Gautier Bon
email: gautier.bon80@gmail.com

Elias Ben Kacem

Pierre-Marie Leprêtre

Thierry Weissland

Patrice Mertl

Massinissa Dehl

Antoine Gabrion

Pierre Marie Lepretre

Does the direct anterior approach allow earlier recovery of walking following total hip arthroplasty? A randomized prospective trial using accelerometry

Keywords: anterior approach, posterior approach, total hip arthroplasty, gait, functional scores

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

Introduction

In total hip arthroplasty (THA), the anterior approach is attractive, being intermuscular, with theoretic functional benefit. Such benefit has been frequently claimed, but there are few data from randomized comparative studies using more precise metrics than patient satisfaction. We therefore conducted a randomized trial comparing early functional results between anterior and posterior approaches on gait analysis and functional scores.

Hypothesis

The study hypothesis was that there is no difference between the two approaches in terms of early recovery of walking.

Materials and method

A single-center single-surgeon prospective randomized study was conducted between February 2017 and April 2018. Inclusion criteria comprised: age <85 years, body-mass index (BMI) <32, and hip osteoarthritis with indication for THA. Preoperatively, the 2 groups were comparable for age, gender, BMI, Charnley, Harris, Postel-Merle-d'Aubigné and Oxford-12 scores and locomotor parameters (triaxial acceleration, step regularity and walking power).

Preoperative and 3-, 6-and 12-week assessment comprised triaxial acceleration in walking and Postel-Merle-d'Aubigné, Harris and Oxford SF-12 scores.

Results

One hundred patients were randomized to the anterior approach (AA: n=50) and posterior approach (PA: n=50) groups. Hospital stay was comparable between groups: PA, 2.8 ± 1.78 days [range, 2.29-3.31 days]; AA, 2.84 ± 1.25 days [range, 2.48-3.2 days] (p=0.8). Operative time was significantly longer in AA: 70.1 ± 11 minutes vs. 56.7 ± 11.79 (p < 0.0001). There were no significant differences in locomotor parameters (p 0.122 to 0.987) or functional scores (p 0.052 to 0.968) over the 3-month follow-up. There was no difference in cup inclination: PA, 39.6 ± 6.87° [range, 37.65-41.55°] vs. AA, 37.74 ± 4.2° [range, 36.55-

Introduction

Total hip arthroplasty (THA) is effective and reproducible, providing functional recovery, pain relief and improved quality of life. Around 150,000 THAs are performed per year in France [START_REF] Caton | Typologie et épidémiologie des prothèses totales de hanche en France[END_REF], and the number can be expected to increase over coming decades as the population ages [START_REF] Caton | Typologie et épidémiologie des prothèses totales de hanche en France[END_REF]. Various surgical approaches have been described. The posterior approach (PA) is classical, but Hueter's anterior approach (AA) has met with renewed interest, being anatomically attractive and having theoretic functional advantages [START_REF] Higgins | Anterior vs. posterior approach for total hip arthroplasty, a systematic review and meta-analysis[END_REF].

The literature reports contradictory findings. In a meta-analysis of the 2 approaches, Higgins et al. [START_REF] Higgins | Anterior vs. posterior approach for total hip arthroplasty, a systematic review and meta-analysis[END_REF] found no superiority, notably in terms of early functional results, which, however, are often highlighted by AA advocates. There have in fact been few randomized trials, and assessment was often based on patient satisfaction, without objective evaluation of benefit [START_REF] Higgins | Anterior vs. posterior approach for total hip arthroplasty, a systematic review and meta-analysis[END_REF].

We therefore conducted a randomized study comparing early functional results between AA and PA, with measurement of triaxial acceleration during walking on a Locometrix™ accelerometer, an easy-to-use device compared to other gait analysis systems, and 3 reference functional scores. The study hypothesis was that the 2 approaches do not differ in terms of early recovery of walking.

Materials and method

Patients

A single-center prospective study involved a single surgeon experienced in the posterior approach and also using the anterior approach for some 10 years. One hundred and eight of the 167 patients on the surgeon's schedule were included in the prospective randomized study conducted from February 2017 to April 2018. Inclusion criteria comprised: age <85 years, body-mass index (BMI) <32 kg/m 2 , and symptomatic hip osteoarthritis with indication for THA. Eligible patients agreeing to participate signed an informed consent form after information on the study procedure. The trial was registered under RCB ID n° 2017-A02875-48 after review board approval (registered with the Clinical Research and Innovation Delegation under n° PI2017-843-0023).

Exclusion criteria comprised: patients not meeting the inclusion criteria, not complying with the follow-up protocol, without health insurance cover, with significant cognitive impairment, with musculoskeletal disease or unable to walk without assistance.

Patients were randomized to the AA and PA groups using the Randomizer for Clinical Trial software (Medsharing, Fontenay-sous-Bois, France).

Methods

PA was Moore's posterolateral approach, sparing the quadratus femoris muscle but not the piriformis, with transosseous reinsertion of the pelvitrochanteric muscles and capsule. AA was Hueter's anterior approach, performed with the patient supine on the traction table, without intraoperative radioscopic control.

Choice of implants, fixation and bearing was at the surgeon's discretion. Preoperative planning used 100%-scale standard radiographs aided by implant templates. The perioperative protocol was the same in both groups. Preoperatively, patients were encouraged to attend an information meeting to prepare for the operation. Intraoperatively, local injection of antiinflammatories (ketoprofen 100mg/4mL) and step-3 analgesics (ropivacaine 200mL at 2mg/mL) was administered. Tranexamic acid was injected at induction, end of surgery and 5 hours after. Postoperatively, patients were raised during the first evening. Discharge was authorized, generally on postoperative day 2, only if walking and unassisted climbing up and down stairs was possible. Fifteen physiotherapy sessions were prescribed; rehabilitation in a residential center was authorized only for patients living alone.

Assessment

accelerometry close to the subject's center of gravity (Locometrix, Centauremetrix, Evry, France) [START_REF] Auvinet | Reference data for normal subjects obtained with an accelerometric device[END_REF][START_REF] Auvinet | Gait analysis in coxarthrosis using an accelerometric device[END_REF][START_REF] Auvinet | Analyse de la marche humaine dans la pratique hospitalière par une méthode accélérométrique[END_REF]. The device was positioned dorsally at lumbar levels 3 and 4. Data were recorded in a single corridor to analyze 20 seconds' stabilized gait: rhythm, regularity, mediolateral instability, and power in the craniocaudal, anteroposterior and mediolateral planes and total power. Perioperative changes in the 3 reference functional scores (Harris [6], Postel-Merled'Aubigné [START_REF] Merle | Numerical classification of the function of the hip[END_REF] and the self-reported Oxford-12) were also analyzed [START_REF] Delaunay | Cross-cultural adaptations of the Oxford-12 HIP score to the French speaking population[END_REF][START_REF] Dawson | Questionnaire on the perceptions of patients about total hip replacement[END_REF], along with the Lequesne algofunctional index [START_REF] Lequesne | The algofunctional indices for hip and knee osteoarthritis[END_REF] to assess preoperative osteoarthritis severity. Assessments were conducted the day before surgery and at 3, 6 and 12 weeks.

Other parameters comprised cup inclination, global offset measured radiologically by 2 independent observers, and onset of complications within 3 months. Cup anteversion was not studied, as it is difficult to analyze reliably and reproducibly on plain X-ray.

Statistics

Statistical analysis used SPSS 23.0 software (IBM, Bois-Colombes, France). Normal distribution was checked on Shapiro-Wilk test. The Student test was used to compare independent quantitative variables: mean functional scores and gait analysis data. The chi² test with Yates correction or Fisher test as appropriate were used to compare qualitative variables: demographic data, implant distribution and Harris subscores. With step regularity as criterion, bilateral alpha risk of 5% and 90% power, each group required at least 39 subjects. As the study was to be conducted over an extended period of time, 25% attrition was anticipated, and group size was set at >49.

Results

Four AA and 3 PA subjects were excluded for missing the first postoperative consultation (due to organizational issues). One further PA subject was excluded following early infection requiring 1-step implant exchange. Finally, each group comprised 50 subjects (Figure 1). The groups were comparable for all preoperative parameters: demographic data, gait analysis and functional scores (Table 1).

Operative time was significantly longer in the AA group (p < 0.0001). Hospital stay was similar in both groups (p = 0.897), as was the post-operative rehabilitation conditions. Dual mobility X.NOV X.CUP MOB ® cups predominated in the PA group (p < 0.0001) and Mathys RM Pressfit ™ cups in the AA group (p < 0.0001). Cup inclination was comparable between groups (p = 0.0993). Global offset was restored comparably between groups (Table 2).

Postoperatively, locomotor parameters (rhythm, regularity, power in the 3 planes and mediolateral instability) showed no intergroup difference in recovery of walking at 3, 6 and 12 weeks (Table 3). There were no significant intergroup differences in the 3 scores, including Harris subscores (notably, pain, walking distance and global function), at the various postoperative time-points (Table 4).

The rate of neurapraxia of the lateral cutaneous nerve of the thigh was 8/50 (16%) in AA and zero in PA. One anterior dislocation occurred in the AA group, before week 2, occasioned by trauma in a very active patient with excellent postoperative results. Other complications did not differ between groups (Table 5).

Discussion

In view of the scarcity of randomized comparative studies using more precise metrics than patient satisfaction, we conducted a prospective randomized trial associating reference scores and locomotion analysis. Analysis of gait parameters during the first 3 months failed to demonstrate superiority for either the AA or the PA approach. This was in agreement with previous comparative studies using spatiotemporal gait analysis [START_REF] Rathod | Similar improvement in gait parameters following direct anterior & posterior approach total hip arthroplasty[END_REF][START_REF] Maffiuletti | Spatiotemporal parameters of gait after total hip replacement: anterior versus posterior approach[END_REF][START_REF] Reininga | Comparison of gait in patients following a computer-navigated minimally invasive anterior approach and a conventional posterolateral approach for total hip arthroplasty: a randomized controlled trial[END_REF][START_REF] Ward | Functional recovery of muscles after minimally invasive total hip arthroplasty[END_REF][START_REF] Taunton | John Charnley Award: Randomized Clinical Trial of Direct Anterior and Miniposterior Approach THA: Which Provides Better Functional Recovery?[END_REF], and notably the recent prospective comparative study by Taunton et al. [START_REF] Taunton | John Charnley Award: Randomized Clinical Trial of Direct Anterior and Miniposterior Approach THA: Which Provides Better Functional Recovery?[END_REF], with 101 patients, which found no significant difference in gait monitoring results as of the second postoperative month. Only Zhao et al. [START_REF] Zhao | Comparison of early functional recovery after total hip arthroplasty using a direct anterior or posterolateral approach: A randomized controlled trial[END_REF] found superiority for AA in terms of gait at 3 months, but gait analysis results

were not detailed and no data were collected before month 3 in their prospective randomized study with 20 patients [START_REF] Zhao | Comparison of early functional recovery after total hip arthroplasty using a direct anterior or posterolateral approach: A randomized controlled trial[END_REF]. Some authors suspect the anterior approach might have negative impact on posture. Van Driessche et al. [START_REF] Van Driessche | Short-term comparison of postural effects of three minimally invasive hip approaches in primary total hip arthroplasty: Direct anterior, posterolateral and Röttinger[END_REF] and Bernard et al. [START_REF] Bernard | Electromyographic study of hip muscles involved in total hip arthroplasty: Surprising results using the direct anterior minimally invasive approach[END_REF] stressed the importance of trauma induced by the retractors or by simply ligating the anterior circumflex artery onto the tensor fasciae latae or sartorius muscle, in which postoperative amyotrophy greatly impairs posture.

In the present study, there were no significant differences in Harris scores during the first 3 months, including analysis of the various subscores. Most other studies likewise found no differences in Harris scores over comparable periods [START_REF] Rykov | Posterolateral vs Direct Anterior Approach in Total Hip Arthroplasty (POLADA Trial): A randomized controlled trial to assess differences in serum markers[END_REF][START_REF] Christensen | Comparison of patient function during the first six weeks after direct anterior or posterior total hip arthroplasty (THA): A randomized study[END_REF][START_REF] Rodriguez | Does the direct anterior approach in THA offer faster rehabilitation and comparable safety to the posterior approach?[END_REF][START_REF] Taunton | Direct anterior total hip arthroplasty yields more rapid voluntary cessation of all walking aids: a prospective, randomized clinical trial[END_REF]. Taunton et al. [START_REF] Taunton | John Charnley Award: Randomized Clinical Trial of Direct Anterior and Miniposterior Approach THA: Which Provides Better Functional Recovery?[END_REF] reported 2-month Harris scores of 95 ± 6 for the anterior and 92 ± 8 for the posterior approach (p = 0.07). Zhao et al. [START_REF] Zhao | Comparison of early functional recovery after total hip arthroplasty using a direct anterior or posterolateral approach: A randomized controlled trial[END_REF], in contrast, found significantly better scores for the anterior approach at 3 months (p = 0.04). Barret et al. [START_REF] Barrett | Prospective randomized study of direct anterior vs postero-lateral approach for total hip arthroplasty[END_REF] likewise reported better total Harris score (p< 0.0001), better function (p = 0.0027), easier putting on of shoes and socks (p <0.0001) and climbing stairs (p = 0.0023) with the anterior approach at 6 weeks. Throughout the first 3 months, a greater percentage of patients were able to walk without restricted distance in the AA group (p= 0.026) [START_REF] Barrett | Prospective randomized study of direct anterior vs postero-lateral approach for total hip arthroplasty[END_REF]; other scores displayed no significant differences over this period.

Cheng et al. [START_REF] Cheng | A prospective randomized clinical trial in total hip arthroplasty-comparing early results between the direct anterior approach and the posterior approach[END_REF] likewise reported no significant differences in Oxford SF12 scores at 2 weeks, 6 weeks or 3 months; nor did Taunton et al., at 2 months [START_REF] Taunton | John Charnley Award: Randomized Clinical Trial of Direct Anterior and Miniposterior Approach THA: Which Provides Better Functional Recovery?[END_REF] (Tables 4 and6).

In the present series, operative times were shorter in AA, in contrast with the surgeon's experience. Hospital stay did not differ according to approach. Higgins, on the other hand, in a meta-analysis, found no significant difference in operative time (7.9 minutes; 95% CI: -1.8 to 17.7 minutes), while hospital stay was significantly shorter with an anterior approach (-0.53 days; 95% CI: -1.01 to 0.04 days) [START_REF] Higgins | Anterior vs. posterior approach for total hip arthroplasty, a systematic review and meta-analysis[END_REF]. That no difference emerged for cup inclination is in agreement with the literature [START_REF] Higgins | Anterior vs. posterior approach for total hip arthroplasty, a systematic review and meta-analysis[END_REF][START_REF] Zhao | Comparison of early functional recovery after total hip arthroplasty using a direct anterior or posterolateral approach: A randomized controlled trial[END_REF][START_REF] Cheng | A prospective randomized clinical trial in total hip arthroplasty-comparing early results between the direct anterior approach and the posterior approach[END_REF][START_REF] Martin | A comparison of hospital length of stay and short-term morbidity between the anterior and the posterior approaches to total hip arthroplasty[END_REF][START_REF] Sugano | Comparison of miniincision total hip arthroplasty through an anterior approach and a posterior approach using navigation[END_REF]. Complications rates were similar between the two groups, as in most reports [START_REF] Rodriguez | Does the direct anterior approach in THA offer faster rehabilitation and comparable safety to the posterior approach?[END_REF][START_REF] Barrett | Prospective randomized study of direct anterior vs postero-lateral approach for total hip arthroplasty[END_REF][START_REF] Maratt | No difference in dislocation seen in anterior vs posterior approach total hip arthroplasty[END_REF][START_REF] Malek | A comparison between the direct anterior and posterior approaches for total hip arthroplasty: the role of an "Enhanced Recovery" pathway[END_REF]. Neurapraxia of the lateral cutaneous nerve of the thigh is, however, specific to the anterior approach [START_REF] Reininga | Comparison of gait in patients following a computer-navigated minimally invasive anterior approach and a conventional posterolateral approach for total hip arthroplasty: a randomized controlled trial[END_REF][START_REF] Cheng | A prospective randomized clinical trial in total hip arthroplasty-comparing early results between the direct anterior approach and the posterior approach[END_REF][START_REF] Goulding | Incidence of lateral femoral cutaneous nerve neuropraxia after anterior approach hip arthroplasty[END_REF], and probably still underestimated [START_REF] Patton | Clinical outcomes of patients with lateral femoral cutaneous nerve injury after direct anterior total hip arthroplasty[END_REF] due to the wide anatomic variations in this nerve [START_REF] Ropars | Anatomical study of the lateral femoral cutaneous nerve with special reference to minimally invasive anterior approach for total hip replacement[END_REF]. The case of dislocation in the AA group occurred earlier than week 2, following trauma in a very active patient who had had excellent postoperative results.

Study bias was minimized by the prospective randomized and single-surgeon design.

There were, however, some limitations. 1) To be interpretable, Locometrix TM data have to be based on stabilized gait; initial swing and the slow-down in final swing were therefore excluded. Moreover, the apparatus cannot deal with walking assisted by a frame, crutch or cane, and such patients had to be excluded from gait analysis. 2) Identical autonomy criteria were required for discharge, but no immediate postoperative analysis was made, with data being first collected at postoperative week 3. Special attention should be paid to the possible benefit of the anterior approach during the first postoperative days, before the 3-week timepoint, which is already too late for any difference to appear. In the study by Taunton et al. [START_REF] Taunton | John Charnley Award: Randomized Clinical Trial of Direct Anterior and Miniposterior Approach THA: Which Provides Better Functional Recovery?[END_REF], patients operated on by an anterior approach gave up walking aids a mean 7 days earlier than with a posterior approach (day 17 ± 8 vs. 24 ± 14; p = 0.04), bearing out this hypothesis.

We were unable to collect such data, for organizational reasons and the confusion bias such early analysis would have entailed: with whichever approach, patients were unable to walk for the distance required by locomotion analysis until the third postoperative week. 3) Analgesic intake and blood loss were not measured, whereas for some authors the benefit of the anterior approach is found in the early postoperative period, especially in terms of pain [START_REF] Barrett | Prospective randomized study of direct anterior vs postero-lateral approach for total hip arthroplasty[END_REF][START_REF] Zawadsky | Early outcome comparison between the direct anterior approach and the mini-incision posterior approach for primary total hip arthroplasty: 150 consecutive cases[END_REF].

Intraoperative injections further biased the early results, masking the postoperative pain induced by the respective approaches. Over the first 3 weeks, however, other authors reported no functional superiority according to approach [START_REF] Rodriguez | Does the direct anterior approach in THA offer faster rehabilitation and comparable safety to the posterior approach?[END_REF][START_REF] Cheng | A prospective randomized clinical trial in total hip arthroplasty-comparing early results between the direct anterior approach and the posterior approach[END_REF]. In the short term, these benefits are thus far from certain. 4) The groups were not comparable for cup characteristics in terms of the proportion of dual-mobility models, and it can therefore not be affirmed with certainty that the results depended entirely on the approach, especially as regards dislocation. On the other hand, the wide diameter of dual-mobility cups did not seem to impact walking kinematics [START_REF] Zagra | No difference in gait recovery after THA with different head diameters: a prospective randomized study[END_REF] or functional improvement [START_REF] Allen | Do larger femoral heads improve the functional outcome in total hip arthroplasty?[END_REF][START_REF] Delay | Is there any range-of-motion advantage to using bearings larger than 36mm in primary hip arthroplasty: A case-control study comparing 36-mm and large-diameter heads[END_REF].

Conclusion

The study hypothesis was confirmed: early functional results in THA with Hueter's anterior approach were comparable to those for a posterior approach in non-obese patients.

The supposed functional advantages of the anterior approach seem uncertain. If they exist, they are slight, early and transient. It would therefore be worth undertaking a prospective randomized study comparing results between the two approaches during the first 3 postoperative weeks. The choice of approach seems finally to be a matter of the individual surgeon's experience. To anterior approach (n =54) • Underwent attributed approach (n =54)

Disclosure of interest:

  None of the authors have conflicts of interest to disclose in relation to the present article. Elsewhere, P Mertl receives fees from Stryker, DePuy, Zimmer, X-Nov and Adler and A Gabrion from X-Nov. The other authors have no further disclosures. Funding: None Author contributions: Gautier Bon performed study design and data collection, analysis and interpretation, and wrote the article. Elias Ben Kacem contributed to study design and data collection, analysis and interpretation. Pierre Marie Lepretre contributed to study design, provided the measuring equipment and training in its use, and contributed to data analysis and interpretation. Thierry Weissland contributed to study design, and provided equipment and training in its use. Patrice Mertl contributed to study design and revised the article. Massinissa Dehl contributed to study design, data analysis and interpretation and article revision. Antoine Gabrion contributed to study design and to revising the article. RCB ID n°: 2017-A02875-48 IRB approval registered with the Clinical Research and Innovation Delegation: PI2017-843-0023

Figure 1 :

 1 Figure 1: CONSORT recruitment flowchart.

Figure 1 .

 1 Figure 1. CONSORT recruitment flowchart.

Table 1 .

 1 Preoperative data

	Variables (Mean ± standard deviation	Posterior approach	Anterior approach	p-value
	[95%CI]**)
	Age (years)	68.98 ± 7.93 [66.73-71.23]	67.26 ± 10 [64.42-70.1]	0.3432
	Male/female	23 / 27	21 / 29	0.8403
	BMI (kg/m²)	26.69 ± 3.12 [25.8-27.58]	26.46 ± 3.58 [25.44-27.47]	0.7311
	Right side*	20 (40%)	28 (56%)	0.1612
	Charnley
	A*	25 (50%)	28 (56%)	0.6886
	B*	15 (30%)	18 (36%)	0.6706
	C*	10 (20%)	4 (8%)	0.1496
	Lequesne algofunctional index(0-24) [10]	13.7 ± 4.29 [12.48-14.92]	13.1 ± 3.98 [11.92-14.18]	0.4343
	Postel Merle d'Aubigné (0-18) [7]	11.66 ± 2.51 [10.95-12.37]	11.62 ± 2.21 [10.99-12.25]	0.9328
	Harris Hip Score [6]
	Stairs normally*	36 (72%)	37 (74%)	1
	Distance unrestricted*	3 (6%)	9 (18%)	0.1239
	Shoes and socks easily*	4 (8%)	9 (18%)	0.2343
	Unassisted walking*	31 (62%)	30 (60%)	1
	Pain (0-44)	19 ± 7.07 [16.99-21.01]	18.2 ± 8 [15.93-20.47]	0.5975
	Function (0-46)	26.9 ± 10.53 [23.91-29.89]	28.16 ± 11.16 [24.99-31.33]	0.5628
	Total (0-100)	52.31 ± 13.06 [48.6-56.03]	54.04 ± 14.94 [49.79-58.28]	0.5410
	Oxford SF12 (0-48) [8,9]	20.72 ± 7.69 [18.54-22.9]	20.86 ± 7.66 [18.68-23.04]	0.9275
	Locometrix TM
	Rhythm (Hz)	0.84 ± 0.19 [0.78-0.89]	0.84 ± 0.17 [0.79-0.89]	0.8220
	Regularity (no unit)	145.18 ± 57.09 [128.95-161.41]	145.92 ± 57.77 [129.5-162.34]	0.9488
	Craniocaudal power (W/kg)	1.44 ± 1.08 [1.13-1.74]	1.42 ± 0.86 [1.18-1.66]	0.9389
	Anteroposterior power (W/kg)	0.89 ± 0.63 [0.71-1.07]	0.93 ± 0.56 [0.77-1.09]	0.7251
	Mediolateral power (W/kg)	0.94 ± 0.75 [0.73-1.16]	0.96 ± 0.65 [0.78-1.15]	0.8838
	Mediolateral instability (no units)	29.48 ± 8.58 [27.04-31.92]	30.2 ± 8.98 [27.65-32.75]	0.6827
	Total power (W/kg)	3.27 ± 2.33 [2.61-3.93]	3.32 ± 1.87 [2.78-3.85]	0.9331
	* N (%) ** 95% confidence interval

Table 2 .

 2 Perioperative data

	Variables (Mean ± standard deviation [95%CI]**)	Posterior approach	Anterior approach	p-value
	Surgery time (minutes)	56.7 ± 11.79 [53.35-60.05]	70.1 ± 11 [66.99-73.25]	< 0.0001
	Hospital stay (days)	2.8 ± 1.78 [2.29-3.31]	2.84 ± 1.25 [2.48-3.2]	0.8970
	Postoperative course
	Home*	41 (82%)	40 (80%)	1
	Rehabilitation center*	9 (18%)	10 (20%)	1
	Femoral implants
	Cemented*	7 (14%)	7 (14%)	1
	Non-cemented*	(86%)	43 (86%)	1
	Non-cemented acetabular implants
	XNOV X.CUP MOB ® *	30 (60%)	1 (2%)	< 0.0001
	XNOV X.CUP ® *	18 (36%)	14 (28%)	0.5201
	MATHYS RM Pressfit ® *	1 (2%)	35 (70%)	< 0.0001
	Cup inclination (°)	39.6 ± 6.87 [37.65-41.55]	37.74 ± 4.2 [36.55-38.93]	0.0993
	Global offset (mm)
	Preoperative	82.9 ± 9.78 [80.12-85.68]	80.4 ± 8.24 [78.06-82.74]	0.1700
	Postoperative	83.58 ± 8.43 [81.18-85.98]	81.34 ± 7.71 [79.15-83.53]	0.1689

Table 3 .

 3 Postoperative gait data-Locometrix ™

	Variables (Mean ± standard deviation		Week 3
	[95%CI]**)	Posterior approach	Anterior approach	p-value
	Rhythm (Hz)	0.82 ± 0.17 [0.77-0.87]	0.83 ± 0.17 [0.78-0.87]	0.8743
	Regularity (no unit)	133.44 ± 49.55 [128.95-161.41]	148.16 ± 44.88 [135.41-160.1]	0.1228
	Craniocaudal power (W/kg)	1.11 ± 0.59 [0.94-1.27]	1.12 ± 0.54 [0.97-1.28]	0.8856
	Anteroposterior power (W/kg)	0.77 ± 0.45 [0.64-0.89]	0.81 ± 0.4 [0.69-0.92]	0.6349
	Mediolateral power (W/kg)	0.75 ± 0.47 [0.62-0.89]	0.78 ± 0.51 [0.63-0.93]	0.7727
	Mediolateral instability (no units)	28.44 ± 6.93 [26.47-30.41]	28.16 ± 7.55 [26.01-30.31]	0.6827
	Total power (W/kg)	2.62 ± 1.42 [2.22-3.03]	2.71 ± 1.33 [2.33-3.09]	0.7513
	Variables (Mean ± standard deviation		Week 6
	[95%CI]**)	Posterior approach	Anterior approach	p-value
	Rhythm (Hz)	0.9 ± 0.14 [0.86-0.94]	0.9 ± 0.11 [0.87-0.93]	0.9876
	Regularity (no unit)	171.94 ± 55.7 [156.11-187.77]	173.54 ± 54.13 [158.16-188.92] 0.8845
	Craniocaudal power (W/kg)	1.68 ± 0.89 [1.43-1.94]	1.63 ± 0.87 [1.38-1.87]	0.7515
	Anteroposterior power (W/kg)	1.1 ± 0.59 [0.93-1.27]	1.05 ± 0.54 [0.9-1.21]	0.6876
	Mediolateral power (W/kg)	1.03 ± 0.64 [0.85-1.21]	0.98 ± 0.64 [0.8-1.16]	0.6839
	Mediolateral instability (no units)	27.08 ± 7.48 [24.95-29.21]	26.64 ± 6.92 [24.67-28.61]	0.7608
	Total power (W/kg)	3.76 ± 1.89 [3.22-4.29]	3.66 ± 1.85 [3.13-4.19]	0.7958
	Variables (Mean ± standard deviation		Month 3
	[95%CI]**)	Posterior approach	Anterior approach	p-value
	Rhythm (Hz)	0.94 ± 0.1 [0.91-0.96]	0.93 ± 0.12 [0.9-0.96]	0.7544
	Regularity (no unit)	190.78 ± 57.31 [174.49-207.07]	192 ± 63.34 [174-210]	0.9198
	Craniocaudal power (W/kg)	1.97 ± 1.1 [1.66-2.28]	1.95 ± 0.98 [1.67-2.23]	0.9146
	Anteroposterior power (W/kg)	1.26 ± 0.62 [1.09-1.44]	1.31 ± 0.63 [1.13-1.48]	0.7250
	Mediolateral power (W/kg)	1.23 ± 0.77 [1.01-1.45]	1.27 ± 0.82 [1.03-1.5]	0.8213
	Mediolateral instability (no units)	26.66 ± 8.23 [24.32-29]	27.22 ± 8.13 [24.91-29.53]	0.7329
	Total power (W/kg)	4.44 ± 2.23 [3.81-5.07]	4.51 ± 2.17 [3.89-5.13]	0.8764
	* N (%) ** 95% confidence interval

Table 6 .

 6 Main literature results within 3 months for scores used in the present study

	Study (date)	Sample size (PA/AA)	Functional scores	Follow-up	Significant differences (PA/AA)	p-value	Superiority
	Prospective randomized
	studies
	Tauton et al. [15]	49/52	Harris Hip Score	2 months	Total		None
					92 ± 8/95 ± 6	0.07
			Oxford SF12	2 months	Total		None
					42 ± 8/45 ± 10	0.12
	Cheng et al. [24]		Oxford SF12	2 weeks	Total		None
					26.8 ± 1.5/28.5 ± 1.56	0.44
				6 weeks	Total		None
					37.3 ± 1.01/39.8 ± 1.05	0.1
				3 months	Total		None
					42.8 ± 0.84/43.8 ± 0.87	0.14
	Rykov et al. [19]	23/23	Harris Hip Score	6 weeks	Total		None
					90 ± 9.14/93 ± 10.87	0.36
	Zhao et al. [16]	60/60	Harris Hip Score	3 months	Total		AA
					79.6 ± 11.87/85.9 ± 17.36	0.04
	Christensen et al. [20]	23/28	Harris Hip Score	6 weeks	Total (results not shown)	>0.05	None
					Distance unrestricted*		None
					5 (22%)/4 (14%)	0.71
					Stairs normally*		None
					7 (30%)/8 (29%)	>0.99
					Shoes and socks easily*		None
					9 (39%)/12 (43%)	>0.99
	Barret et al. [23]	44/43	Harris Hip Score	6 weeks	Stairs normally *		AA
					7 (18%)/21 (50%)	0.0023
					Distance unrestricted *		AA
					17 (55%)/34 (81%)	0.0005
					Shoes and socks easily *		AA
					1 (3%)/28 (67%)	<0.0001
					Pain		None
					38.4 ± 5.4/39.8 ± 4.4	0.2056
					Function		AA
					25.5 ± 5.3/28.7 ± 3.7	0.0027
					Total		AA
					81.4 ± 9.8/89.5 ± 8.1	0.0001
				3 months	Distance unrestricted *		AA
					28 (74%)/33 (94%)	0.0260
					Other	>0.05	None
	Taunton et al. [22]	27/27	Harris Hip Score	3 weeks	Pain		None
					44/44	0.432
					Function		None
					32/37.5	0.08
					Total		None
					81/86.5	0.085
				6 weeks	Pain		None
					44/44	0.224
					Function		None
					43/45	0.079
					Total		None
					93/97	0.135
	Prospective non-randomized study
	Rodriguez et al. [21]	60/60	Harris Hip Score	2 weeks	Total		None
					64 ± 9.4/69 ± 13	0.09
				6 weeks	Total		None
					80 ± 11/83 ± 12	0.13
				3 months	Total		None
					88 ± 10/89 ± 10	0.29

* N (%); PA, posterior approach; AA, anterior approach


Jimmy Bordarie
email: jimmy.bordarie@univ-tours.fr

Predicting intentions to comply with speed limits using a 'decision tree' applied to an extended version of the theory of planned behaviour

Keywords: Theory of Planned Behaviour, Self-Report Habit Index, decision trees, 30km/h speed limit

Predicting intentions to comply with speed limits using a 'decision tree' applied to an extended version of the theory of planned behaviour

Highlights

-The extended version of the Theory of Planned Behaviour can be used to predict drivers' intentions to comply with a 30km/h speed limit.

-Perceived importance, perceived behaviour control and past behaviours are the most important factors.

-A decision tree helps optimize this prediction and makes it possible to compare reported intentions and theoretically expected intentions.

Introduction

Speed is a major factor in road traffic accidents and deaths [START_REF] Aarts | Driving speed and the risk of road crashes: A review[END_REF]Ayuso, Guillen and Alcaniz, 2010;[START_REF] De Winter | The Driver Behaviour Questionnaire as a predictor of accidents: A meta-analysis[END_REF][START_REF] Nilsson | The effects of speed limits on traffic accidents in Sweden[END_REF][START_REF] Nilsson | Traffic safety dimensions and the power model to describe the effect of speed on safety[END_REF]). This study focuses on drivers' intentions to comply with new legislation and public policies to reduce the speed limit. The research was carried out within the framework of the project of Angers (France) to extend the 30km/h speed limit throughout the city, except on boulevards and major roads where the limit remains 50km/h. The aim of the study was to predict intentions to respect the speed limit using an extended version of the TPB to test several variables including beliefs and past behaviours. The latter were explored through the SRHI. In addition to drivers' self-reported intentions to respect the 30km/h speed limit, the current study used a decision tree to predict their intentions. The interest of the study lies in the comparison of drivers' self-reported intentions and their intentions as predicted by the decision tree.

Calming traffic by extending the 30km/h speed limit

In some French cities, the speed limit has been reduced from 50km/h (current legal speed limit in city centres) to 30km/h in order to promote well-being and improve safety. Indeed, the 30km/h speed limit considerably reduces the risk of fatality [START_REF] Davis | Relating severity of pedestrian injury to impact speed in vehicle-vehiclepedestrian crashes[END_REF][START_REF] Richards | Relationship between speed and risk of fatal injury: pedestrians and car occupants[END_REF]Rosén and Sander, 2009;Rosén, Stigson and Sander, 2011) and the number of accidents in town [START_REF] Bunn | Area-wide traffic calming for preventing traffic related injuries[END_REF][START_REF] Elvik | Area-wide urban traffic calming schemes: a meta-analysis of safety effects[END_REF][START_REF] Grundy | Effect of 20 mph traffic speed zones on road injuries in London, 1986-2006: controlled interrupted time series analysis[END_REF]. It is also associated with other effects related to the improvement of quality of life and well-being, such as reducing noise pollution [START_REF] Spessert | Vergleichende messtechnische Untersuchungen zum Einfluss einer nächtlichen Geschwindigkeitsbegrenzung von 50 km/h 25 auf 30 km/h auf die Lärmimmissionen durch den Straßenverkehr[END_REF] and enhancing social and commercial activities [START_REF] Appleyard | The environmental quality of city streets: the residents' viewpoint[END_REF][START_REF] Certu | Zones de circulation apaisée[END_REF][START_REF] Rogers | Des Villes durables pour une petite planète[END_REF]. Research has demonstrated that heavy traffic leads to a decrease in the number of relationships and acquaintances [START_REF] Appleyard | The environmental quality of city streets: the residents' viewpoint[END_REF][START_REF] Hart | Driven to excess: Impacts of motor vehicles on the quality of life of residents of three streets in Bristol UK[END_REF]) and social interactions with other people and neighbours [START_REF] Sauter | Liveable streets and social inclusion[END_REF]. [START_REF] Bordarie | Représentations sociales et mobilité urbaine durable[END_REF] and [START_REF] Gaymard | The perception of the ideal neighborhood in a changing city : a preamble to implementation of a street use code[END_REF] found that social representation of the ideal neighbourhood is associated with notions of "calm", "social interactions" and "access to shops and services".

These aspects have been confirmed by other studies (Amérigo andAragonés, 1988, 1990): calm and quietness of the area (Bender, Din, Faverger, Hoesli and Laakso, 1997), possibility of social links (Fine- [START_REF] Fine-Davis | Predictors of Satisfaction with Environmental Quality in Eight European Countries[END_REF], and access to shops and services [START_REF] Buys | Residential satisfaction in inner urban higher-density Brisbane, Australia: role of dwelling design, neighborhood and neighbors[END_REF][START_REF] Reynolds | Residential satisfaction of older adults in age segregated facilities[END_REF][START_REF] Sam | The perception of residential environment quality and neighbourhood attachment in a metropolitan city: A study on Bursa, Turkey[END_REF].

Theory of Planned Behaviour and Self-Report Habit Index

This research is based on the Theory of Planned Behaviour (TPB) [START_REF] Ajzen | From intentions to actions: A theory of planned behavior[END_REF][START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF][START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF][START_REF] Ajzen | Predicting and changing behavior: A reasoned action approach[END_REF][START_REF] Ajzen | Prediction of goal-directed behavior: Attitudes, intentions, and perceived behavioral control[END_REF]. The aim is to examine the 3 influence of social-cognitive factors on the intention to comply with speed limits. The results of this study could have important implications for implementing speed limit reductions, and also for developing road safety guidelines. The validity of the TPB has been largely demonstrated [START_REF] Sheppard | The theory of reasoned action: A metaanalysis of past research with recommendations for modifications and future research[END_REF]. According to the TPB, three factors can predict the intention to enact a behaviour: attitude, subjective norms and perceived behavioural control (PBC). This model also postulates that intention is the most relevant predictor of individuals' behaviours [START_REF] Ajzen | From intentions to actions: A theory of planned behavior[END_REF][START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF][START_REF] Armitage | Efficacy of the theory of planned behaviour: A metaanalytic review[END_REF][START_REF] Madden | A comparison of the theory of planned behavior and the theory of reasoned action[END_REF][START_REF] Yzer | Perceived behavioral control in reasoned action theory: A dual-aspect interpretation[END_REF]. Attitude refers to the individual's positive or negative evaluation of a specific behaviour. Subjective norms are based on whether individuals think that people of importance to them (e.g. parents, friends) approve or disapprove of the behaviour. Finally, PBC refers to individuals' perceptions of their capacity to achieve the behaviour.

Multidimensional approaches within the TPB have shown that belief in the importance or impact of the behaviour can influence the individual's attitude or PBC [START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF].

Moreover, past behaviours contribute to the prediction of behavioural intentions [START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF] and constitute the best predictor of future behaviour [START_REF] Conner | Extending the theory of planned behavior: A review and avenues for further research[END_REF][START_REF] Ouellette | Habit and intention in everyday life: The multiple processes by which past behavior predicts future behavior[END_REF]. This finding was supported by [START_REF] Cestac | Habitude et principe de compatibilité dans le modèle du comportement planifié: décisions pro-environnementales et automobile[END_REF], who used the Self-Report Habit Index (SRHI) [START_REF] Verplanken | Reflections on Past Behavior: A Self-Report Index of Habit Strength1[END_REF] to predict the intention to buy a car. The SRHI measures several dimensions of habit: automatic activation, perceived ease, behavioural frequency, relevance to self-identity and history of enactment. It has been used in various fields, including dietary habits (Brug, de Vet, Wind, de Nooijer and Verplanken, 2006;[START_REF] Honkanen | Intention to consume seafood-the importance of habit[END_REF] and mental habits [START_REF] Verplanken | Mental habits: Metacognitive reflection on negative self-thinking[END_REF].

Application to traffic issues

The SRHI has been used in the field of transportation and travel mode choices (Aarts, Verplanken and von Knippenberg, 1997;[START_REF] Verplanken | The measurement of habit[END_REF], but it has never been used to understand drivers' habits with regard to speed or compliance with speed limits. On the other hand, research has shown the relevance of the TPB for mobility, risktaking and traffic issues; for example, the consumption of alcohol while driving [START_REF] Marcil | Motivational factors underlying the intention to drink and drive in young male drivers[END_REF][START_REF] Mcghie | The influence of conformity and group identity on drink walking intentions: comparing intentions to drink walk across risky pedestrian crossing scenarios[END_REF][START_REF] Moan | Predicting intentions not to "drink and drive" using an extended version of the theory of planned behavior[END_REF][START_REF] Poulter | An application of the Theory of Planned Behaviour to truck driving behaviour and compliance with regulations[END_REF], the use of mobile phones while driving [START_REF] Nemme | Texting while driving: psychosocial influences on young people's texting intentions and behaviour[END_REF][START_REF] Przepiorka | Factors influencing intentions to text while driving among Polish drivers[END_REF][START_REF] Waddell | What's driving illegal mobile phone use? Psychosocial influences on drivers' intentions to use handheld mobile phones[END_REF][START_REF] White | Mobile phone use while driving: An investigation of the beliefs influencing drivers' hands-free and hand-held mobile phone use[END_REF], the behaviour of pedestrians [START_REF] Xu | Pedestrians' intention to jaywalk: Automatic or planned? A study based on a dual-process model in China[END_REF][START_REF] Zhou | The effect of conformity tendency on pedestrians' road-crossing intentions in China: An application of the Theory of Planned Behavior[END_REF] and motorcyclists [START_REF] Chen | Speeding for fun? Exploring the speeding behavior of riders of heavy motorcycles using the theory of planned behavior and psychological flow theory[END_REF]Özkan, Dogruyol, Lajunen, Yıldırım and Çoymak, 2012), and the importance of taking into account cultural differences [START_REF] Warner | Cross-cultural differences in drivers' speed choice[END_REF]. Concerning the compliance with speed limits, numerous studies have used the TPB for motorists and motorcyclists [START_REF] Chorlton | Identifying the psychological determinants of risky riding: An application of an extended Theory of Planned Behaviour[END_REF]Conner, Lawton, Parker, Chorlton, Manstead and Stradling, 2007;[START_REF] Elliott | Predicting motorcyclists' intention to speed: Effects of selected cognitions from the theory of planned behaviour, self-identity and social identity[END_REF][START_REF] Elliott | Exploring the beliefs underpinning drivers' intentions to comply with speed limits[END_REF]Elliott and Armitage, 2009;[START_REF] Elliott | The social cognitive determinants of offending drivers' speeding behaviour[END_REF][START_REF] Eyssartier | Transgression de la limitation de vitesse par les motards : facteurs incitateurs et inhibiteurs/ Motorcyclists transgression of speed limits[END_REF][START_REF] Eyssartier | Dépassement de la limitation de vitesse sur route limitée à 90km/h : étude sur les motards peu expérimentés du département de la Sarthe[END_REF][START_REF] Leandro | Young drivers and speed selection: A model guided by the Theory of Planned Behavior[END_REF]Wallén Warner andÅberg, 2006, 2008).

However, drivers often object to speed limit reduction measures (Australian Transport Safety Bureau, 2005). Compliance with speed limits usually depends on two major factors.

First, speed is influenced by curved or straight sections, visibility and reliability of road signs and posted speed limits [START_REF] Fitzpatrick | Design factors that affect driver speed on suburban streets[END_REF]. Secondly, drivers generally drive faster than the limit that they themselves regard as being safe [START_REF] Goldenbeld | The credibility of speed limits on 80km/h rural roads: the effects of road and person(ality) characteristics[END_REF]. Regarding the 30km/h speed limit in particular, Dinh and Kubota (2013a[START_REF] Dinh | Speeding behavior on urban residential streets with a 30km/h speed limit under the framework of the theory of planned behavior[END_REF][START_REF] Duy Dinh | Drivers' perceptions regarding speeding and driving on urban residential streets with a 30 km/h speed limit[END_REF] found different profiles of drivers. Likewise, Toy, Tapp, Musselwhite and [START_REF] Toy | Can social marketing make 20mph the new norm[END_REF] and [START_REF] Bordarie | Représentations sociales et mobilité urbaine durable[END_REF][START_REF] Bordarie | A highlight of the relationship between thêmata and social representations using a hierarchical clustering method[END_REF] identified several categories of drivers (in the United Kingdom and France respectively): 'champions' of the 30km/h speed limit, 'pragmatists' and 'opponents'.

Decision trees

In order to understand drivers' intentions to change some of their behaviours, we used decision trees [START_REF] Quinlan | C4.5: Programs for Machine Learning[END_REF], which have already been used in medicine and other research fields [START_REF] Hastie | The elements of statistical learning[END_REF]. The interest of this tool is its ability to predict certain behaviours. First of all, decision trees are easy to interpret and understand, notably the difference between acceptable and unacceptable scenarios. They can thus be used to predict situations and/or determine outcome preferences in different contexts. In the latter case, alternative scenarios can be added. In this study, the decision tree compares drivers' selfreported intentions and their intentions predicted by their answers to questions related to the TPB and SRHI variables.

Ordinary trees consist of a root, branches, nodes and leaves. In statistics, decision trees are composed of circles (nodes) and segments (branches). The first node is the root. Two or several branches may grow from it. The last node of the chain is a leaf and no branches grow from it. Each node represents a variable, and branches give a set of values (called "x" in Figure 1), which can be predicted from observations of individuals, social groups, or specific characteristics.

Figure 1. Example of a 'theoretical' decision tree

Decision trees have already been used in medicine [START_REF] Li | Treestructured subgroup analysis of receiver operating characteristic curves for diagnostic tests[END_REF]Nativ, Raz, Winkler, Hosaka, Boyle, Therneau, Farrow, Meyers, Zincke and Lieber, 1988;[START_REF] Podgorelec | Decision trees: an overview and their use in medicine[END_REF], and notably to identify significant predictors of child abuse in Canada [START_REF] Fallon | Opportunities for prevention and intervention with young children: lessons from the Canadian incidence study of reported child abuse and neglect[END_REF]. There are many ways of constructing a decision tree, but methods can be divided broadly into two groups: strictly optimum trees and approximately optimum trees. The main drawback of the former is that it involves a finite number of variables, while others could also influence the results. The latter has the disadvantage of being approximate and of relying on the population under study to construct the tree. According to [START_REF] Song | Decision tree methods: applications for classification and prediction[END_REF]: "when the sample size is large enough, study data can be divided into training and validation datasets, using the training dataset to build a decision tree model and a validation dataset to decide on the appropriate tree size needed to achieve the optimal final model." This seems to be a good alternative to confirm the relevance of the decision tree.

The current study

Despite the considerable literature and the political measures taken to address issues of road safety, speed and traffic, drivers continue to take risks. The purpose of the current study is twofold. First, the main goal is to propose a model in which we expect (H1) that the TPB components could predict the intention to comply with the 30km/h speed limit, and (H2) that

leaf a leaf b leaf c leaf d < < root < 'x' > = 'x' node a node b node c < 'x' > = 'x' < 'x' > = 'x'
6 past behaviours and habits identified from variables in the Self-Report Habit index would have a significant effect on this intention. Secondly, the study aims to show the relevance of constructing decision trees directly from TPB data. This would make it possible to compare self-reported intentions and the theoretical intentions expected from the answers given to different variables. We assume (H3) that these would include the TPB variables. The discussion will seek to understand the results and explain various discrepancies. From an applied perspective, this research aims to provide information to understand the sociocognitive determinants of drivers' decisions and risk-taking behaviour and hence facilitate the implementation of speed limit reduction measures. It could also be of use when setting up road safety campaigns targeting drivers who do not comply with the speed limit.

Method

Participants and procedure

The sample (n = 391) comprised 78% females (n = 305) and 22% males (n = 86) with a mean age of 21.79 years (SD = 2.37) (range: 18-30). All participants were car drivers and students at the University of Angers. All the students at the University were sent an email

inviting them to answer a questionnaire anonymously about the new public policy to extend the 30km/h speed limit throughout the city. Data were collected via an online questionnaire in French. In accordance with the ethics committee, participants were informed that their responses would be anonymous and confidential, and that their participation was voluntary and unpaid. In line with the recommendations of [START_REF] Song | Decision tree methods: applications for classification and prediction[END_REF] regarding construction of decision trees, the sample was split randomly into two groups with the same characteristics.

The first group (n = 129) was used to construct the decision tree, and the second (n = 262) to validate the reliability of the tree.

Instruments

The questionnaire comprised fifteen items, based on the TPB and the SRHI. There were five items related to the TPB, based on the traditional dimensions of the model (attitude, subjective norms, PBC); the three items related to subjective norms concerned different social referents (parents, friends, motorists). Five further items, based on multidimensional approaches of the TPB, were related to cognitive aspects such as beliefs. Four items were related to behavioural aspects such as frequency, automaticity, history of enactment and ease; these items and the "identification" question were based on the SRHI.

The five items related to the traditional theory of planned behaviour were:

-Attitude: I am in favour of driving within the 30km/h speed limit.

-Parental social norm: I think my parents are in favour of driving within the 30km/h speed limit.

-Social norm of friends: I think my friends are in favour of driving within the 30km/h speed limit.

-Social norm of motorists: I think motorists in general are in favour of driving within the 30km/h speed limit.

-PBC: I feel able to drive within the 30km/h speed limit.

The four items measuring beliefs relative to the behaviour were:

-Personal concern: driving within the 30km/h speed limit concerns me personally.

-Importance: driving within the 30km/h speed limit is important.

-Perceived effect: driving within the 30km/h speed limit has an effect.

-Perceived impact: driving within the 30km/h speed limit has an impact.

The five items measuring behavioural dimensions based on the SRHI were:

-Frequency: I often drive within the 30km/h speed limit.

-Automaticity: I automatically drive within the 30km/h speed limit, without thinking about it.

-Perceived ease: It's easy for me to drive within the 30km/h speed limit.

-History of enactment: I have driven within the 30km/h speed limit for a long time.

-Self-identity relevance (identification): driving within the 30km/h speed limit is typically 'me'.

Finally, one item measured intention:

-I will drive within the 30km/h speed limit wherever it is indicated.

Questions were presented randomly. Answers were given on a 6-point scale from 1 (completely disagree) to 6 (totally agree) in order to avoid neutral answers. We chose a scale of 1 to 6 rather than -3 to +3 in order to limit the impact of negative values on the answers [START_REF] Schwarz | Rating scales: Numeric values may change the meaning of scale labels[END_REF]). Cronbach's alpha (α=.92)

indicates very good reliability according to [START_REF] Nunnaly | Psychometric theory[END_REF].

Data Analysis

All analyses were conducted using SPSSStatistics version 21 and R software. This study aimed to show the interest of using Bayesian analysis to understand the levers predicting drivers' intentions to drive at 30km/h. Although some psychological studies have used Bayesian analysis (van de Schoot, Winter, Ryan, Zondervan-Zwijnenburg and Depao, 2016), this approach is still very rare in this field. Bayesian calculations are based on linear regressions. Regarding our methodology with R software, we used the BayesFactor package and the regressionBF function. The calculation method is based on the JZS [START_REF] Rouder | Bayesian t-tests for accepting and rejecting the null hypothesis[END_REF]. Here, intention is the dependent variable. By using the 14 other questions as independent variables, we compared 16383 different models with R.

Results

Descriptive statistics and correlations

Correlations (Table 1) were calculated between TPB and SRHI determinants and behavioural intention with SPSS. Intention to comply with speed limits was strongly correlated with all the variables (p<.005). The SRHI variables were correlated with TPB variables, except for the perceived importance of the 30km/h speed limit, which was not correlated with identification. These findings support the view that habits are positively correlated with predictors of complying with speed limits.

Predicting intention using a model combining TPB and SRHI

Hierarchical regression analysis was conducted to analyse the impact of TPB, beliefs and SRHI variables on behavioural intentions (Table 2). In the current study, the variables relative to the TPB explained 43% of the variance [F(5, 385)=57.997, p<.0001, r2=.43]. This is a good value. In a meta-analysis of 154 studies, [START_REF] Armitage | Efficacy of the theory of planned behaviour: A metaanalytic review[END_REF] found that TPB generally explained 39% of the intention variance and 27% of the behaviour variance. In comparison, by taking into account all the determinants of our model (Table 3), we explained 53% of the variance for intention to comply with the 30km/h speed limit [F(14, 376) 2) is a model predicting participants' intentions to comply with the 30km/h speed limit. The first node (importance) refers to the question that is most decisive for predicting intention. By following the tree, we can find the other decisive questions. For example, to predict the intention to comply with the speed limit of a participant choosing a value higher than 2.5 for the variable related to the perceived importance of driving at 30km/h, we need to follow the right side of the decision tree. Next, we must read the participant's answers to the questions regarding frequency, PBC, attitude and eventually perceived parental norm. At the end of the tree, we obtain a number that corresponds to the theoretically expected intention of the participant. We can then compare this theoretical answer, corresponding to a prediction, with the participant's self-reported intention. To confirm the relevance of our model, we need to show its predictive value. Table 4 shows the comparison between reported intention and the prediction obtained with the decision tree (data in bold in Table 4, i.e. the diagonal). These numbers reveal the relationships between the two dimensions -reported and expected intention. The numbers in bold correspond to the number of participants for whom the predicted and self-reported intention values were the same (between 1 and 6). The number of participants for whom the value of the self-reported intention was the same as that of a different predicted intention (value of 1 to 6) is also shown. For instance, eight participants (number in italics) rated their intention with a value of 3, but the decision tree prediction would have yielded a value of 5.

2 1 7 3 2 3 0 3 0 3 6 3 8 0 4 0 2 0 19 12 2 5 1 0 0 4 23 3
6 0 0 0 1 5 15
We can see that the decision tree suggests an exact prediction for 75 participants (i.e.

58.1%

). Random predictions would obtain an exact prediction for 16.67% of the participants.

The difference between exact predictions and random predictions is significant (χ 2 Yates Correction (YC) = 14.47, df = 5, p < .013). We can thus conclude that the decision tree influences exact predictions.

We can also analyse acceptable predictions, in other words, those equal to or within one point of difference with the participant's answer. In that situation, the decision tree makes an acceptable prediction for 84.5% participants (i.e. 109 participants). Random predictions taking into account this degree of freedom would be acceptable for 44.4% of the participants.

The difference between acceptable predictions and random predictions is significant (χ 2 YC = 22.84, df = 5, p < .001). We can therefore also conclude that the decision tree influences acceptable predictions. Thus, the decision tree in our model has a better predictive value than random predictions.

Validation of the decision tree

We performed the same calculation with another group of participants (n = 262) in order to predict their intention with the help of the decision tree. We can see from Table 5 that the decision tree suggests an exact prediction for 97 participants (i.e. 37%; 0.370 = 97/262).

Random predictions would give an exact prediction for 16.67% of participants. The difference between exact predictions and random predictions is significant (χ 2 YC = 41.86, df = 5, p < .001). We can thus conclude that the decision tree always influences exact predictions.

We also examined acceptable predictions; the decision tree provided acceptable predictions for 79.4% of participants (i.e. 111 participants) (0.794 = (97+111)/262). Random predictions taking into account this degree of freedom would be acceptable for 44.4% of participants. The difference between acceptable predictions and random predictions is significant (χ 2 YC = 72.94, df = 5, p < .001). We can thus conclude that the decision tree always influences acceptable predictions. The difference between predictions for the two groups is due to the data for the samples, as the decision tree was constructed from the data of the first group, composed of 129 participants. The tree is therefore related specifically to the data for that group, which explains the lower scores on the validation test. This is in fact one of the main criticisms of decision trees [START_REF] Podgorelec | Decision trees: an overview and their use in medicine[END_REF]. Nonetheless, the decision tree in our model has a better predictive value than random predictions.

Discussion

Speed is a major cause of road traffic deaths and injuries. To address this problem, many

European cities, such as Angers in France, introduce speed limit reductions. The purpose of the current study was to investigate the determinants of drivers' intentions to comply with the new speed limit of 30km/h. We wished to test TPB factors (attitude, subjective norms, PBC) [START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF][START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF]) (H1) and variables linked to drivers' habits using variables from the Self-Report Habit Index (Verplanken and Orbell, 2003) (H2). Finally, we constructed a decision tree in order to compare self-reported intentions and the intentions predicted by the participants' responses to TPB and SRHI factors (H3).

Predictive factors of the intention to comply with the 30km/h speed limit

The results confirmed the relevance of the TPB for predicting the intention to comply with the 30km/h speed limit. However, subjective norms of parents, friends or motorists in general were not significant. Thus, we cannot confirm our first hypothesis. This result is in line with findings that social norms constitute a minor predictor [START_REF] Krueger | Competing models of entrepreneurial intentions[END_REF], whereas other studies have found that they are the strongest predictor of driving violations [START_REF] Parker | Intention to commit driving violations: An application of the theory of planned behavior[END_REF]Reason, 1992a, 1992b;Wallén Warner andÅberg, 2006, 2008). The additional dimensions of the extended version of the TPB show that beliefs influence attitudes, subjective norms and PBC [START_REF] Ajzen | The theory of planned behaviour: Reactions and reflections[END_REF]. However, regarding the subjective norms, our results can be explained in two ways: either we did not measure a reference group that is large enough for respondents regarding the specific behaviour of driving at 30km/h. It would probably have been wise to add an item such as "Most people who are important to me think that I should drive within the 30km/h limit". Though, the results of a previous study show that drivers with less than 3 years of driving licence like in our sample seem to be more influenced by their parents' models than by their friends or motorists in general with regard to 30km/h [START_REF] Gaymard | The perception of the ideal neighborhood in a changing city : a preamble to implementation of a street use code[END_REF]. Or maybe our results are explained by the fact that we measured attitudinal beliefs attributed to others about driving at 30 km/h rather than their beliefs or expectations about what the respondent should do according to each reference group. Perhaps we could have formulated the item as follows:

"My parents expect me to drive within the 30km/h limit".

Legitimacy concerned the belief that lowering the speed limit could reduce the number of accidents [START_REF] Kanellaidis | A survey of drivers' attitudes toward speed[END_REF]. Research has also shown that past behaviour plays a role in determining intentions [START_REF] Bamberg | Choice of travel mode in the theory of planned behavior: The roles of past behavior, habit and reasoned action[END_REF][START_REF] De Bruijn | Adult active transportation: Adding habit strength to the theory of planned behavior[END_REF][START_REF] Conner | Extending the theory of planned behavior: A review and avenues for further research[END_REF][START_REF] Forward | The theory of planned behavior: The role of descriptive norms and past behavior in the prediction of drivers' intention to violate[END_REF][START_REF] Potard | Driving under the influence of alcohol and perceived invulnerability among young adults: An extension of the theory of planned behavior[END_REF]. Moreover, our results indicate the role of several variables related to habits in general [START_REF] Bordarie | Représentations sociales et mobilité urbaine durable[END_REF][START_REF] Cestac | Habitude et principe de compatibilité dans le modèle du comportement planifié: décisions pro-environnementales et automobile[END_REF]; three out of five dimensions of the SRHI (frequency, perceived ease and automaticity) were found to predict intention. This confirms our second hypothesis. However, identification with the issue and duration of the behaviour were not significant. We observed a link between the three predictive aspects of the SRHI and the PBC, which could thus be directly influenced by these aspects.

Relevance of using a decision tree

In this study, we used Bayesian analysis to analyse the data. The creation of a decision tree to predict intention confirms our third hypothesis (H3). This method is relevant for at least two reasons. First, the study of the intention is easier, faster and more effective because the tree takes into account the most predictive variables. Secondly, the decision tree makes it possible to compare drivers' reported intentions to respect the 30km/h speed limit and their theoretical intentions expected from their answers about the other variables. When the two values (self-reported intention and theoretical intention) are equal, the predictive value of our model and the relevance of the tree are confirmed. When they differ, it would be interesting to examine in more depth the reasons for the discrepancy. Individuals' explanations provide important data to understand acceptance of speed limits and the intention to comply with them. Recent studies have shown the role of the rationalization process when a person is faced with contradictory aspects of cognition and behaviour [START_REF] Bordarie | Représentations sociales et mobilité urbaine durable[END_REF][START_REF] Bordarie | Rationalization processes between social representations and semantic blocks theory[END_REF]. It would be interesting to focus on participants whose answers reveal a discrepancy between self-reported and expected intentions.

The tree underlines the role of TPB factors (attitude, subjective norms, and PBC) in predicting the intention to comply with the 30km/h speed limit. However, linear regression analysis suggests that subjective norms were not significant. The tree also confirms the role of beliefs, such as the perceived importance of the speed limit. This validates the idea that drivers are more likely to respect speed limits when they consider that they are legitimate [START_REF] Goldenbeld | The credibility of speed limits on 80km/h rural roads: the effects of road and person(ality) characteristics[END_REF] and can reduce accidents [START_REF] Kanellaidis | A survey of drivers' attitudes toward speed[END_REF]. Finally, the tree includes one of the SRHI factors (frequency) that can be linked to PBC. Indeed, we can assume that when a behaviour is frequently enacted, it is then easier to feel able to carry it out in the future. As a result, the PBC is stronger.

Limitations

Some limitations can be mentioned. First of all, the study is based on self-reported data.

Regarding compliance with the law, in this case, respecting the 30km/h speed limit, this raises questions about validity and social desirability. However, we attempted to minimize this problem by guaranteeing anonymity and confidentiality. Secondly, the sample is not representative of the general population, as it was composed uniquely of students with a majority of females. This could be relevant, because males generally take more risks and are more involved in driving offences [START_REF] Cordellieri | Gender Effects in Young Road Users on Road Safety Attitudes, Behaviors and Risk Perception[END_REF]. Thirdly, studying behavioural intentions is useful, because it is one the most predictive factors of behaviour; however, it is important to note that intentions and behaviours are different. Bordarie andGaymard (2015a, 2015b) studied self-reported and actual behaviours with regard to the 30km/h speed limit, and they found that drivers' practices were strongly influenced by specific situations. It would be interesting to extend this study by following up behaviour in-situ.

Conclusion and practical implications

This research has a number of implications. First, it confirms the efficacy of an extended version of the TPB in predicting drivers' intentions to comply with a speed limit that may appear problematic, such as a reduction from 50km/h to 30km/h. Secondly, using a decision tree is an interesting way to understand certain discrepancies between self-report questionnaires and behaviour that can be predicted from TPB variables. This study can thus be seen as a bridge between behavioural intentions and social thinking, helping understand why people sometimes say they will do something but fail to do so.

From an applied perspective, the current study could be of interest to local authorities wishing to extend the 30km/h speed limit. First, before starting such a project, the tool we created could be used to gain information about citizens' and drivers' intentions with regard to this measure. Policy makers can imagine specific applications of this tool to determine the kind of streets in which the 30km/hr speed limit could be more relevant than in others according to drivers' intentions. Indeed, as we have seen in the theoretical framework, studies have already shown that some street configurations are more conducive to the implementation of such a speed limit. Policy makers and road engineers could thus, in a transparent approach, question the population and rely on their expertise as users to determine to what extent the system would really be interesting and respected.

Secondly, data obtained by this type of tool can be used in communication campaigns.

Indeed, communication can be enhanced by taking into account individuals' attitudes, ideas and actual practices, and communications officers could use the decision tree to create effective campaigns. For instance, the decision tree showed us that when drivers feel they can't drive at 30km/h speed limit, then their attitude towards 30km/h is negative and their intention is even lower. Therefore, communication officers may decide to communicate on aspects related to the "perceived capacity" to drive at 30 km/hr speed limit in order to increase this feeling among drivers to optimize their intention to comply with this speed limit, in particular by improving their attitude towards it.

Figure 2 .

 2 Figure 2. Decision tree contributing to predict the intention of driving at 30km/h

Table 1 . Bravais-Pearson correlations

 1

		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15 Mean SD
	1. Intention	1.00 .6289 1.12
	5. Motorists norms					1.00 .28** .20** .12* .36** .28** .26** .29** .25** .31** .30** 2.45 1.07
	6. PBC						1.00 .34** .26** .46** .34** .45** .38** .50** .44** .40** 4.24 1.45
	7. Concerning degree							1.00 .26** .36** .30** .40** .26** .21** .37** .35** 3.66 1.43
	8. Impact								1.00 .21** .17** .15** .11* .05 .15** .15** 4.35 1.21
	9. Importance									1.00 .44** .48** .41** .38** .54** .51** 3.03 1.37
	10. Effect										1.00 .31** .22** .26** .29** .27** 4.50 1.40
	11. Frequency											1.00 .63** .41** .66** .68** 3.01 1.35
	12. Automaticity												1.00 .45** .63** .62** 2.56 1.29
	13. Perceived ease													1.00 .47** .35** 2.84 1.49
	14. Identification														1.00 .64** 2.86 1.31
	15. Duration															1.00 2.87 1.40
	* p < .05
	** p < .005

** .40** .37** .27** .55** .38** .28** .50** .44** .57** .48** .45** .49** .47** 4.11 1.40 2. Attitude 1.00 .64** .56** .46** .59** .45** .29** .73** .50** .51** .45** .49** .55** .52** 3.54 1.49 3. Parents norms 1.00 .57** .50** .44** .39** .21** .54** .39** .38** .29** .35** .38** .35** 3.47 1.42 4. Friends norms 1.00 .55** .43** .28** .15** .51** .31** .38** .30** .27** .39** .37** 2.

Table 2 . Summary of models

 2

	=30.25,

Table 3 . Hierarchical regression analysis to predict intentions to comply with the 30km/hr speed limit

 3

	Non-standardized	standardized
	coefficients		coefficients	t	Sig.
	A	SD	β

** p ≤ .005 The decision tree (Figure

Table 4 . Data of the first group for constructing the decision tree

 4

	Prediction

Table 5 . Data of the second group in order to validate the decision tree

 5

	Prediction

Acknowledgements

There is no conflict of interest. This work was supported by Angers City Hall (France) [grant: 1689/2011].

The author specially acknowledges Alexandre Laurent from the University of Angers for his support, his help and advice during this research.