REF] Demian | AC magnetic circuits using non segmented shifted grain oriented electrical steel sheets: Impact on induction machine magnetic noise[END_REF] allows reducing all the magnetic noise components.

This paper concerns the control of the switching effects on the magnetic noise and, more particularly, the definition of a PWM control strategy for suppressing a force component. That is obtained by suppressing the STPH that generates the force. To do that, the authors show that, for the classical sinus-triangle PWM, the spectral content of the voltages delivered by the inverter can be controlled by choosing appropriate three-phase triangular carriers that make the homopolar an intermediate STPH system, leading to delete the output annoying STPH. The problem requires characterizing the switching harmonic components not in terms of magnitude but in terms of phase sequences.

The first part presents an analytical method for modeling the PWM output voltages without switching instant determination. It is built by considering sinusoidal carriers (sinus-sinus PWM) in order to determine the harmonic phase sequences. The results, which are validated with numerical simulations and experiments, are extended to the sinus-triangle PWM to demonstrate that the analytical relationships are also valuable in this case. Upper indices "s" for a sinusoidal carrier and "Δ" for a triangular carrier will be used to distinguish the variables according to the carrier waveforms. No index means that the relations are valuable whatever the case. The second part is dedicated to the switching voltage harmonic control. The authors show how any rotating STPH system can be canceled by using three different appropriate carriers. Experiments considering the sinus-triangle PWM validate the theoretical approach and the STPH control strategy. The last part presents results that show the impact of this strategy on the radial vibrations of an induction machine.

II. PWM MODELING

Let us denote v ref

q and v Δ cq as phase q's (q = 1, 2, or 3) sinusoidal reference and triangular carrier signals, respectively, whose angular frequencies are ω (frequency f ) and mω (frequency f PWM = mf ), respectively, where m is defined as the modulation index. In order to easily determine the PWM three-phase v q output voltage characteristics, a v s cq sinusoidal carrier is substituted to v Δ cq ; these two signals present the same peak values, as shown in Fig. 1. The analytical study is done considering that the r adjusting coefficient is equal to the unit. In the following, the time referential is linked to v ref 1 as it appears in Fig. 1. Thus, v ref q and v s cq can be expressed as:

v ref q = v sin (θ -φ q ) (1)
v s cq = v sin [m(θ -ξ q )] (2)
where θ = ωt, and φ q = (q -1)2π/3. ξ q is phase q's adjustable carrier phase difference. For the classical PWM, ξ q is the same for whatever q is. Fig. 2 presents the three-phase inverter and the main notations.

• The control strategy is similar to that defined for the classical sinus-triangle PWM when v ref q > v s cq , the K q switch is closed, and w s q = U 0 /2; for v ref q < v s cq , K q is closed, and w s q = -U 0 /2. The inequality v ref q > v s cq , taking into account (1) and (2), can be written as cos (m+1)θ-φ q -mξ q 2 sin (m-1)θ+φ q -mξ q 2 ≤ 0.

Let us introduce the f a and f b logic functions defined as follows.

• f a = 1 or 0 if the cosine is positive or negative, respectively.

• f b = 1 or 0 if the sine is negative or positive, respectively. It can be shown that the w s q three-phase intermediate system can be expressed as Fig. 3 shows the principle applied to determine w s q . The f a and f b Fourier series can be written as

w s q = U 0 (2f a f b -f a -f b + 1/2). (4)
f a = 1 2 + 2 π ∞ n 1 =0 (-1) n 1 2n 1 +1 cos 2n 1 +1 2 [(m+1)θ-φ q -mξ q ] f b = 1 2 + 2 π ∞ n 2 =0 -1 2n 2 +1 sin 2n 2 +1 2 [(m-1)θ+φ q -mξ q ] ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ (5)
where n 1 and n 2 are positive or null integers. Let us denote W s 0 = -4U 0 /π 2 . Considering (5), w s q can be expressed as

w s q = ∞ n 1 =0 ∞ n 2 =0 w s q(k 1 ) -w s q(k 2 ) (6)
where

w s q(k 1 ) = ŵs (k 1 ) sin (k 1 θ -N -φ q -mN + ξ q ) w s q(k 2 ) = ŵs (k 2 ) sin (k 2 θ -N + φ q -mN -ξ q ) (7)
N + = 1 + n 1 + n 2 N -= n 1 -n 2 (8
)

k 1 = mN + + N - k 2 = mN -+ N + (9) ŵs (k 1 or k 2 ) = (-1) n 1 W s 0 / [(2n 1 + 1)(2n 2 + 1)]. (10)
Elementary considerations on ŵs (k 1 or k 2 ) make it possible to show that a harmonic of k-rank belongs to the k 1 or k 2 group only considering one term corresponding to the [n 1 , n 2 ] couple, which carries the highest weight (smallest n 1 and n 2 values compared with the rest of the other concerned couples). Thus, (6) can be written as

w s q = k w s q(k) = k 1 w s q(k 1 ) - k 2 w s q(k 2 ) . ( 11
)
• These STPH systems are defined by their phase sequences: clockwise (C), anticlockwise (A), and homopolar (H). As for a balanced and star-connected load, i.e., v q = (2w qw q+1w q+2 )/3, it is possible to consider a similar relationship for each k harmonic. As for the (C) and (A) systems, q w q(k) = 0, and it can be deduced that

v q(k) = w q(k) , for (C) and (A) systems v q(k) = 0, for (H) systems . ( 12
)
One can first note that these developments are valid whatever the PWM is, i.e., synchronous or asynchronous. Then, it shows that a homopolar intermediate STPH system disappears from the output signals. It is also true, in the steady state, for a load that is delta connected by considering the equivalent star-connected load. • It appears that this analytical model has considerable advantages because it makes it possible to determine the w s q (or v s q ) spectral contents and the harmonic phase sequences without calculating the switching instants. As some k 2 values lead to STPH systems of negative frequency, their phase sequence determination is done by first considering k 2 positive; then, for negative k 2 , (C) is replaced by (A), and vice versa.

The problem now is to analyze under what conditions these results are applicable for the sinus-triangle PWM and how the r value affects this property established for r = 1. The developments will be done considering a synchronous PWM.

III. VALIDATION OF PWM MODELING

The validation concerns the v q spectral content for sinusoidal v ref q , where m = 55, f = 50 Hz, and U 0 = 520 V, and a single carrier wave by comparing analytical, numerical, and experimental results for r = 1 and then for r = 1.

All the experiments are made by connecting to the inverter outputs a three-phase star-connected 50-Hz 15-kW two-polepair cage induction machine operating at no load. The switching is controlled with a Focusrite sound card programmed with the Csound language. It allows generating single (or multiple) carrier(s) with a sinusoidal (or triangular) shape. A spectrum analyzer allows providing the v q spectral content, both in amplitude and phase. Numerical results are obtained using a fast Fourier transform (FFT) made with Matlab or a computer program, which determines the different quantities from the switching instants.

A. Single Sinusoidal Carrier

• For r = 1, the w s q analytical harmonic ranks and phase sequences are given in Table I for the first n 1 and n 2 values. The δ| ŵs q(k) | corresponding absolute relative amplitudes deduced from [START_REF] Kim | A Study on the design process of noise reduction in induction motors[END_REF], which are defined as percentage, are given by Thus, δ| ŵs q(k) | very quickly decreases when n 1 and n 2 increase so that the analysis may only cover the first n 1 and n 2 values.

δ ŵs q(k) = 100 ŵs q(k) ŵs q(1) = 100/ [(2n 1 +1)(2n 2 +1)]. ( 13
)
• The v s q characteristics experimentally obtained for ξ q = 0 are given in Fig. 4, where the bold lines correspond to the terms resulting from the k 1 group (deduced from the analytical study). The relative amplitudes, which are defined by a similar expression as [START_REF] Covic | Noise quieting with random PWM AC drives[END_REF], are given in Fig. 4(a), where vs

q(1) = |W s 0 | = 210.75 V. A cross spectrum of v s 1(k) and v s 2(k)
is made with a Bruël & Kjaer PULSE analyzer platform. It gives the phase differences presented in Fig. 4(b) for the main components (δ|v s q(k) | > 3%). Let us point out that a 0 difference corresponds to an (H) system; a 2π/3 difference, to a (C) system; and a 4π/3 difference, to an (A) system. There is no (H) system according to [START_REF] Habetler | Acoustic noise reduction in sinusoidal PWM drives using a randomly modulated carrier[END_REF].

It appears that the number of components from the k 1 group is very limited and that these components only appear in the harmonics families centered on m multiples.

Analytical and experimental results are in excellent correlation. It validates the theoretical results and the hypothesis that consists of using the relation [START_REF] Hashemi | Acoustic noise reduction for an inverter-fed three-phase induction motor[END_REF] instead of the relation (6) to express w s q . • The characteristics of the main harmonics have been calculated for different values of ξ q and r.

-For r = 1, the previous relative amplitudes are found, whatever the values of ξ q are. For the phases, the analytical and numerical values, for a given value of ξ q , are almost the same, with the error being increased with m. For example, the error obtained with the FFT is inferior to 1 • for the 3m + 4 component, and it is lower when the switching instants are calculated. Due to the numerical errors, it can be underlined that considering the term of a higher weight is perfectly justified to analytically characterize a harmonic. -r = 1 leads to a similar spectral content obtained than for r = 1, with differences on the relative amplitudes (the reference value is the fundamental component magnitude obtained for the considered r value). However, a notable result appears concerning the phases and, therefore, the phase sequences that are the same as those for r = 1 ∀ r.

B. Triangular Carrier

Fig. 5 shows the relative v Δ q spectrum (δ|v Δ q(k) |, vΔ q(1) = rU 0 / 2 = 260 V for r = 1) for r = 1 [see Fig. 5(a)] and r = 0.8 [see Fig. 5(b)], which is experimentally obtained with a single triangular carrier. Comparing the vΔ q(k) relative amplitudes given in Figs. 4(a) and 5(a), it appears that, independent of the magnitude differences on the fundamental components according to the carrier type, sinusoidal and triangular carriers practically lead to the same harmonic ranks. The magnitude differences are notably amplified with the sinus-sinus PWM for components of low ranks (5 and 7), although they do not predominantly intervene on the spectral content. It is also noticeable that there is an inversion concerning the components of the highest am-plitude around 3m. The analysis of the phase sequences shows that they are independent from the carrier type and from the r and ξ q values. Consequently, they can be always deduced from Fig. 4(b). This property can be expressed as follows: The phase angles at t = 0 determined for a given ξ q , which are calculated with the expression established for the sinus-sinus PWM and, thus, for r = 1, are also valuable for the harmonic components, which appear for the sinus-triangle PWM and this, whatever the value of r is. The fact that r does not intervene appears in [START_REF] Bowes | New sinusoidal pulsewidth-modulated invertor[END_REF]. That property is exploited in the following section. Compared with other methods [START_REF] Holmes | A general analytical method for determining the theoretical harmonic components of carrier based PWM strategies[END_REF], the method proposed by the authors allows simplifying the analytical expression of the PWM due to the use of logical functions. For example, it has the advantage of not using a Fourier series with Bessel functions as for the double-Fourier series methods used in [START_REF] Sun | Fast time-domain simulation by waveform relaxation methods[END_REF].

IV. VOLTAGE HARMONIC CONTROL

A. Principle of the Method

• Let us consider a harmonic of rank x belonging to the k 1 group, which is denoted by k

(x)
1 . This harmonic is defined by the [n

(x) 1 , n (x)
2 ] couple, which leads to the N +(x) and N -(x) quantities. Its expression, which is deduced from [START_REF] Mihaila | A simulation method to predict the turn-to-turn voltage spikes in a PWM fed motor winding[END_REF], is given by

w s q k (x) 1 = ŵs k (x) 1 sin k (x) 1 θ-N -(x) φ q -mN +(x) ξ (x) q . (14) It becomes homopolar if N -(x) φ q +mN +(x) ξ (x) q = C (x) 1 ∀ q, where C (x) 1 is a constant. It leads to mξ (x) q = C (x) 1 -N -(x) φ q /N +(x) . ( 15
)
When mξ (x) q verifies (15), the modified STPH systems, which are also denoted by an upper index (x), are given by ( 16), shown at the bottom of the page.

• The method is identical to cancel a k (x) 2 -rank harmonic belonging to the k 2 group. Introducing a constant denoted by C (x) 2 , it can be deduced from ( 7) that, to make this STPH system (H), it suffices to satisfy the following equality:

mξ (x) q = C (x) 2 -N +(x) φ q /N -(x) ( 17
)
so that the modified STPH systems are expressed as [START_REF] Tischmacher | Sound optimisation of a converterfed drive system using an acoustic camera in combination with modal analysis[END_REF], shown at the bottom of the page. • One can note that ξ (x) q depends on q. In addition, ξ (x) q does not modify the fundamental insofar as N -, which multiplies ξ (x) q , is null. It appears that the coefficients of φ q are not necessarily integers, which means that the modified STPH systems become unbalanced. This imbalance only concerns the phase difference between the three terms, which present the same amplitudes. If the coefficients of φ q are integers, the modified STPH systems are still balanced, but their phase sequence can be changed.

Thereafter, the ξ (x) q values analytically determined with the sinus-sinus PWM will be used in the sinus-triangle PWM control to suppress a v Δ q STPH system. As C (x) 1

and

C (x) 2
have no influence a priori, they will be assumed to be null.

s(x) q(k 1 ) = ŵs (k1) sin k 1 θ -1 N +(x) N -N +(x) -N + N -(x) φ q -N + N +(x) C (x) 1 w s(x) q(k 2 ) = ŵs (k2) sin k 2 θ -1 N +(x) N + N +(x) -N -N -(x) φ q -N - N +(x) C (x) 1 ⎫ ⎬ ⎭ (16) w s(x) q(k 1 ) = ŵs (k 1 ) sin k 1 θ -1 N -(x) N -N -(x) -N + N +(x) φ q -N + N -(x) C (x) 2 w s(x) q(k 2 ) = ŵs (k 2 ) sin k 2 θ -1 N -(x) N + N -(x) -N -N +(x) φ q -N - N -(x) C (x) 2 ⎫ ⎬ ⎭ (18)

B. Cancelation of Harmonic Around m (k 2 Group)

• Let us assume that one choice to suppress the m + 2 rank is the (A) STPH system that belongs to the k 2 group. It is denoted by

k (m+2) 2
, and it is defined for n = 0 (see Table I). That leads to N +(m+2) = 2 and N -(m+2) = 1. This STPH system, which was deduced from [START_REF] Mihaila | A simulation method to predict the turn-to-turn voltage spikes in a PWM fed motor winding[END_REF], is expressed as

w s q k (m+2) 2 = ŵs k (m+2) 2 sin k (m+2) 2 θ+φ q -mξ (m+2) q . ( 19
)
To obtain an (H) system, expression [START_REF] Ojeda | An active piezoelectric absorber for vibration control of electrical machine[END_REF] leads to

ξ (m+2) q = φ q /m. ( 20
)
The modified STPH systems can be expressed as

w s(m+2) q(k 1 ) = ŵs (k 1 ) sin [k 1 θ -(1 + 2n 1 )φ q ] w s(m+2) q(k 2 ) = ŵs (k 2 ) sin [k 2 θ -(1 + 2n 1 )φ q ] . ( 21
)
It can be noted that the phase sequences only depend on n 1 and, for the terms of the k 2 group, on the sign of k 2 . Table II presents the w s q analytical spectral content modifications, which only concern the system phase sequences. For instance, (H) → (C) means that a system that is initially (H) becomes (C). It appears that the harmonic components, which do not depend on m, and those around 3m and 6m keep the same characteristics (see the grayed cells in Table III). When the m + 2 component disappears, other terms are suppressed, but, in return, other components appear as the component of rank m, which presents a high amplitude because it is defined for n 1 = n 2 = 0.

From an experimental point of view, the Focusrite sound card has been programmed to generate three triangular carriers with m = 55 and ξ given by [START_REF] Demian | AC magnetic circuits using non segmented shifted grain oriented electrical steel sheets: Impact on induction machine magnetic noise[END_REF]. Fig. 6 shows the relative v Δ 1 experimental spectrum without [see Fig. 6(a)] and with [see Fig. 6(b)] the harmonic cancelation. It shows that the properties concerning the suppression or the generation of STPH systems are verified. It confirms that the law established for the sinus-sinus PWM is also true for the sinus-triangle PWM. On the other hand, there is still the problem concerning the amplitudes. Fig. 7 shows that the same properties are found for r = 0.8 than for r = 1.

It means that the phase sequence is independent of r. The modeling method to find the phase shift of the three carriers for canceling an STPH system stays valid whatever r is.

• The same procedure can be used to suppress the m -2 rank (C) STPH system. It shows that, to get an (H) system, ξ (m-2) q must be equal to

ξ (m-2) q = -φ q /m ( 22
)
so that the modified STPH systems can be written as:

w s(m-2) q(k 1 ) = ŵs (k 1 ) sin [k 1 θ + (1 + 2n 2 )φ q ] w s(m-2) q(k 2 ) = ŵs (k 2 ) sin [k 2 θ -(1 + 2n 2 )φ q ] . (23)
• In this case, the phase sequence only depends on n 2 and on the sign of k 2 . Table III presents the w s q analytical spectral content modifications, which only concern the system phase sequences. The same terms as earlier keep the same characteristics (see the grayed cells in Table III). Fig. 6 shows the relative amplitudes of the v Δ 1 experimental spectra without [see Fig. 6(a)] and with [see Fig. 6(c)] the harmonic suppression for ξ (m-2) q given by ( 22) and r = 1.

C. Cancelation of Harmonic Around 2m (k 1 Group)

In this case, only the case where r = 1 will be studied.

• The harmonic of rank 2m+1 is considered. Its rank, which is denoted by k

(2m+1) 1
, is defined for n (2m+1) 1

= 1 and n (2m+1) 2 = 0 that gives N +(2m+1) = 2 and N -(2m+1) = 1, respectively. This (C) STPH system, which was deduced from [START_REF] Mihaila | A simulation method to predict the turn-to-turn voltage spikes in a PWM fed motor winding[END_REF], is given by q spectra resulting from m + 2 rank harmonic cancelation for r = 0.8.

w s q k (2m+1) 1 = ŵs k (2m+1) 1 sin k (2m+1) 1 θ-φ q -2mξ (2m+1) q . (24)

TABLE IV THEORETICAL IMPACT OF THE 2m + 1 HARMONIC (GROUP k 1 )

SUPPRESSION ON THE w s q SPECTRAL CONTENT To make it homopolar, ξ (2m+1) q must be equal to

ξ (2m+1) q = -φ q /2m. ( 25
)
The modified STPH systems can be expressed as follows:

w s(2m+1) q(k 1 ) = ŵs (k 1 ) sin k 1 θ -n 1 -3n 2 -1 2 φ q w s(2m+1) q(k 2 ) = ŵs (k 2 ) sin k 2 θ -n 1 +3n 2 +2 2 φ q . ( 26
)
In that case, many systems that are initially balanced become unbalanced. Table IV shows the modifications of the STPH system phase sequences. (HCA) means that a system that is initially (C), (A), or (H) becomes unbalanced. Only the harmonic components, which do not depend on m, and those around 6m keep the same characteristics (see the grayed cells in Table IV). In that case, the comparison with the experimental measurements is more complicated insofar as most of the STPH systems are unbalanced. It is thus necessary to characterize each of them with its (C), (A), and (H) components, which result from the following classical expressions if phase 1 is considered, which use time phasor variables and where a = exp(j2π/3):

W s(x) 1(k)(C) = W s(x) 1(k) + aW s(x) 2(k) + a 2 W s(x) 1(k) /3 W s(x) 1(k)(A) = W s(x) 1(k) + a 2 W s(x) 2(k) + aW s(x) 1(k) /3 W s(x) 1(k)(H) = W s(x) 1(k) + W s(x) 2(k) + W s(x) 1(k) /3 ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ . ( 27
)
Let us consider, for example, the k 1 group unbalanced system defined for n 1 = n 2 = 0, i.e., k 1 = m. Using the first expression of (26), it can be written as w s(2m+1) q(m)

= ŵs

(m) sin (mθ + (q -1)π/3) . and 66.6%, respectively. Fig. 9 shows the relative amplitudes of the v Δ 1 experimental spectra without [see Fig. 9(a)] and with [see Fig. 9(b)] the harmonic suppression considering the v Δ q(C) and v Δ q(A) components, which were determined from the measurements and the analysis of the v Δ q system for ξ (2m+1) q

given by (25).

• In order to cancel the 2m -1 rank, i.e., (A) STPH system, one has to satisfy the following equality:

ξ (2m-1) q = φ q /2m. ( 29
)
This leads to the modified STPH systems as follows:

w s(2m-1) q(k 1 ) = ŵs (k 1 ) sin k 1 θ -3n 1 -n 2 +1 2 φ q w s(2m-1) q(k 2 ) = ŵs (k 2 ) sin k 2 θ -3n 1 +n 2 +2 2 φ q . ( 30
)
It can be shown that, as for the previous case, the components, which are not influenced, are those that do not depend on m and those of rank around 6m. By considering the k 1 group STPH system of rank m, it can be written as

w s(2m-1) q(m) = ŵs (m) sin (mθ -(q -1)π/3) . ( 31
)
In a similar way, the use of the time phasor leads to the (C) and (A) component relative values that are equal to 66.6% and 33.3%, respectively. The relative importance of these systems is changed compared with the previous case. Fig. 9(c) shows the relative amplitudes of the v Δ q(C) and v Δ q(A) spectra, which were determined from the measurements and the analysis of the v Δ q system obtained for ξ (2m-1) q

given by (29). • The suppression of the component of rank 2m + 1 or 2m -1 leads to new components of rank 2m ± 3, which are both (C) and (A), as determined with the analytical model. Contrary to the suppressions of the m + 2 and m -2 components, the rank m component is separated into (C) and (A) components. The amplitudes of the latter are reduced, but their sum, without any physical signification, is always equal to 100%.

V. APPLICATION TO CONTROL OF RADIAL VIBRATIONS

The following study is simplified insofar as the toothing effect is not taken into account. Each v Δ q(k) STPH system generates a b Δ (k) harmonic rotating magnetic field. Because of the definition of Maxwell's forces, only the components that result from the b Δ (1) b Δ (k) products are considered. In these conditions, the force frequencies are given by (k ± 1)f . The spectral analysis of the radial accelerations show that the switching effect appear at frequencies located around 2m, 3m, . . .. The experimental accelerations of the vibrations situated around 2m and the acoustic pressure measured at 80 cm from the machine in a semianechoic room are presented in Fig. 10(a). Table I shows that the ranks of the STPH systems that must be considered are 2m ± 1 (the k 1 group) and 2m ± 3 (the k 2 group). This leads to the following force frequencies: 2m-1 → 5400 Hz, 5500 Hz; 2m+1 → 5500 Hz, 5600 Hz; 2m-3 → 5300 Hz, 5400 Hz; 2m+3 → 5600 Hz, 5700 Hz.

It can be emphasized that a force component is not associated to a unique STPH system. Therefore, with this simplified analysis, it is not possible to determine which force component has the highest amplitude, although the experimental measurements show that 5500 and 5600 Hz have overriding effects. The 5300and 5700-Hz components have low amplitudes, which can be explained by the (H) nature of the 2m ± 3 STPH systems. Let us suppose that the 5600-Hz force component has to be reduced. It can be done by changing the 2m + 1 STPH system in (H). The study presented in Section IV-C explains the control, and Table IV shows that the 2m ± 3 STPH systems, which were initially (H), become (A) and that the (A) (2m -1) STPH systems become (C). In fact, concerning these components, the same result can be obtained by making (H) the (m + 2) STPH system (see Table II). As a result, the phase adjustment can be chosen. Applying the value given by ( 20) leads to the experimental spectra shown in Fig. 10(b). In terms of noise, the 5600-, 5500-, and 5400-Hz components are reduced of 4, 13, and 5 dBA, respectively, whereas the 5300-and 5700-Hz components are increased because the 2m ± 3 STPH systems, which were initially (H), become (A). Consequently, these components, which are negligible without the phase adjustment, have amplitudes of 47.5 and 53 dBA, respectively. These variations are in accordance with the theory. Practically, the aim of the method is to control noise components with frequencies close to a natural resonance. In that case, their amplitudes are greatly amplified, which is not the case for the considered example.

VI. CONCLUSION

In this paper, the authors have proposed to reduce some undesirable effects generated by the switching. The principle is to suppress some annoying STPH systems of the output sinus-triangle PWM. To do that, the phase sequences of all the STPH systems have to be determined to define a control, making some of them homopolar. Thus, the authors have developed an analytical model based on an associated "sinus-sinus" PWM. It is shown that this model makes accurate phase sequence determination possible and that the results remain valid for the sinus-triangle PWM whatever the modulation index and the adjusting index are. Based on this property, the authors present the control strategy that uses three distinct carriers. The experiments confirm the theoretical developments and point out the possibility to analyze the impact of the STPH cancelation on other uncanceled harmonic components, which is an aspect that is not often studied in literature. That method, which is based on analytical formulation, is used to modify the induction machine's radial vibrations. It constitutes the basis for further studies as the possibility to simultaneously act on several harmonic components.

Fig. 1 .

 1 Fig. 1. PWM with triangular and sinusoidal carriers.

Fig. 2 .

 2 Fig. 2. Three-phase PWM inverter.

Fig. 3 .

 3 Fig. 3. Principle of the w s q determination.

Fig. 4 .

 4 Fig. 4. Experimental v s q harmonic content for a single sinusoidal carrier (r = 1).

Fig. 5 .

 5 Fig. 5. Experimental v Δ q harmonic content for a single triangular carrier (r = 1, 0.8). (a) r = 1. (b) r = 0.8.

  w

Fig. 6 .

 6 Fig. 6. Relative experimental v Δ q spectra resulting from (b) m + 2 and (c) m -2 rank harmonic cancelations for r = 1.

Fig. 7 .

 7 Fig. 7. Relative experimental v Δq spectra resulting from m + 2 rank harmonic cancelation for r = 0.8.

Fig. 8 .

 8 Fig. 8. Suppression of the 2m + 1 harmonic: Characterization of the (C), (A), and (H) components of the rank m unbalanced system.

( 28 ) 2 .

 282 It leads to Fig.8(a), where the modulus of each time phasor variable is W s (m) = ŵs (m) / √ Using (27) leads to the phase 1 time phasor variable of each component given in Fig.8(b). It can be noted that the (H) and (A) systems have the same modulus equal to 2W s (m) /3, whereas the (C) modulus is W s (m) /3. As, theoretically, the relative value of the m harmonic is equal to 1 (see TableI), it can be deduced that the relative absolute values of the (C) and (A) systems of v s(2m+1) (m) are 33.3%

Fig. 9 .

 9 Fig. 9. Relative experimental v Δ q(C) and v Δ q(A) spectra resulting from the (b) 2m + 1 and (c) 2m -1 rank harmonic cancelations for r = 1.

Fig. 10 .

 10 Fig. 10. (a) Acceleration (in meters per second squared) of the vibrations. (b) Acoustic noise (in A-weighted decibels) without and with carrier phase adjustment with frequency (in Hertz).

TABLE I ANALYTICAL

 I RANKS AND PHASE SEQUENCES OF w s q HARMONICS

TABLE II THEORETICAL

 II IMPACT OF THE SUPPRESSION OF THE m + 2 RANK HARMONIC (GROUP k 2 ) ON THE w s

q SPECTRAL CONTENT TABLE III THEORETICAL IMPACT OF THE m -2 HARMONIC (k 2 GROUP) SUPPRESSION ON THE w s q SPECTRAL CONTENT

(m+2) q

Jean-François Brudny (M'92-SM'04) received the Ph.D. and D.Sc. degrees from Lille University, Villeneuve d'Ascq, France, in 1984 and 1991, respectively.

In 1992, he joined Artois University (UArtois), Béthune, France, as a Full Professor, and he is currently the Head of the Laboratoire Systèmes Electrotechniques et Environnement (LSEE). His research interests include noise and vibrations of electromechanical systems and new designs for the efficiency increase of ac rotating electrical machines.

Tifany Szkudlapski is currently working toward the Ph.D. degree at the Laboratoire Systèmes Electrotechniques et Environnement, Artois University, Béthune, France.

His research interests include noise and vibrations of electrical machines.

Fabrice Morganti was born in 1965. He received the Ph.D. degree from Lille-I University, France, in 1994.

He is currently an Associate Professor with Artois University (UArtois), Béthune, France, where he joined Laboratoire Systèmes Electrotechniques et Environnement (LSEE). His research interests include signal processing and electromagnetic design. He is currently a Full Professor with the Laboratoire Systèmes Electrotechniques et Environnement (LSEE), Artois University. His research interests include electromagnetic design, and the efficiency and noise of electrical machines.


Me ´lanie Ne
email: melanie.nee@u-bordeaux2.fr

Marta Avalos

Audrey Luxcey

Benjamin Contrand

Louis- Rachid Salmi

Annie Fourrier-Re ´glat

Blandine Gadegbeku

Emmanuel Lagarde

Ludivine Orriols

Prescription medicine use by pedestrians and the risk of injurious road traffic crashes: A case-crossover study

Background

While some medicinal drugs have been found to affect driving ability, no study has investigated whether a relationship exists between these medicines and crashes involving pedestrians. The aim of this study was to explore the association between the use of medicinal drugs and the risk of being involved in a road traffic crash as a pedestrian.

Methods and findings

Data from 3 French nationwide databases were matched. We used the case-crossover design to control for time-invariant factors by using each case as its own control. To perform multivariable analysis and limit false-positive results, we implemented a bootstrap version of Lasso. To avoid the effect of unmeasured time-varying factors, we varied the length of the washout period from 30 to 119 days before the crash. The matching procedure led to the inclusion of 16,458 pedestrians involved in an injurious road traffic crash from 1 July 2005 to 31 December 2011. We found 48 medicine classes with a positive association with the risk of crash, with median odds ratios ranging from 1.12 to 2.98. Among these, benzodiazepines and benzodiazepine-related drugs, antihistamines, and anti-inflammatory and antirheumatic drugs were among the 10 medicines most consumed by the 16,458 pedestrians. Study limitations included slight overrepresentation of pedestrians injured in more severe crashes, lack of information about self-medication and the use of over-the-counter drugs, and lack of data on amount of walking.

Introduction

Walking is rightly being promoted for its benefits for physical and mental health and for the environment. This comes, however, with a caveat: pedestrians are among the most vulnerable road users [START_REF] Constant | Protecting vulnerable road users from injury[END_REF]. The World Health Organization's 2013 global status report on road traffic safety revealed that pedestrians account for 22% of the world's road traffic deaths [START_REF]Global status report on road safety[END_REF].

A pedestrian crash is defined as any incident occurring on a public thoroughfare that involves at least 1 person on foot and 1 or more vehicles, at least 1 of which is moving. Cognitive, perceptive, and motor skills are involved in a pedestrian's ability to move safely in a traffic setting. A decrease in motor skills may prevent pedestrians from crossing the road in time. For instance, a study in England compared the walking speed in the population with the speed required to utilize pedestrian crossings among 3,145 adults aged 65 and older and concluded that most of them were unable to cross the road in time [START_REF] Asher | Most older pedestrians are unable to cross the road in time: a cross-sectional study[END_REF]. Identified risk factors for the occurrence and severity of injury include environmental factors (e.g., lighting conditions, weather), roadway characteristics (e.g., speed limit, lack of pedestrian facilities), and pedestrian characteristics and behaviors (age, sex, maneuvers, alcohol intoxication) [START_REF] Sze | Diagnostic analysis of the logistic model for pedestrian injury severity in traffic crashes[END_REF][START_REF] Mueller | Factors associated with pedestrian-vehicle collision injuries and fatalities[END_REF][START_REF] Aziz | Exploring the determinants of pedestrian-vehicle crash severity in New York City[END_REF][START_REF] Dai | Identifying clusters and risk factors of injuries in pedestrian vehicle crashes in a GIS environment[END_REF][START_REF] Gårder | The impact of speed and other variables on pedestrian safety in Maine[END_REF]. Because medicines have the potential to impair the skills needed to perform road users' tasks safely, the association between the use of medicines and the risk of road traffic crash has been studied among vehicle drivers. The association between drivers' use of benzodiazepines and the risk of road crash is now consistently documented [START_REF] Kurzthaler | Alcohol and/or benzodiazepine use: different accidents-different impacts?[END_REF][START_REF] Ray | Psychoactive drugs and the risk of injurious motor vehicle crashes in elderly drivers[END_REF][START_REF] Movig | Psychoactive substance use and the risk of motor vehicle accidents[END_REF][START_REF] Orriols | Benzodiazepine-like hypnotics and the associated risk of road traffic accidents[END_REF][START_REF] Leveille | Psychoactive medications and injurious motor vehicle collisions involving older drivers[END_REF][START_REF] Fournier | Concurrent use of benzodiazepines and antidepressants and the risk of motor vehicle accident in older drivers: a nested case-control study[END_REF]. Other medicines have also been studied: antidepressants [START_REF] Ray | Psychoactive drugs and the risk of injurious motor vehicle crashes in elderly drivers[END_REF][START_REF] Leveille | Psychoactive medications and injurious motor vehicle collisions involving older drivers[END_REF][START_REF] Fournier | Concurrent use of benzodiazepines and antidepressants and the risk of motor vehicle accident in older drivers: a nested case-control study[END_REF][START_REF] Orriols | Prescription of antidepressants and the risk of road traffic crash in the elderly: a case-crossover study[END_REF][START_REF] Rapoport | At-fault motor vehicle crash risk in elderly patients treated with antidepressants[END_REF][START_REF] Orriols | Risk of injurious road traffic crash after prescription of antidepressants[END_REF], opioids used in pain treatment and in substitution treatment for opioid dependence [START_REF] Movig | Psychoactive substance use and the risk of motor vehicle accidents[END_REF][START_REF] Leveille | Psychoactive medications and injurious motor vehicle collisions involving older drivers[END_REF][START_REF] Drummer | The involvement of drugs in drivers of motor vehicles killed in Australian road traffic crashes[END_REF][START_REF] Gomes | Opioid dose and risk of road trauma in Canada: a population-based study[END_REF], and cardiovascular drugs [START_REF] Engeland | Risk of road traffic accidents associated with the prescription of drugs: a registry-based cohort study[END_REF][START_REF] Mcgwin | Relations among chronic medical conditions, medications, and automobile crashes in the elderly: a population-based case-control study[END_REF]. A positive association was found in these studies, except for 1 study [START_REF] Engeland | Risk of road traffic accidents associated with the prescription of drugs: a registry-based cohort study[END_REF] that found no association between calcium channel blockers and the risk of crash, and 2 studies [START_REF] Movig | Psychoactive substance use and the risk of motor vehicle accidents[END_REF][START_REF] Gomes | Opioid dose and risk of road trauma in Canada: a population-based study[END_REF] in which there was an increased risk with opioid use, but the increase was not statistically significant.

Very few studies have investigated the association between the use of medicinal drugs and the risk of road traffic crashes involving pedestrians, and available data remain descriptive, with no comparison group. One study analyzed postmortem blood and urine specimens from victims of road traffic fatalities between 2000 and 2006 in England and Wales. Benzodiazepines and antidepressants were detected in 30% and 20% of pedestrians' blood and urine specimens, respectively [START_REF] Elliott | The prevalence of drugs and alcohol found in road traffic fatalities: a comparative study of victims[END_REF]. In 2003, the Australian Transport Safety Bureau reported that 5.4% of male pedestrians aged 15-54 years killed in a road safety crash between 1997 and 1999 had taken benzodiazepine tranquilizers, and 1.3% had taken an antidepressant [START_REF]Monograph 14-male pedestrian fatalities[END_REF]. The non-comparative design of these studies excludes all conclusions about the actual role of medication use.

The aim of this study was to investigate the association between the use of medicines and the risk of road traffic crash in pedestrians.

Methods

We extracted and matched data from 3 French nationwide databases: the national healthcare insurance database, police reports, and the police national database of injurious crashes. Drivers were included by means of their national healthcare ID number, extracted from police reports by an automatic procedure. This national ID number was used to link pedestrians to medicine reimbursement data around the crash date. Police reports were matched to records in the injurious crashes database by a probabilistic linkage method [START_REF] Orriols | Prescription medicines and the risk of road traffic crashes: a French registry-based study[END_REF].

Ethics statement

Confidentiality was ensured by using the personal information anonymization function of the healthcare insurance system [START_REF] Trouessin | FOIN: a nominative information occultation function[END_REF]. The study was approved by the French Data Protection Authority.

Data sources

Police reports. French police officers are required to fill out a police report for each injurious crash occurring in the country (about 70,000 reports each year). An injurious crash is defined as a crash occurring in a road open to public circulation involving at least 1 vehicle and resulting in at least 1 victim needing medical attention or being killed. All reports are scanned and stored as image files. A manual validation study of 141 police reports involving pedestrians showed that national ID number was recorded for 39% of the pedestrians involved in these injurious road traffic crashes. These ID numbers were extracted from image files for later matching against dispensing records in the healthcare insurance database. All police reports available from 1 July 2005 to 31 December 2011 were compiled.

Police national database of injurious crashes. Information collected by the police for each injurious road traffic crash is stored in the police national database of injurious crashes, including information on the crash, vehicles, and persons involved. The variables used in this study were sex and age of the pedestrian, presumed responsibility for the crash as assessed by police officers, injury severity, weather, season, hour, day of week, lighting conditions, pedestrian action, and pedestrian location.

National healthcare insurance database. The healthcare insurance database covers the entire population of France. A record is added each time a reimbursed prescription medicine is dispensed to an outpatient at a pharmacy; the record includes national ID number, date of dispensing, and the 7-digit code that identifies medicines.

Participant inclusion

A pedestrian was excluded if the police report did not contain his or her national ID number or if the extraction procedure failed or a link could not be established with the corresponding record in the police national database of injurious crashes. If a pedestrian was involved in several crashes during the study period, only the first crash was considered, to ensure that the dispensing of a drug was not a consequence of a previous crash.

Participant and crash characteristics

Pedestrian characteristics (including age, sex, responsibility attributed by police officers, injury severity, and the pedestrian's action and location) and crash characteristics (including weather, season, time and day of the crash, and lighting) were described. These characteristics were also used to investigate the factors associated with the probability of being part of the study.

Medicine and exposure periods

In France, a classification of medicines that could affect the ability to drive, use machines, and implement tasks requiring attention and precision has been developed by the French National Agency for Medicines and Health Products Safety (ANSM) and gradually applied since 2005 [START_REF] Riche | Medicinal products and driving[END_REF]. This classification, with its 4-level ranking from 0 (no or negligible risk) to 3 (major risk), has been validated in a study on drivers using the same databases as used in this study [START_REF] Orriols | Prescription medicines and the risk of road traffic crashes: a French registry-based study[END_REF]. For the present study, only prescription medicines ranking from level 1 to 3 were included in the analysis. These medicines account for 37% of the medicines sold in France [START_REF] Franc ¸aise De Se ´curite ´sanitaire Des Produits De Sante | Mise au point: Me ´dicaments et conduite automobile[END_REF].

The exposure periods were determined for each pharmacotherapeutic class according to the Anatomical Therapeutic Chemical (ATC) classification (fourth level). Medication exposure was defined as starting 1 day after dispensing, and exposure duration was estimated from median values reported in a survey on medicine prescription in France [START_REF]Enquête Permanente sur la Prescription Me ´dicale (EPPM)[END_REF]. To ensure that the medicines were not prescribed as a consequence of injuries sustained in the crash, medicines dispensed on the day of the crash were not considered in the analysis.

Case-crossover analysis

The case-crossover design allows study of the effect of transient exposure on the risk of acute events. The exposure frequency during a period just before the crash (case period) is compared with the exposure frequency during an earlier period (control period) in the same individual [START_REF] Maclure | Should we use a case-crossover design?[END_REF]. In the case-crossover analysis, only records with discordant exposures in case and control windows (either exposed on the case day and unexposed on the control day or unexposed on the case day and exposed on the control day) contribute to the analysis. The period between the case and control periods is called the washout. It corresponds to the period needed to ensure that exposure in the control period is not mixed with exposure in the case period.

The optimal washout period for a given medicine depends on its indication and prescription patterns. Since all prescribed drugs with non-null risk level were considered here, we could not make any assumption concerning the choice of the washout period. This period was thus varied from 30 to 119 days before from the crash day, resulting in the implementation of 90 case-crossover designs with distinct washout periods (Fig 1). Data on reimbursed medicines dispensed within 6 months before the crash were available. To ensure that the pedestrian was not exposed to a medicine at the beginning of the observation period without us knowing (dispensing date before the beginning of the observation period), we chose a 4-month study period. This approach of using multiple washout periods provided an indication of the robustness of the observed associations.

The conditional logistic regression model was the standard tool used for the analysis.

Lasso analysis

We designed the analysis protocol assuming that few medicines increased the risk of road crash. A variable selection procedure thus had to be performed to identify these medicines from a large list of potential candidates. To address multiple testing problems, we implemented a Lasso (least absolute shrinkage and selection operator) regression analysis [START_REF] Tibshirani | Regression shrinkage and selection via the Lasso[END_REF] for each washout period. In this multivariable modeling approach, a penalty term shrinks each coefficient estimate and sets some of them to zero. Estimation and selection of the subset of covariates showing the strongest association from a longer list of covariates occur simultaneously.

The Lasso approach tends to retain not only the relevant exposures but also a few additional irrelevant ones (though typically their estimates are small). To circumvent this problem, we used the Bolasso (bootstrap-enhanced least absolute shrinkage operator) method [START_REF] Bach | Bolasso: model consistent Lasso estimation through the bootstrap[END_REF]. Only exposures frequently chosen by the Lasso analysis over the bootstrap samples were selected, which improved the stability of the results [START_REF] Avalos | Variable selection on large case-crossover data: application to a registry-based study of prescription drugs and road traffic crashes[END_REF]. In the Bolasso procedure, 2 parameters have to be tuned. The optimal amount of shrinkage was estimated by cross-validation. The frequency threshold was tuned with the Akaike information criterion over 1,000 bootstrap samples. To correct bias in the estimated coefficients, we fitted the unpenalized logistic regression model with the exposures retained in the model (those having a nonzero point estimate of log-odds ratio) [START_REF] Belloni | Least squares after model selection in high-dimensional sparse models[END_REF].

Results for each of the 90 control periods were combined in a figure to investigate whether patterns could be found according to the length of the washout period (e.g., medicines selected with narrow washout). A colored square was used to indicate that a medicine class was selected by the model. The color intensity and the size of this square were proportional to the bias-corrected odds ratio obtained at the end of the Bolasso procedure.

All statistical analyses were performed using the package Penalized in R statistical software (version 3.2.3; R Foundation for Statistical Computing, Vienna, Austria). The bootstrap was implemented manually.

Results

National ID number, sex, and date of birth of individuals involved in a traffic crash were extracted for 215,032 of the 439,518 police reports of traffic crashes from 1 July 2005 to 31 December 2011. Among these, 186,636 (86.8%) were matched with a corresponding record in the police national database of injurious crashes. The linkage failed for national ID numbers corresponding to road users involved in a crash but not captured in the police national injurious crashes database and for individuals not involved in the crash (e.g., witnesses).

The procedure led to the inclusion of 16,458 pedestrians involved in a road traffic crash between 1 July 2005 and 31 December 2011 (19.1% of the pedestrians registered in the national database of injurious crashes; see Fig 2). Among these, 7,535 pedestrians (45.8%) were never exposed to any medicine under study during the time period considered (crash day and 120 days before), and 2,339 pedestrians (14.2%) were exposed to at least 1 medicine of interest, but without interruption. Consequently, these pedestrians were not included in the analyses. When varying the washout period, the sample size (pedestrians with unequal exposure in the case and control periods) varied from 5,009 (30.4% of pedestrians; washout = 37 days) to 5,315 (32.3% of pedestrians; washout = 107 days). The probability of being part of the study was associated with sex, age, injury severity, weather conditions, and day of the week (S1 Table ).

Almost 60% of the participants were women, and almost one-third were 65 years old or older (Table 1). The majority of crashes occurred during favorable weather and lighting conditions. In all, 12,474 pedestrians (75.8%) were crossing the street at the time of the crash, and 7,823 (47.6%) were in a crosswalk. More precisely, most of the crashes occurred in a crosswalk with a traffic light (29.4%) or less than 50 m from a crosswalk (20.8%).

When varying the washout period from 30 days ( A second pattern included 8 medicines that were consistently associated with increased risk in models with a wide washout period (yellow triangles). This pattern included 3 insulins and analogues (A10AC, A10AD, and A10BD). A third pattern included 3 medicine classes that were regularly associated with increased risk regardless of the washout period (green circles). Among these 3, alpha-adrenoreceptor antagonists (G04CA) showed the most regular association profile (showing association with increased risk in more than 90% of the designs). Finally, 32 medicines showed irregular associations with pedestrian crash risk (black squares) with respect to the length of the washout period.

Table 2 presents the variation of the bias-corrected odds ratios and the total number of designs in which each exposure was selected (L value).

Table 3 shows that benzodiazepine derivatives and benzodiazepine-related drugs have the highest consumption rates in our cohort. Medicines with frequent use also include 4 classes of drugs used either as analgesics or as anti-inflammatory and antirheumatic drugs (R05DA, N02BG, N02AX, and M01AB), 2 classes of antihistamines (R06AX and R06AD), plain ACE inhibitors (C09AA), and 1 class of antidepressants (N06AX).

Discussion

The analysis of 16,458 pedestrians involved in a road crash between 1 July 2005 and 31 December 2011, among which 6,584 were included in the analyses, identified 48 medicine classes associated with an increased risk for pedestrians of being involved in an injurious road traffic crash. Among them, the 10 most consumed medicines included benzodiazepines and benzodiazepine-related drugs, antihistamines, and anti-inflammatory and antirheumatic drugs. Injury severity and age were associated with the probability of being part of the study. This is due to 2 combined factors: (1) the healthcare number was more frequently noted for injured pedestrians admitted to hospital, leading to a slight overrepresentation of pedestrians injured in more severe crashes, and (2) older road users involved in a road crash are more likely to be more severely injured [START_REF] Loo | Pedestrian injuries in an ageing society: insights from hospital trauma registry[END_REF].

Computerized records of reimbursed prescriptions were used to determine exposure to medications. Compared with self-reporting methods, this method avoids memory bias. However, these databases have 2 main limitations. First, there is a lack of information about selfmedication and the use of over-the-counter drugs because only dispensing of reimbursed drugs is recorded. Second, there is a lack of information about treatment compliance. Because of the use of the dispensing date to determine exposure periods, these limitations can result in exposure misclassification. A study using the same reimbursement database showed that healthcare insurance data are reliable indicators of actual exposure for medicines used over a long time, but less so for episodically used medicines [START_REF] Noize | Comparison of health insurance claims and patient interviews in assessing drug use: data from the Three-City (3C) Study[END_REF].

In studies on medicines, both the treatment and the condition for which the treatment was prescribed can be associated with the outcome of interest. Because the case-crossover design compares each individual with himself/herself, it has the advantage of eliminating control selection bias and confounding by time-invariant factors such as age, sex, and chronic conditions [START_REF] Maclure | The case-crossover design: a method for studying transient effects on the risk of acute events[END_REF]. However, confounding by indication remains for non-chronic conditions or if there is a change in the severity of the disease over time. Confounding may also remain for other time-varying factors such as increased enforcement of speeding laws. However, the effect on our estimates is likely insignificant because exposures of only the 4 months preceding the crash day were considered for each pedestrian. The probability of such an event occurring during these 4 months is therefore small. Another reason the effect of these potential confounding factors is likely to be insignificant is that these 4-month periods were different for every pedestrian and therefore were spread over a 6-year period. The choice of the control periods has to be independent of exposure, and only periods in which an event can occur must be considered [START_REF] Mittleman | Exchangeability in the case-crossover design[END_REF].

One limitation of our study is that no information was available on how much the participants walked during the control versus case periods. Thus, we were not able to control for the amount of walking. If the probability of being a pedestrian is correlated with exposure, then the results may be biased. Indeed, consumption of some of the medicines under study may result in an increased probability of walking instead of driving because of the warning pictogram on medicine packaging. However, a recent study exploring trends in medicine consumption (restricted to hypnotics and anxiolytics) before and after the implementation of pictograms in France showed no impact of pictograms on exposure level to these medicines among drivers. Consequently, it is very unlikely that the pictogram system resulted in a substantial shift in transportation means for consumers of those medicines [START_REF] Orriols | Road traffic crash risk associated with benzodiazepine and z-hypnotic use after implementation of a colour-graded pictogram: a responsibility study[END_REF]. Medicines can also lead to an increase in walking due to an increased sense of well-being. However, there will be a bias only if the reason for taking this medicine already existed during the control period and led to a decrease in walking. This is unlikely, as control periods were at least 30 days before the crash, and there is no reason to think that people affected by a debilitating disease for at least 1 month would not take medicines. Consequently, taking medicines during the case period was assumed to enable the individual to get back to his or her previous walking habits. Analyses were not adjusted for alcohol consumption because the information was not available during control periods. Alcohol has been found to be associated with a higher risk of crash for pedestrians [START_REF] Eriksson | Pedestrian fatalities and alcohol[END_REF] and could also be a confounding factor for medicines such as benzodiazepines. Information about blood alcohol level, as recorded in the police national database of injurious crashes, was unknown for 41.6% of the pedestrians. Among the 9,617 pedestrians with data for blood alcohol level, 95.7% had a level below the legal limit. A comparison between pedestrians with an alcohol level below the legal limit and pedestrians with missing alcohol status suggested that the latter were not tested for alcohol because the police officers did not consider it necessary. Pedestrians with a blood alcohol level above the legal limit were more likely to be male, aged 30 to 49 years, and presumed responsible for the crash, compared with pedestrians with an alcohol level below the legal limit or with missing alcohol status. They were also less likely to be exposed to level 1 medicines and more likely to be exposed to level 3 medicines. Removing the individuals with an alcohol level above the legal limit from the analysis would most likely be inconsequential because they represent only 412 individuals, thus resulting in a very small number of discordant exposures.

Among the 16,458 pedestrians included in the present study, older adults and women were overrepresented. These findings are in agreement with national statistics on injurious crashes [START_REF] L'observatoire | National Interministe ´riel de la Se ´curite ´Routière. Donne ´es brutes[END_REF]. This is probably the combined result of a greater fragility and exposure of the elderly, along with a higher proportion of women among the elderly. Two urological drugs (G04CA and G04BD) were selected for almost all case-crossover designs regardless of the washout period. This can be interpreted as the result of treatment initiation (they were exposed during the case period, but never before). These drugs can affect a pedestrian's level of attention (e.g., reaction time) or mobility (e.g., walking speed). For instance, alpha-adrenoceptor antagonists induce vasodilatation and subsequently lower blood pressure, with potential symptoms including asthenia, dizziness, fatigue, and orthostatic hypotension, particularly upon treatment initiation [START_REF] Bird | Tamsulosin treatment for benign prostatic hyperplasia and risk of severe hypotension in men aged 40-85 years in the United States: risk window analyses using between and within patient methodology[END_REF][START_REF] Chrischilles | Initiation of nonselective alpha1antagonist therapy and occurrence of hypotension-related adverse events among men with benign prostatic hyperplasia: a retrospective cohort study[END_REF][START_REF] Oelke | Cardiovascular and ocular safety of α1-adrenoceptor antagonists in the treatment of male lower urinary tract symptoms[END_REF]. Similarly, urinary antispasmodics have a high potential of producing anticholinergic effects, which can result in cognitive side effects including memory changes, blurred vision, somnolence, hallucinations, confusion, and delirium [START_REF] Geller | Effect of anticholinergic use for the treatment of overactive bladder on cognitive function in post-menopausal women[END_REF][START_REF] Munjuluri | Anticholinergic drugs for overactive bladder: a review of the literature and practical guide[END_REF].

Eight medicines (ATC level 4) were selected in case-crossover designs with control periods away from the crash day. Risk associations with long washout periods may be the consequence of longer duration of medicine use, requiring a longer washout period in order to have discordant exposures between case and control periods. The exposures selected in this profile, including antidiabetic drugs (A10AC, A10AD, and A10BD) and antimigraine preparations (N02CX) prescribed in chronic treatment of migraine, tend to support this assumption. Hypoglycemia is a common adverse effect of antidiabetic treatment [START_REF] Shorr | Incidence and risk factors for serious hypoglycemia in older persons using insulin or sulfonylureas[END_REF][START_REF] Edic) | Design, implementation, and preliminary results of a long-term follow-up of the Diabetes Control and Complications Trial cohort[END_REF][START_REF] Pramming | Symptomatic hypoglycaemia in 411 type 1 diabetic patients[END_REF] and can result in decreased motor skills, visual acuity, or auditory processing and deterioration of a variety of cognitive processes [START_REF] Sommerfield | Short-term, delayed, and working memory are impaired during hypoglycemia in individuals with type 1 diabetes[END_REF][START_REF] Brands | The effects of type 1 diabetes on cognitive performance a meta-analysis[END_REF]. However, in this pattern, the increased risk is most likely linked to disease-related complications. Indeed, in the case-crossover design, the longer the washout period, the higher the risk of potential confounding by unmeasured time-varying factors including disease severity. Medicines of the R06AX group were mostly second-generation antihistamines, which may have fewer sedative effects than those of the first generation. Rhinitis, for which they are prescribed, can affect the quantity and quality of sleep and so lead to fatigue and daytime somnolence [START_REF] Cola ´s | Disease severity impairs sleep quality in allergic rhinitis (The SOMNIAAR study)[END_REF][START_REF] Muliol | Sleep and allergic rhinitis[END_REF]. Acetic acid derivatives and related substances (M01AB) are nonsteroidal anti-inflammatory drugs used in the treatment of various painful inflammatory conditions including rheumatoid arthritis and osteoarthritis. Rheumatoid arthritis, which may affect pedestrians' walking ability, is characterized in most people by alternating periods of remission and relapse, which can explain the narrow washout despite it being a chronic condition [START_REF] Van Laar | Pain treatment in arthritis-related pain: beyond NSAIDs[END_REF]. Antihistamines (R06AX) and acetic acid derivatives (M01AB) were among the 10 most consumed medicines selected in our analyses.

Risk associations with exposure periods close to the crash suggest an effect of acute, shortterm exposure to the medicine. Both Parkinson disease symptoms (e.g., muscle rigidity, slowing of physical movement) and side effects of dopamine agonists (N04BC)-including dizziness, somnolence, insomnia, and orthostatic hypotension-can affect a pedestrian's walking ability. Because of the chronicity of Parkinson treatment, the increased risk of crash can be the result of a treatment change or a change in the disease condition. However, because of the proximity with the crash, the first possibility is more likely. This is also true for other antipsychotic drugs (N05AX) and barbiturates and derivatives (N03AA), 2 medicines used in chronic conditions. Moreover, lack of compliance with treatment is frequent in patients with schizophrenia, and barbiturates and derivatives (N03AA) have been found to be associated with drowsiness and cognitive effects, including diminished attention, executive function, and processing speed [START_REF] Cramer | Adverse effects of antiepileptic drugs: a brief overview of important issues[END_REF][START_REF] Pellock | Treatment considerations: traditional antiepileptic drugs[END_REF]. Piperazine derivatives (R06AE) were associated with an increased risk of crash, but with a low risk level (median bias-corrected odds ratio of 1.3). Like medicines grouped as "other antihistamines for systemic use drugs" (R06AX), they are prescribed for the treatment of allergic rhinitis and urticaria and are mostly second-generation antihistamines. However, cetirizine and levocetirizine (R06AE) were found to be associated with a higher risk of sedation than loratadine (R06AX) [START_REF] Salmun | Loratadine versus cetirizine: assessment of somnolence and motivation during the workday[END_REF][START_REF] Mann | Sedation with "non-sedating" antihistamines: four prescription-event monitoring studies in general practice[END_REF].

Among medicines showing risk associations with a less consistent pattern in terms of the length of the washout period, benzodiazepine derivatives (N05BA), benzodiazepine-related drugs (N05CF), and plain ACE inhibitors (C09AA) were 3 medicines inconsistently but frequently selected among the 90 models. Moreover, they were among the 10 most consumed medicines. The association between the use of benzodiazepines and the risk of road traffic crashes has been documented with consistent results among drivers. Benzodiazepines have also been shown to be associated with an increased risk of falling in the elderly, which may be due to attention, gait, and balance impairment [START_REF] Rossat | Association between benzodiazepines and recurrent falls: a cross-sectional elderly population-based study[END_REF], effects that might also increase the risk of crash for pedestrians. One study has reported a significantly higher risk of at-fault crash involvement with the use of ACE inhibitors in the elderly, medicines commonly used to treat hypertension [START_REF] Mcgwin | Relations among chronic medical conditions, medications, and automobile crashes in the elderly: a population-based case-control study[END_REF].

Results for 3 medicines were unexpected: plain antiandrogens (G03HA), amino acids (B02AA), and gonadotropin-releasing hormone analogues (L02AE) showed a strong association with the risk of pedestrian crash. However, their levels of use in our sample of injured pedestrians were all under 0.3%, and their estimated odds ratios were based on a small number of discordant pairs. In addition, these medicines were all attributed a level 1 warning pictogram, which means that their risk is low, heterogeneous, and strongly dependent on individuals' pharmacodynamic parameters.

In summary, our results suggest that several classes of medicine are associated with an increased risk of pedestrian crash. Improving awareness of this risk is, therefore, a necessity, as the risks of medicines in road safety have hitherto been thought to concern drivers only. Most of the crashes occurred when the pedestrian was crossing the street, which requires certain levels of physical ability (e.g., walking speed, head mobility), perception (e.g., vision, hearing), and cognitive processing (e.g., attention, processing speed) [START_REF] Dommes | The role of perceptual, cognitive, and motor abilities in street-crossing decisions of young and older pedestrians[END_REF]. Despite an association between medicine use and pedestrian crashes, it is not recommended to drive instead.

Fig 1 .

 1 Fig 1.The case-crossover design of the study, with multiple drug exposures and a varying washout period. In the casecrossover design, only individuals with unequal exposures for the control period and the case period contribute to the analysis. For instance, with a control day defined at 120 days before the crash day, the individual shown in this figure has unequal exposures for the second drug (exposed during case day and unexposed during control day), but concordant exposures for the first drug (exposed both days) and the third drug (unexposed both days). In a case-crossover analysis, only the exposure to the second drug is used. https://doi.org/10.1371/journal.pmed.1002347.g001

  Fig 3, right) to 119 days (Fig 3, left), we found 48 medicine classes (ATC level 4) associated with an increased risk of being involved in a road crash as a pedestrian in at least 1 of the 90 models, and 4 association patterns (Fig 3). A pattern with a narrow washout period characterized 5 medicine classes (labeled with blue stars in Fig 3), including dopamine antagonists (N04BC) and piperazine derivatives (R06AE).

Fig 2 .

 2 Fig 2. Flowchart of the inclusion procedure. Note that the discrepancy between the number of police reports and the number of records in the police national database of injurious crashes is explained by the fact that a small proportion of unavailable reports were being used for ongoing legal investigations. *Modified from Orriols et al. [24]. https://doi.org/10.1371/journal.pmed.1002347.g002

Fig 3 .

 3 Fig 3.Results of the 90 case-crossover designs obtained when varying the washout period from 30 days to 119 days. A blank cell means that the medicine class was not retained in the final model for this control period, and a colored square means that the medicine class was selected by the model. Both the size and color intensity of the squares depend on the absolute value of the bias-corrected estimated coefficients. When varying the washout period, the frequency thresholds estimated using the Akaike information criterion varied from a minimum of 50% (washout = 40) to a maximum of 74% (washout = 104). A frequency threshold of 74% means that medicines selected in at least 74% of the 1,000 bootstraps were considered as associated risk factors for pedestrian road crash. The different colored forms on the far left indicate groups of medicines according to the location of the control periods (with respect to the crash day) for which there was an association of the medicine with increased risk of being involved in a road crash as a pedestrian: blue stars indicate increased risk in control periods close to the crash; yellow squares indicate increased risk in control periods far from the crash; green circles indicate increased risk in control periods both close to and far from the crash; black squares indicate increased risk in discontinuous control periods. https://doi.org/10.1371/journal.pmed.1002347.g003

a

  ATC: the Anatomical Therapeutic Chemical classification system. b L: number of case-crossover designs in which the exposure was selected. c OR: median, first quartile, and third quartile of bias-corrected odds ratio. d Case period: median, first quartile, and third quartile of the number of cases exposed only during the case period. e Control period: median, first quartile, and third quartile of the number of cases exposed only during the control period. *ATC classes with risk associations for control periods close to the crash day (blue stars in Fig 3). # ATC classes with risk associations for control periods both close to and far from the crash day (green circles in Fig 3). † ATC classes with risk associations for control periods far from the crash day (yellow triangles in Fig 3). ‡ ATC classes with risk associations for discontinuous control periods (black squares in Fig 3). https://doi.org/10.1371/journal.pmed.1002347.t002

Table 1 . Pedestrian and crash characteristics.

 1

	Characteristic	Subcategory	Number (%)
	Total		16,458
	Gender male		6,803 (41.3)
	Age (years)	<18	1,455 (8.8)
		18-24	1,641 (10.0)
		25-34	1,731 (10.5)
		35-44	1,810 (11.0)
		45-54	2,122 (12.9)
		55-64	2,255 (13.7)
		65-74	2,022 (12.3)
		!75	3,395 (20.6)
		Missing	27 (0.2)
	Pedestrian responsible for crash (as determined by		2,369 (14.4)
	police officer)
	Injury severity	Unhurt	123 (0.7)
		Slightly injured	8,197 (49.8)
		Seriously injured	7,741 (47.0)
		Killed	397 (2.4)
	Risk ranking of medicine a	Level 1	3,460 (21.0)
		Level 2	3,379 (20.5)
		Level 3	983 (6.0)
	Weather	Not reported	1 (0.0)
		Normal	12,844
			(78.0)
		Light rain	1,852 (11.2)
		Heavy rain	473 (2.9)
		Snow/hail	118 (0.7)
		Fog/smoke	76 (0.5)
		Strong windstorm	34 (0.2)
		Blinding weather	381 (2.3)
		Cloudy	572 (3.5)
		Other	107 (0.7)
	Season	Spring	3,289 (20.0)
		Summer	3,475 (21.1)
		Autumn	5,601 (34.0)
		Winter	4,093 (24.9)
	Time of day	05:00-10:59	4,464 (27.1)
		11:00-13:59	2,865 (17.4)
		14:00-19:59	7,762 (47.2)
		20:00-22:59	923 (5.6)
		23:00-01:59	286 (1.7)
		02:00-04:59	158 (1.0)
	Crash day	Weekday	13,500
			(82.0)
		Saturday	1,958 (11.9)
		Sunday	1,000 (6.1)
	Lighting	Daylight	12,028
			(73.1)
		Dawn or dusk	1,007 (6.1)
			(Continued)

Table 1 .

 1 (Continued)

	Characteristic	Subcategory	Number (%)
		Dark, no street lights	498 (3.0)
		Dark, street lights off	132 (0.8)
		Dark, street lights on	2,793 (17.0)
	Pedestrian's action	Not reported	715 (4.3)
		Moving	1,340 (8.1)
		Crossing	12,474
			(75.8)
		Playing/running	470 (2.9)
		Other	1,459 (8.9)
	Pedestrian's location	Not reported	1,632 (9.9)
		>50 m from a crosswalk	2,064 (12.5)
		50 m from a crosswalk	3,416 (20.8)
		Crosswalk without a traffic	2,990 (18.2)
		light
		Crosswalk with a traffic light 4,833 (29.4)
		Sidewalk	1,028 (6.2)
		Other	495 (3.0)

a Exposure on the crash day. For this study, only medicines ranking from levels 1 to 3 were included in the analysis. Some pedestrians may have been exposed to several medicines of different risk level. https://doi.org/10.1371/journal.pmed.1002347.t001

Table 2 . Selection frequency of 48 medicine classes among the 90 case-crossover models, bias-corrected odds ratios, and unequal exposures. ATC class a (fourth level) ATC class description L b OR c Case period d Control period e

 2

	G03HA*	Antiandrogens, plain	43 2.66 (2.59-	10 (9-10)	4 (3-4)
			3.10)
	N03AA*	Barbiturates and derivatives	10 2.16 (2.00-	13 (13-13)	6 (6-7)
			2.30)
	N04BC*	Dopamine agonists	13 1.85 (1.80-	22 (20-23)	12 (11-12)
			1.99)
	N05AX*	Other antipsychotics	9 1.48 (1.45-	45 (44-45)	31 (30-32)
			1.55)
	R06AE*	Piperazine derivatives	47 1.35 (1.28-	122 (113-	85 (82-88)
			1.49)	126)
	B02AA #	Amino acids	64 2.60 (2.23-	13 (12-13)	4 (3-5)
			3.93)
	G04BD #	Urinary antispasmodics	74 1.87 (1.61-	42 (40-44)	22 (21-25)
			2.01)
	G04CA #	Alpha-adrenoreceptor antagonists	84 1.50 (1.44-	59 (56-63)	39 (36-42)
			1.61)
	A10AC †	Insulins and analogues for injection, intermediate-acting	46 2.10 (1.88-	18 (16-18)	9 (7-9)
			2.33)
	A10AD †	Insulins and analogues for injection, intermediate-acting combined with fast-	14 2.30 (2.15-	20 (18-21)	9 (8-9)
		acting	2.41)
	A10BD †	Combinations of oral blood glucose-lowering drugs	40 2.89 (2.49-	11 (10-13)	4 (4-4)
			3.40)
	C09DA †	Angiotensin II antagonists and diuretics	26 1.34 (1.28-	102 (95-107) 74 (70-79)
			1.38)
	L02AE †	Gonadotropin-releasing hormone analogues	48 2.98 (1.87-	13 (11-18)	4 (3-10)
			3.44)
	M01AB †	Acetic acid derivatives and related substances	15 1.30 (1.27-	90 (89-94)	68 (64-70)
			1.39)
	N02CX †	Other antimigraine preparations	36 2.21 (2.09-	13 (12-13)	6 (5-6)
			2.44)
	R06AX †	Other antihistamines for systemic use	36 1.20 (1.18-	209 (206-	172 (166-176)
			1.23)	213)
	A04AD ‡	Other antiemetics	27 2.16 (1.84-	18 (18-19)	9 (7-10)
			2.53)
	A10BX ‡	Other blood glucose-lowering drugs, excluding insulins	2 1.69 (1.69-	19 (19-19)	11 (11-11)
			1.69)
	C08CA ‡	Dihydropyridine derivatives	16 1.32 (1.30-	81 (75-83)	61 (56-62)
			1.35)
	C09AA ‡	ACE inhibitors, plain	18 1.26 (1.23-	125 (120-	96 (95-100)
			1.28)	128)
	C09BA ‡	ACE inhibitors and diuretics	1 1.37 (1.37-	48 (48-48)	36 (36-36)
			1.37)
	C09BB ‡	ACE inhibitors and calcium channel blockers	5 2.45 (2.41-	9 (9-9)	4 (4-4)
			2.45)
	G01AA ‡	Antibiotics	32 2.44 (2.10-	13 (13-13)	5 (5-6)
			2.58)
	G03DA ‡	Pregnen (4) derivatives	13 1.46 (1.42-	44 (43-45)	30 (28-31)
			1.49)
	J01FA ‡	Macrolides	12 2.55 (2.30-	11 (11-11)	4 (4-5)
			2.98)
	J01MA ‡	Fluoroquinolones	21 1.54 (1.42-	45 (44-45)	28 (27-29)
			1.61)
	L02BA ‡	Anti-estrogens	2 2.48 (2.46-	8 (8-8)	3 (3-3)
			2.49)
	M03BA ‡	Carbamic acid esters	4 2.42 (2.30-	14 (13-14)	6 (5-6)
			2.57)
					(Continued)

Table 2 .

 2 (Continued)

ATC class a (fourth level) ATC class description L b OR c Case period d Control period e

	M03BX ‡	Other centrally acting agents	24 1.37 (1.33-	70 (67-71)	50 (47-52)
			1.43)
	N02AA ‡	Natural opium alkaloids	1 1.24 (1.24-	112 (112-	89 (89-89)
			1.24)	112)
	N02AX ‡	Other opioids	1 1.16 (1.16-	214 (214-	184 (184-184)
			1.16)	214)
	N02BG ‡	Other analgesics and antipyretics	2 1.31 (1.30-	77 (76-78)	60 (60-60)
			1.32)
	N03AG ‡	Fatty acid derivatives	13 1.90 (1.80-	22 (21-23)	11 (10-12)
			2.25)
	N05AD ‡	Butyrophenone derivatives	10 2.01 (1.97-	16 (16-17)	10 (9-11)
			2.04)
	N05AN ‡	Lithium	5 2.68 (2.67-	8 (8-8)	3 (3-3)
			2.69)
	N05BA ‡	Benzodiazepine derivatives	19 1.12 (1.11-	462 (437-	411 (391-413)
			1.13)	470)
	N05BX ‡	Other anxiolytics	7 1.49 (1.43-	37 (37-38)	26 (25-26)
			1.57)
	N05CF ‡	Benzodiazepine-related drugs	47 1.17 (1.16-	251 (238-	212 (200-217)
			1.20)	256)
	N05CX ‡	Hypnotics and sedatives in combination, excluding barbiturates	2 1.40 (1.39-	54 (54-54)	37 (37-37)
			1.41)
	N06AX ‡	Other antidepressants	3 1.28 (1.26-	112 (111-	89 (89-89)
			1.30)	112)
	N06DX ‡	Other antidementia drugs	5 2.68 (

Table 3 . The 10 most consumed medicines among those listed in Table 2 as associated with road traf- fic crash involvement. ATC a class (fourth level) Number (%) b L c

 3 L: number of case-crossover designs in which the exposure was selected. ‡ ATC classes with risk associations for discontinuous control periods (black squares in Fig3). † ATC classes with risk associations for control periods far from the crash (yellow triangles in Fig3).

	Total

b

Frequency and proportion of individuals with at least 1 delivery over the study period. c

PLOS Medicine | https://doi.org/10.1371/journal.pmed.1002347July 18, 2017

Acknowledgments

The DRUGS-SAFE program aims at providing an integrated system allowing the concomitant monitoring of drug use and safety in France. The potential impact of drugs (e.g., psychotropics), frailty of populations, and seriousness of risks drive the research program. This publication expresses the views of the authors and does not necessarily represent the opinion of the French National Agency for Medicines and Health Products Safety (ANSM).

by the French National Health Insurance (CNAMTSThe CESIR-A project was supported by the French Direction de la se ´curite ´et de la circulation routières (DSCR) and the French National Institute of Health and Medical Research (Equipe INSERM). The present study is part of the Drugs Systematized Assessment in real-liFe Environment (DRUGS-SAFE) research program funded by the French Medicines Agency (Agence Nationale de Se ´curite ´du Me ´dicament et des Produits de Sante ´, ANSM); grants received for the year 2015: 900,000 euros. Employees of ANSM participated in data collection. The funders had no role in study design and analysis, decision to publish, or preparation of the manuscript.

Access to the French national healthcare insurance database, the police reports and the national police database of injurious crash have been respectively provided fr/etudes-recherches or email requests

Supporting information