Pytha Albers-Heitner

Toine Lagro-Janssen

PhD Manuela A Joore

Bary Berghmans

PhD Fred Nieman

PhD, urologist Pieter L Venema

Prof, PhD Johan L Severens

PhD Ron A G Winkens

MSc, PPT ®1 § C P ) Albers-Heitner

Prof A L M Lagro-Janssen

PhD, PPT ®5 L C M Berghmans

Gaetano Martinolaan

Effectiveness of involving a nurse specialist for patients with urinary incontinence in primary care: results of a pragmatic multicentre randomised controlled trial

come

Conclusion

Involving nurse specialists in care for UI patients supplementary to general practitioners can improve severity and impact of UI, after correction for effect modifiers. This is also the case in specific situations such as anxiety/depression.

Ethical approval and Clinical Trial Registration Number:

The study protocol was approved by the Medical Ethical Committees of all involved centres. Included patients gave their written informed consent. The trial is registered at http://www.controlled-trials.com/isrctn/62722772 and is reported following CONSORT guidelines for RCTs.

What's known?

Urinary incontinence (UI) primary care management is substandard, offering care rather than cure despite the existence of guidelines that help to improve cure. Main reasons for substandard care are lack of time of general practitioners and lack of targeted implementation strategies to adopt and practice guideline recommendations.

What's new?

Involving nurse specialists in care for UI patients supplementary to general practitioners can improve severity and impact of UI: involving nurse specialists in UI primary care reduced severity and impact of UI after three months of intervention, after correction for effect modifiers; this is also the case in specific situations such as anxiety/depression. UI' in middle-aged and older women in the general population appears to be in the range of 30% to 50% (increasing with age). UI is at least twice as prevalent in women as compared with men. [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF] Considering the ageing population a further increase is expected. [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF] UI is infamous for its impact on general well being and social activities. If not treated and monitored, UI is a chronic dynamic disorder, complicated by co-morbidities, with a strong tendency to increase over time. [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF][START_REF] Abrams | Fourth International Consultation on Incontinence (ICI) -July 5 -8[END_REF] National and international primary care guidelines on UI indicate that for most UI patients pelvic floor muscle and/or bladder training is the best noninvasive initial treatment to solve the problem. [START_REF] Abrams | Fourth International Consultation on Incontinence (ICI) -July 5 -8[END_REF][START_REF] Smith | Committee 12. Adult Conservative Management. Fourth International Consultation on Incontinence (ICI)[END_REF] So far, despite guidelines, training is only incidentally offered. [START_REF] Wagg | Overactive Bladder and Continence Guidelines: implementation, inaction or frustration?[END_REF][START_REF] Kirby | Overactive bladder: the importance of new guidance[END_REF][START_REF] Monz | Patient-reported impact of urinary incontinence. Results from treatment seeking women in 14 European countries[END_REF] Most GPs choose a non-curative alternative: prescribing incontinence pads. More than 50% of UI patients use incontinence pads, especially older people. [START_REF] Monz | Patient-reported impact of urinary incontinence. Results from treatment seeking women in 14 European countries[END_REF][START_REF] Coyne | The impact of overactive bladder, incontinence and other lower urinary tract symptoms on quality of life, work productivity, sexuality and emotional well-being in men and women: results from the EPIC study[END_REF] Although UI threatens health-related quality of life, it is not life threatening. [START_REF] Monz | Patient-reported impact of urinary incontinence. Results from treatment seeking women in 14 European countries[END_REF][START_REF] Coyne | The impact of overactive bladder, incontinence and other lower urinary tract symptoms on quality of life, work productivity, sexuality and emotional well-being in men and women: results from the EPIC study[END_REF] Adequate treatment of UI can be complex and time consuming. So far, UI has not been receiving much attention in general practice, despite the large number of patients who suffer from it.

Probably, there are several reasons, such as lack of knowledge, other clinical priorities, lack of time and lack of targeted implementation strategies to adopt and practice guideline recommendations. [START_REF] Wagg | Overactive Bladder and Continence Guidelines: implementation, inaction or frustration?[END_REF][START_REF] Kirby | Overactive bladder: the importance of new guidance[END_REF][START_REF] Kirby | Managing stress urinary incontinence -a primary care issue[END_REF][START_REF] Shaw | A qualitative study of the assessment and treatment of incontinence in primary care[END_REF][START_REF] Albers-Heitner | Adherence to professional guidelines for patients with urinary incontinence by general practitioners: a cross-sectional study[END_REF][START_REF] Albers-Heitner | How do patients with urinary incontinence perceive care given by their general practitioner? A cross-sectional study[END_REF][START_REF] Staskin | The five 'Ps' of an incontinence clinical practice guideline[END_REF] Therefore, employing nurse specialists may offer a solution to improve the quality of care in general practice provided to UI patients. We envisioned that nurse specialists, after thorough training, would be well equipped to support GPs after the initial consultation and assessment of a UI patient by the GP. acceptance by patients and GPs, feasibility, usefulness in management [START_REF] Laurant | Revision of professional roles and quality improvement: a review of the evidence[END_REF][START_REF] Voogdt ; Pruis | Effectiveness of nurse delivered cardiovascular risk management in primary care: a randomised trial British[END_REF] and the specific effectiveness in treating UI have been reported. [START_REF] Du Moulin | The role of the nurse in community continence care: a systematic review[END_REF] However, little information is available from randomised controlled trials (RCT) with longterm follow-up on the effectiveness of involving nurse specialists for UI compared to usual care in general practice. [START_REF] Du Moulin | The role of the nurse in community continence care: a systematic review[END_REF][START_REF] Du Moulin | Effects of Introducing a Specialized Nurse in the Care of Community-Dwelling Women Suffering From Urinary Incontinence: A Randomized Controlled Trial[END_REF] Therefore, we set up a trial to study whether involving nurse specialists for UI could improve the quality of care for adult UI patients in general practice. [START_REF] Albers-Heitner | Study protocol. The effects of involving a nurse practitioner in primary care for adult patients with urinary incontinence: the PromoCon study (Promoting Continence)[END_REF] We envisioned that this change in process of care would also improve quality of care in terms of treatment outcome.

We addressed the following main research question: "Does the involvement of a nurse specialist for adult persons with UI reduce the overall UI severity including symptoms of frequency, volume and the impact on the health-related quality of life compared to care-asusual?".

Materials and Methods

From May 2005 until March 2008 we performed a pragmatic multicentre RCT comparing UI patients (randomly assigned following simple randomisation procedures) receiving nurse specialist care with UI patients receiving care-as-usual in general practice in four Dutch regions (Maastricht, Nijmegen, Helmond, The Hague). A detailed study protocol and description of the intervention is reported elsewhere. [START_REF] Albers-Heitner | Study protocol. The effects of involving a nurse practitioner in primary care for adult patients with urinary incontinence: the PromoCon study (Promoting Continence)[END_REF] In short, adult patients with stress, urgency or mixed UI, already known or newly diagnosed by their GP, were eligible and actively recruited by their GP to participate in the study and followed during one year. To identify patients known to suffer from UI, GPs searched in their electronic medical record system using the International Classification of Primary Care (ICPC) coding system and obtained a list with pad users from the local pharmacies. Patients who met the in-and exclusion criteria were invited to participate in the trial (Table 1 Based on a mean UI severity sum score on our primary outcome, the International Consultation on Incontinence Questionnaire Short Form (ICIQ-UI SF), [START_REF] Avery | ICI-Q: a brief and robust measure for evaluating the symptoms and impact of urinary incontinence[END_REF] of 7.18 (sd 6.64), an expected clinical important improvement of two points on the outcome scale (delta value of 2/6•64 = 0.301), a power of 80% and a two-sided significance level of 0.05, we needed 175 patients per arm, 350 in total.

Intervention

Six nurse specialists provided the intervention (Figure 1). The nurse specialists received special training in tasks related to diagnostics, intervention and monitoring of incontinence based on guidelines and protocols and proved their competencies afterwards in an assessment.

After the initial medical UI diagnosis by the GP, the nurse specialists, further specified the diagnosis, registered problems in pelvic floor/bladder function (impairment), activities (disability), participation problems and the influence of personal and external factors following the International Classification of Functioning, Disability and Health (ICF). [19] The nurses used micturition diaries and advised on lifestyle, toilet habits, bladder-and pelvic floor muscle training and, when appropriate, the choice of incontinence pads. Patients were treated during one year, with five to seven visits during the first three months, followed by consultations at six and 12 months to monitor effect and adherence. Details of the training of the nurse specialists and the intervention are described and free full text available elsewhere. Care-as-usual Patients randomised to care-as-usual could not get a referral to the nurse specialist. We assumed that GPs would not change their care-as-usual, which is mostly restricted to pads prescription, where only a minority of UI patients gets active treatment or a referral to either physical therapist or specialist. [START_REF] Kirby | Managing stress urinary incontinence -a primary care issue[END_REF][START_REF] Albers-Heitner | Adherence to professional guidelines for patients with urinary incontinence by general practitioners: a cross-sectional study[END_REF][START_REF] Albers-Heitner | How do patients with urinary incontinence perceive care given by their general practitioner? A cross-sectional study[END_REF][START_REF] Gerwen Van | Management of urinary incontinence in general practice: data from the Second Dutch National Survey[END_REF]

Outcome measures

The primary outcome was the International Consultation on Incontinence Questionnaire Short Form (ICIQ-UI SF) severity sum score of self-reported UI frequency, perceived UI quantity (weighted items) and the UI impact on health-related quality of life (Visual Analogue Scale (VAS). [START_REF] Avery | ICI-Q: a brief and robust measure for evaluating the symptoms and impact of urinary incontinence[END_REF] Overall score ranges from zero (no UI) to 21 (most severe UI). UI definitions followed International Continence Society (ICS) standards. [START_REF] Haylen | An international urogynecological association (IUGA)/international continence society (ICS) joint report on the terminology for female pelvic floor dysfunction[END_REF] Effects were controlled for accepted baseline effect modifiers (conditions or risk factors that may influence the effects, such as age, UI type, parity, type of delivery, BMI, restricted mobility, anxiety/depression). [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF] The self-completed EuroQol health-related quality of life questionnaire (EQ-5D), provided a five dimensional descriptive profile of mobility, self-care, usual activities, pain/discomfort and anxiety/depression for general health status. [START_REF] Brooks | EuroQol: the current state of play[END_REF] Each dimension had three levels: no, some or severe problems.

Data collection and statistical analysis

Data was collected through postal questionnaires at baseline and for the two study end-points, three and 12 months. Non-responders were reminded by telephone two to three weeks later.

Kolmogorov-Smirnov tests were used to test normality of distributions in metric variables.

Comparability of groups at baseline was checked for demographics, medical history, and general health. To test the overall effects in outcome at three months paired t-tests of differences with baseline were used by summing results over both groups. Repeated measures ANOVA was used to test outcome time differences from baseline between both groups, both at three months and for the duration of the total follow-up. Repeated measures ANCOVA was used to adjust for baseline outcome measurements, UI type, age, BMI, parity, complications at delivery and baseline EuroQol scales mobility and anxiety/depression. Dummy regression analysis was used on both the three months difference in outcome and on the linear-weighted trend over all outcome measurements in time. To test overall one-year follow-up results for both groups a one-sample t-test was done on the linear weighted trend. Missing data were imputed by using the mean of observed scores for both groups. A p-value of less than 0.05 was assumed to be statistically significant. Data analysis was done according intention-totreat principles, using SPSS-pc 15.0 and 16.0.

Results

109 GPs in 65 practices participated. They identified 4055 UI patients. As expected because of the broad recruitment strategy 47% (n = 1889) had exclusion criteria (mostly comorbidities) for the study. The remaining 2166 patients were invited to participate. 667

Patients were interested and wished to be informed; 206 then refused and 77 were excluded due to co-morbidities.

Finally, 384 patients met the study criteria; 186 were randomly allocated to the intervention and 198 to care-as-usual (Figure 2). Both groups were comparable for factors such as age, gender, parity etc (Table 2). No separate analysis could be performed for gender since only very few males participated in the study.

Of the 186 patients randomised to the nurse specialist, 137 (73.6%) had seven to nine consultations (mean time spent 3.1 hours). Fewer consultations were related to poor health (n = 14) or no motivation/too much burden (n = 15). Adverse events were unrelated to the nurse intervention.

Main results

Overall, both the difference between both groups in ICIQ score at three months and the one-year linear trend was not significant (p = 0.06 and p = 0.15 respectively) (Table 3). In contrast to our expectations, patients in both groups improved on the ICIQ score at three months and on the oneyear linear trend (both endpoints p < 0.001). However, when controlling for the accepted effect modifiers UI type, BMI and baseline ICIQ score we found that, compared to the care-as-usual group, the ICIQ score differences at three months significantly improved in the intervention group (B = -0.56, p = 0.04; n = 381) (Table 3).

Neither BMI, nor UI type was significantly related to the one-year linear trend of the ICIQ score.

Relation with general health

As suggested in literature, we checked the influence of aspects of general health on improvements of the ICIQ sum scores, but found no influences, except for anxiety/depression. Although no differences after three months were found, after one year anxiety/depression was 3).

Discussion

Summary of main findings

Significant differences between groups in favour of the intervention group were found after correction for known effect modifiers (UI type and BMI) after three months intervention.

Surprisingly, both study groups improved in ICIQ sum score at three months and the one-year linear trend. Also, after one year of intervention we found effects in specific situations (anxiety/depression). Before drawing any conclusion a few remarks must be made.

Strenghts and limitations of the study

The choice for a pragmatic design ensured that the intervention was as close as possible to treatment options in daily practice. This will facilitate future implementation. We enrolled patients in our study who were typical for the normal GP-caseload. Nevertheless, in terms of external validity, our results may only be valid for patients with a more than mild UI or who are prepared to play an active role towards their UI. As already mentioned our study population had a higher mean baseline ICIQ sum score [START_REF] Albers-Heitner | How do patients with urinary incontinence perceive care given by their general practitioner? A cross-sectional study[END_REF] as compared to the mean sum-score of 7 for a primary care UI population as used in our power calculation. [START_REF] Abrams | Incontinence Proceedings 2nd International Consultation on Incontinence -July 1[END_REF] It is generally assumed that mild UI forms do profit most from bladder and pelvic floor muscle training. Our results however, show that also UI patients with severe or complex UI can profit from this intervention. [START_REF] Klovning | Comparison of two questionnaires for assessing the severity of urinary incontinence: The ICIQ-UI SF versus the incontinence severity index[END_REF][START_REF] Shaw | How people decide to seek health care: A qualitative study[END_REF][START_REF] Dumoulin | Pelvic floor muscle training versus no treatment, or inactive control treatments, for urinary incontinence in women[END_REF] In patients with mild UI, the effects of our intervention may be higher.

The assumption prior to the study was that the care-as-usual group -as in many years beforewould stay unchanged during the one-year study period. [START_REF] Mcgrother | Storage symptoms of the bladder: prevalence, incidence and need for services in the UK[END_REF][START_REF] Wennberg | A Longitudinal Population-based Survey of Urinary Incontinence, Overactive Bladder, and Other Lower Urinary Tract Symptoms in Women[END_REF] Given this assumption, the However, reality was different. Unexpectedly, the care-as-usual group also improved on the main outcome parameter. Consequently, the difference between both groups on the outcome became lower than expected. This would signify an unforeseen study effect that might be caused by several factors. GPs may have changed their care-as-usual policy, now being aware their UI approach is monitored (Hawthorne-effect). Theoretically, contamination might have occurred, but from our data we have no indication that this indeed occurred. A learning effect in GPs is in our view unlikely as the average GP included (only) 6 patients in the trial. Next to this, patients in the care-as-usual group may be influenced by being actively recruited for the study. An increased awareness about possible solutions for their UI problem may have occurred by extra contact with the GP for enrolment, the informed consent procedure and by repeatedly completing voiding diaries and questionnaires. [START_REF] Burgio | Behavioral Training With and Without Biofeedback in the Treatment of Urge Incontinence in Older Women: A Randomized Controlled Trial[END_REF][START_REF] Melville | Urinary Incontinence in US Women: A Population-Based Study[END_REF] Finally, the general mean imputation of missing items for the intention-to-treat-analysis leads to a regression to the mean in effects.

Altogether, when any improvement in the care-as-usual group was to be factored in for the power calculation, more patients would have been needed. As a result, our findings may be quite conservative.

Comparison with existing literature

This is one of few pragmatic RCTs comparing nurse involvement for UI patients supplementary to care-as-usual by GPs with a long term follow-up of one year. [START_REF] Du Moulin | The role of the nurse in community continence care: a systematic review[END_REF][START_REF] Du Moulin | Effects of Introducing a Specialized Nurse in the Care of Community-Dwelling Women Suffering From Urinary Incontinence: A Randomized Controlled Trial[END_REF] Our findings are in line with RCTs of nurse interventions for incontinent community-dwelling patients. [START_REF] Du Moulin | The role of the nurse in community continence care: a systematic review[END_REF][START_REF] Du Moulin | Effects of Introducing a Specialized Nurse in the Care of Community-Dwelling Women Suffering From Urinary Incontinence: A Randomized Controlled Trial[END_REF] However, comparability of results is limited due to varying populations, settings, outcome measurements, controls, nurse education level and duration of follow-up (often less than one year). Also, our finding that baseline reported anxiety/depression was associated with less UI data collection, supervised the project, participated in the data interpretation, preparation and critical revision and approval of the manuscript for important intellectual content. Fred Nieman was helpful in the conception and design of the study, was responsible for methodology and the statistical analysis and interpretation, and was involved in revising and approval of the manuscript for important intellectual content. Pieter Venema was helpful in the conception and design of the study, facilitated data collection and critically revised and approved the final drafts of the manuscript for important intellectual content.

Johan Severens gave advice regarding the conception and design of the study, supervised the project, advised in data analysis and interpretation and was involved in revising and approval of the manuscript for important intellectual content. Ron Winkens (project leader) was responsible for the conception and design of the study, supervised the project, facilitated data collection, participated in the data interpretation, preparation and critical revision and approval of the manuscript for important intellectual content. • urinary tract infection, hematuria without urinary tract infection

International

• male < 65 years with unclear reason for UI

• ongoing other treatment for UI

• failure after surgery for UI or failure of conservative therapy

• severe cognitive problems

• living in nursing home

• otherwise severe medical or psychiatric diseases

  in the one-year linear trend (p = 0.15). Patients in the intervention group without baseline anxiety/depression improved significantly better compared to care-asusual after one year (p = 0.03).

Introduction

  Urinary incontinence (UI) is a frequent clinical condition. The estimated prevalence of 'any

Deleted:

  General health (mobility, selfcare, usual activities, pain/discomfort, anxiety/depression) was measured with t

  Over the study period 40 (10.4%) (19 intervention, 21 control) patients dropped out.

  responsible for less improvement of the ICIQ sum score (interactive effect B = 1.02, p = 0.03; n B effect for patients without baseline anxiety/depression = -.63, p = 0.03; n = 272) (Table

  should have been sufficient to trace a significant difference.

Figure 1 .

 1 Figure 1. Flow chart intervention nurse specialist for patients with UI PFM (T)= Pelvic Floor Muscle (Training); GP = general practitioner; PPT = pelvic physiotherapist; NS = nurse specialist PFM (T)= Pelvic Floor Muscle (Training); GP = general practitioner; PPT = pelvic physiotherapist; NS = nurse specialist PFM (T)= Pelvic Floor Muscle (Training); GP = general practitioner; PPT = pelvic physiotherapist; NS = nurse specialist PFM (T)= Pelvic Floor Muscle (Training); GP = general practitioner; PPT = pelvic physiotherapist; NS = nurse specialist Definitions following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards.

  Nurse specialists have specific skills and have extra time to inform and motivate patients compared to GPs. Their general

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  following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards. Definitions following International Continence Society (ICS) standards. Flow of participants through each stage of the randomised trial and analysed for primary outcome

	Figure 2.
				Patients with urinary incontinence	Not meeting inclusion
				identified and assessed for	criteria (n=1889)
				eligibility (n=4055)
					Invited by post (n=2166)
				Enrollment	Non response (n=1499) Not meeting inclusion
					criteria (n=283)
				Randomised (n=384)
				Existing UI (n=173)	Existing UI (n=181)
	Allocation	o r GP + intervention nurse specialist (n=186) F Newly diagnosed UI (n=13)	Care-as-usual by GP (n=198) Newly diagnosed UI (n=17)
	Follow up	3 m	P e known (8); unknown (1) r Refused participation reasons: e Loss to follow-up (n=14) Reasons: deceased (3) Moved away / unreachable (2)	known (12); unknown (1) Refused participation reasons: Loss to follow-up (n=14) Reasons: Moved away / unreachable (1)
	Follow up Analysis	6m 3m	PFM OK Refused participation reasons: PFM not OK consult GP: Loss to follow-up (n=2) Reasons: deceased (1) known (2) Loss to follow-up (n=3) e i Bladder diary not improved after 3 weeks e Loss to follow-up (n=2) w Reasons: deceased (1) Refused participation reasons: known (3) v Loss to follow-up (n=4) R Intention-to-treat analysis (n=172) Intention-to-treat analysis (n=184)	3-5x weekly visites 20 minutes Follow-up contact 15 minutes at 6 weeks
		9m	PFMT	check PFM Reasons: deceased (2)	Consultation / report GP: PPT, medication n Refused participation reasons: known (2) O Reasons:
	Analysis	12 m 12 m	Sufficient improvement / cure Follow-up / control Intention-to-treat analysis (n=167) Fall back after 6 weeks, 3 months Intention-to-treat analysis (n=177) specialist medication, improvement report GP: PPT, Failure / insufficient Consultation / Not ok OK l Loss to follow-up (n=0) Loss to follow-up (n=1) y Reasons: deceased (1)	3 months 6 months 12 months
					End study
				Consultation /
				report GP:
				refresher-
				intervention NS	1

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Table 1 .

 1 In-and exclusion criteria other types of UI than SUI, UUI or MUI / signs of reflex-or overflow UI• abdominal tumors• neurological diseases associated with UI (multiple sclerosis, stroke, diabetes, cauda equina syndrome)

	Inclusion criteria
	• age > 18 years
	• SUI, UUI or MUI already or newly diagnosed by GP (according to the guidelines of the Dutch
	College of General Practitioners on UI)
	Exclusion criteria
	• women with prolapse degree III or more
	• pregnancy or delivery < 6 months ago
	patients with
	•

Table 2 .

 2 • comprehension of Dutch language not good enough to fill in questionnaires Demographics and baseline characteristics of patients. N = 384 (100%)

	Abbreviation: SUI=stress urinary incontinence; UUI=urgency urinary incontinence; MUI=mixed urinary
	incontinence; UI=urinary incontinence; GP=general practitioner

Abbreviation: mv=missing value; BMI=body mass index, calculated as weight in kilograms divided by height in meters squared; UI=urinary incontinence; SUI=stress urinary incontinence; UUI=urgency urinary incontinence; MUI=mixed urinary incontinence; NOS=not otherwise specified; FI=fecal incontinence *problems=sum of moderate and severe problems

Acknowledgments

We thank all participating GPs and Zorg Groep Zuid-Gelderland, Groene Kruis Domicura, Maastricht, AZIVO/ PCC of HAGA Hospital, The Hague, De Zorgboog, Elkerliek Hospital, Helmond, The Netherlands, their nurse specialists and the patients for their cooperation in the study. We thank Wendy Engering, Margriet Straver, Liesbeth van Hoef, Joyce Janssen and Nicole Castro for research assistance.

Funding

The study was approved and funded by the Netherlands Organisation for Health Research and Development (ZonMw), grant number 945-04-224. ZonMw was not involved in manuscript preparation and/or publication decisions.

improvement is in line in literature. [START_REF] Nygaard | Urinary incontinence and depression in middleaged United States women[END_REF][START_REF] Gerwen Van | Comorbidities Associated with Urinary Incontinence: A Case-Control Study from the Second Dutch National Survey of General Practice[END_REF][START_REF] Melville | Major depression and urinary incontinence in women: temporal associations in an epidemiologic sample[END_REF] Lack of motivation, especially in those suffering from depression, might explain the lack of effect of our intervention on the one-year linear trend.

Implications for clinical practice and future research

UI is a chronic dynamic disorder and often complicated by comorbidities. [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF] The positive effect of the nurse specialist intervention on the short term would argue in favour of a repeated intervention by trained health care professionals to monitor the condition and achieve long term effects. [START_REF] Holroyd-Leduc | Comment on: Is there a role for estrogen in the prevention and treatment of urinary incontinence?[END_REF] Further research should focus on tailoring the intervention to patients characteristics which are prognostic and predictive for UI and changeable (depression [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF][START_REF] Nygaard | Urinary incontinence and depression in middleaged United States women[END_REF][START_REF] Melville | Major depression and urinary incontinence in women: temporal associations in an epidemiologic sample[END_REF], overweight [START_REF] Milsom | Committee 1. Epidemiology of Urinary (UI) and Faecal (FI) Incontinence and Pelvic Organ Prolapse (POP)[END_REF][START_REF] Subak | Weight loss to treat urinary incontinence in overweight and obese women[END_REF]). Also, research into the cost-effectiveness of involving nurse specialists for UI patients in general practice is needed. [START_REF] Moore | Committee 22. Economics of Urinary and Faecal Incontinence, and Prolapse. Fourth International Consultation on Incontinence (ICI) -July 5 -8[END_REF]

Author contributions

All authors have approved the final draft for submission and had access to the study data. Specific contributions were made in the following area's: Pytha Albers-Heitner was involved in the conception and design of the study, data collection, statistical analysis and interpretation. In addition, she was responsible for the preparation, drafting and critical revision and approval of the manuscript. Toine Lagro-Jansen was helpful in the conception and design of the study, facilitated data collection, supervised the project, participated in the data interpretation, preparation and critical revision of the manuscript for important intellectual content and approval. Manuela Joore assisted in the conception and design of the study, supervised the project and critically revised the drafts of the manuscript for important intellectual content and


Stéphane Vautier

The operationalization of general hypotheses versus the discovery of empirical laws in Psychology

Psychology students learn to operationalize `general hypotheses' as a paradigm of scientic Psychology:

relatively vague ideas result in an attempt to reject the null hypothesis in favour of an alternative hypothesis, a so-called research hypothesis, which operationalizes the general idea.

Such a practice turns out to be particularly at odds with the discovery of empirical laws. An empirical law is dened as a nomothetic gap emerging from a reference system of the form Ω × M (X) × M (Y), where Ω is a set of events or dated objects for which some states in the set M (Y) are hypothetically impossible given some initial conditions depicted in the set M (X). This approach allows the knowledge historian to carefully scrutinize descriptive and nomothetic advances in contemporary empirical Psychology. Résumé L'enseignement de la méthodologie scientique en Psychologie confère un rôle paradigmatique à l'opérationnalisation des "hypothèses générales" : une idée sans rapport précis à l'observation concrète se traduit par la tentative de rejeter une hypothèse statistique nulle au prot d'une hypothèse alternative, dite de recherche, qui opérationnalise l'idée générale. Cette démarche s'avère particulièrement inadaptée à la découverte de lois empiriques. Une loi empirique est dénie comme un trou nomothétique émergeant d'un référentiel de la forme Ω × M (X) × M (Y), où Ω est un ensemble d'événements ou d'objets datés dont certains états dans l'ensemble M (Y) sont par hypothèse impossibles étant données certaines conditions initiales décrites dans l'ensemble M (X). Cette approche permet de préciser le regard que l'historien des connaissances peut porter sur les avancées descriptives et nomothétiques de la Psychologie empirique contemporaine.

This article is the result of the author's need to elaborate on the persistent dissatisfaction he feels with the methodology of scientic research in Psychology, and more precisely with his perception of the way in which it is taught. It would indeed be presumptuous to present the following criticism as being a criticism of the methodology of scientic research in Psychology as a whole, since the latter is a notion which is too all-encompassing in its scope to serve

as a precise description of the diversity of research practice in this vast eld. The source of this dissatisfaction is to be found in what [START_REF] Reuchlin | Introduction à la recherche en psychologie[END_REF] calls the `distance' between `general theory' and a `specic, falsiable hypothesis ' (p. 32). A certain form of academism shapes the approach to scientic research in Psychology according to a three-stage process for the formulation of hypotheses (e.g., [START_REF] Charbonneau | Problématique et hypothèses d'une recherche[END_REF]. When they write the report of an empirical study, researchers in Psychology must supply the grounds for their research by introducing a so-called general (or theoretical) hypothesis, then show how they have tested this hypothesis by restating it as a so-called operational (or research) hypothesis.

In principle, this restatement should involve data analysis, nalised by testing at least one inferential statistical hypothesis, the so-called null hypothesis.

As a socially regulated procedure, the sequencing of theoretical, operational and null hypotheses which we refer to here as operationalization may not pose scientic problems to researchers who are mainly concerned with adhering to a socio-technical norm. The sense of dissatisfaction arises when this desire for socio-technical compliance is considered in the light of the hope (albeit an admittedly pretentious or naïve hope) of discovering one or more empirical laws, i.e. demonstrating at least one, corroborated general empirical statement [START_REF] Vautier | How to state general qualitative facts in pychology? Quality and Quantity[END_REF].

With respect to the discovery of empirical laws, operationalization may be characterised as a paradigm, based on a `sandwich' system, whose workings prove to be strikingly ineective. The `general hypothesis' (the uppermost layer of the `sandwich' system) is not the statement of an empirical law, but a pre-referential statement, i.e. a statement whose empirical signicance has not (yet) been determined. The null hypothesis test (the lower layer of the `sandwich') binds the research procedure to a narrow, pragmatic decision-making approach amid uncertainty rejection or acceptance of the null hypothesis which is not germane to the search for empirical laws if the null hypothesis is not a general statement in the strict sense of the term, i.e. held to be true for all the elements in a given set. Between the external layers of the `sandwich' system lies the psychotechnical and statistical core of the operationalization paradigm, i.e. the production of psychological measurements to which the variables required for the formulation of the operational hypothesis are linked.

Again, the claim here is not that this characterisation of research procedure in Psychology applies absolutely universally; however, operationalization as outlined above does appear to be suciently typical of a certain orthodoxy to warrant a thorough critical analysis. This paradigm governs an approach which is destined to establish a favourable view of `general hypotheses' inasmuch as they have psychotechnical and inferential support. However, the ideological interest of these statements does not automatically confer them with nomothetic import. Consequently, one cannot help wondering whether the rule of operationalization does not in fact serve to prevent those who practise it from ever discerning a possible historical failure of orthodox Psychology to discover its own empirical laws, by training the honest researcher not to hope for the impossible. After all, we are unlikely to I wish to express my thanks to Nadine Matton and Éric Raufaste for their helpful comments on a previous version of this article. This work was funded in part by the ANR-07-JCJC-0065-01 programme. Correspondence about this article should be sent to Stéphane Vautier, Université de Toulouse, OCTOGONE-CERPP, Pavillon de la Recherche, 5 allées A. Machado, 31058 Toulouse Cedex 9, France. E-mail: vautier@univ-tlse2.fr.

worry about failing to obtain something which we were not looking for in the rst place.

We shall see that an empirical law consists precisely of stating an empirical impossibility, i.e. a partially deterministic falsiable statement. As a result, we have inevitably come to question psychological thought as regards the reasons and consequences of an apodictic approach to probabilistic treatment of the empirical phenomena which it is investigating. This article comprises four major parts. First of all, we shall illustrate operationalization on the basis of an example put forward by [START_REF] Fernandez | La recherche en psychologie clinique[END_REF]. Next, we shall identify two logical and empirical diculties which arise from this paradigm and demonstrate that they render it unsuitable for the discovery of empirical laws, then detail the logical structure of these laws. Lastly, we shall identify some methodological guidelines which are compatible with an inductive search for partial determinisms.

An example of operationalization: smoking cessation and anxiety [START_REF] Fernandez | La recherche en psychologie clinique[END_REF] put forward the following sequence (p. 125):

General hypothesis: undergoing smoking cessation tends to increase anxiety in smokers rather than reduce it.

↓

Operational hypothesis: smokers undergoing smoking cessation are more prone to anxiety than non-cessation smokers.

↓

Null hypothesis: there is no dierence between anxiety scores for smokers undergoing smoking cessation and non-cessation smokers. This example can be expanded so as to oer more opportunities to engage with the critical exercise. There is no diculty in taking [START_REF] Fernandez | La recherche en psychologie clinique[END_REF] operational hypothesis as a `general hypothesis'. Their formulation species neither the empirical (nominal) meaning of the notion of smoking cessation, nor the empirical (ordinal or quantitative) signicance of the notion of anxiety, even though it makes reference to the ordinal operator more prone to anxiety than; lastly, the noun smokers signies only an indenite number of people who smoke.

The researcher may have given herself/himself a set of criteria which is sucient to decide whether, at the moment when they examines an individual, the person is a smoker or not, and if they is a smoker, another set of criteria sucient to decide whether or not they is undergoing smoking cessation. These sets of criteria allow the values for two nominal variables to be dened, the rst attributing the value of smoker or non-smoker, and the second, which is conditional on the status of `smoker', attributing the value of undergoing cessation or non-cessation. However, the statistical denition of the `undergoing cessation' variable requires a domain, i.e. elements assigned a value according to its codomain, the (descriptive) reference system of the variable: {undergoing cessation, non-cessation}. The researcher may circumscribe the domain to pairs (smoker, examination date) which they already has obtain or will obtain during the course of their study, and thus dene a so-called independent nominal variable.

They then needs to specify the function which assigns an anxiety score for each (smoker, examination date) pair, in order to dene the `anxiety score' statistical variable, taken as the dependent variable. The usual solution for specifying such a function consists in using the answers to an anxiety questionnaire to determine this score, according to a numerical coding rule for the responses to the items on the questionnaire. Such procedures, in which standardised observation of a verbal behaviour is associated with the numerical coding of responses, constitute one of the fundamental contributions of psychotechnics (or psychological testing) to Psychology; it enables anxiety means conditional on the values of the independent variable to be calculated, whence the operational hypothesis: smokers undergoing smoking cessation are more anxious than non-cessation smokers.

The operational hypothesis constitutes a descriptive proposition whose validity can easily be examined. However, to the extent that she/he considers their sample of observations to be a means of testing a general hypothesis, the researcher must also demonstrate that the mean dierence observed is signicant, i.e. rejects the null hypothesis of the equality of the means for the statistical populations composed of the two types of smokers, using a probabilistic procedure selected from the available range of inferential techniques, for instance Student's t-test for independent samples. Only then can the operational hypothesis, considered in the light of the two statistical populations, acquire the status of an alternative hypothesis with respect to the null hypothesis. Now, let us restate the sequence of hypotheses put forward by [START_REF] Fernandez | La recherche en psychologie clinique[END_REF] thus: General hypothesis: smokers undergoing smoking cessation are more anxious than non-cessation smokers ↓ Operational hypothesis: given a pair of variables (`undergoing cessation', `anxiety score'), mean anxiety conditional on the undergoing cessation value is greater than mean anxiety conditional on the non-cessation value.

↓

Null hypothesis: the two conditional means are equal.

Operationalization criticised

The example which we have just developed is typical of operationalization in Psychology, irrespective of the experimental or correlational nature [START_REF] Cronbach | The two disciplines of scientic psychology[END_REF][START_REF] Cronbach | Beyond the two disciplines of scientic psychology[END_REF] of the study. In this section, we make two assertions by dealing with the operationalization approach in reverse: (i) the empirical relevance of the test of the null hypothesis is indeterminate (ii) the statistical fact of a mean dierence has no general empirical import.

The myth of the statistical population

To simplify the discussion, let us suppose that the researcher tests the null hypothesis of the equality of two means using Student's t procedure. The issue at stake in the test from a socio-technical point of view is that by qualifying the dierence observed as a signicant dierence, the cherished notation "p < .05" or "p < .01" may be included in a research paper. The null hypothesis test has been the subject of purely statistical criticisms (e.g., [START_REF] Krueger | Null hypothesis signicance testing[END_REF][START_REF] Nickerson | Null hypothesis signicance testing: A review of an old and continuing controversy[END_REF] and it is not within the scope of this paper to draw up an inventory of these criticisms. In the empirical perspective under examination here, the problem is that this type of procedure is nothing more than a rhetorical device, insofar as the populations to which the test procedure is applied remain virtual in nature.

In practice, the researcher knows how to dene their conditional variables on the basis of pairs: (smoker undergoing cessation, examination date) and (non-cessation smoker, examination date), assembled by her/him through observation. But what is the signicance of the statistical population to which the inferential exercise makes reference? If we consider the undergoing cessation value, for example, how should the statistical population of the (smoker undergoing cessation/examination date) pairs be dened? Let us imagine a survey which would enable the anxiety score for all the human beings on the planet with the status of `smoker undergoing smoking cessation' to be known on a certain date each month in the interval of time under consideration. We would then have as many populations as we have monthly surveys; we could then consider grouping together all of these monthly populations to dene the population of observations relating to the `cessation' status. There is not one single population, but rather a number of virtual populations. The null hypothesis is therefore based on a mental construct. As soon as this is dened more precisely, questions arise as to its plausibility and the interest of the test. Indeed, why should a survey supply an anxiety variable whose conditional means, subject to change, are identical?

Ultimately, it appears that the null hypothesis test constitutes a decision-making procedure with respect to the plausibility of a hypothesis devoid of any determined empirical meaning. The statistical inference used in the operationalization system is an odd way of settling the issue of generality: it involves deciding whether the dierence between observed means may be generalised, even if the empirical meaning of this generality has not been established.

The myth of the average smoker

The dierence between the two anxiety means may be interpreted as the dierence between the degree of anxiety of the average smoker undergoing cessation and the degree of anxiety of the average non-cessation smoker, which poses two problems. Firstly, the discrete nature of the anxiety score contains a logical dead-end, i.e. the use of an impossibility to describe something which is possible. Let us assume an anxiety questionnaire comprising ve items with answers scored 0, 1, 2 or 3, such that the score attributed to any group of 5 responses will fall within the sequence of natural numbers (0, 1, . . . , 15). A mean score of 8.2 may indeed `summarise' a set of scores, but cannot exist as an individual score.

Consequently, should we wish to use a mean score to describe a typical smoker, it must be recognised that such a smoker is not possible and therefore not plausible. As a result, the dierence between the two means cannot be used to describe the dierence in degrees of anxiety of the typical smokers, unless it is admitted that a typical smoker is in fact a myth.

Let us now assume that the numerical coding technique enables a continuous variable to be dened by the use of so-called analogue response scales. The score of any smoker is by denition composed of the sum of two quantities, the mean score plus the deviation from the mean, the latter expressing the fact that the typical smoker is replaced in practice by a particular specimen of the statistical population, whose variable nature is assumed to be random without it appearing necessary to have empirical grounds for the probability space on which this notion is based. In these conditions, the mean score constitutes a parameter, whose specication is an empirical matter inasmuch as the statistical population is actually dened. An empirical parameter is not, however, the same thing as an empirical law.

Formalisation of an empirical law

According to the nomothetic perspective, scientic ambition consists in discovering laws, i.e. general implications.

1 A general implication is a statement in the following form ∀ x ∈ A, p(x) ⇒ q(x),

(1) which reads thus for any x of A, if p(x) then q(x), where x is any component of a given set A, and p(•) and q(•) are singular statements. This formalisation applies without any diculty to any situation in which the researcher has a pair of variables (X, Y ), from a domain Ω n = {ω i , i = 1, . . . , n}, whose elements ω i are pairs (person, observation date). The codomain of the independent variable X is a descriptive reference system of initial conditions M (X) = {x i , i = 1, . . . , k}, whilst the dependent variable, Y , species a value reference system, M (Y ) = {y i , i = 1, . . . , l}, the eective observation of which depends, by hypothesis, on the independent conditions. Thus, the ontological substrate of an empirical law is the observation reference system Ω×M (X)×M (Y ), where Ω ⊃ Ω n is an extrapolation of Ω n : any element of Ω is, as a matter of principle, assigned a unique value in M (X)×M (Y ) by means of the function (X, Y ).

Two comments arise from this denition. Firstly, as noted by [START_REF] Popper | The logic of scientic discovery[END_REF], [natural laws] do not assert that something exists or is the case; they deny it (p. 48). In other words, they state a general ontological impossibility in terms of Ω × M (X) × M (Y ): a law may indeed by formulated by identifying the initial conditions α(X) ⊂ M (X) for which a non-

empty subset β(Y ) ⊂ M (Y ) exists such that, ∀ ω ∈ Ω, X(ω) ∈ α(X) ⇒ Y (ω) ∈ β(Y ).
(2) This formulation excludes the possibility of X(ω) ∈ α(X) and Y (ω) ∈ β(Y ) being observed, where β(Y ) designates the complementary set β(Y ) with respect to M (Y ). Making a statement in the form of (2) amounts to stating a general empirical fact in terms of Ω n , and an empirical law in terms of Ω, by inductive generalisation. This law can be falsied, simply by exhibiting an example of what is said to be impossible in order to falsify it. The general nature of the statement stems from the quantier ∀ and its empirical limit is found in the extension of Ω. The law may then be corroborated or falsied. If it is corroborated, it is possible to measure its degree of corroboration by the number of observations applying to it, i.e. by the cardinality of the equivalence class formed by the antecedents of α(X) the class is noted Cl Ωn/X [α(X)].

1 This is a more general and radical restatement of the denition given by [START_REF] Piaget | Épistémologie des sciences de l'homme[END_REF] of the notion of laws. For him laws designate relatively constant quantitative relations which may be expressed in the form of mathematical functions, general fact or ordinal relationships [...,] structural analyses, etc. which are expressed in ordinary language or in more or less formalised language (logic, etc.) (p. 17).

The second comment relates to the notion of partial determinism. The mathematical culture passed on through secondary school teaching familiarises honest researchers with the notion of numerical functions y = f (x), which express a deterministic law, i.e. that x being given, y necessarily has a point value. If the informative nature of the law is envisaged in negative terms [START_REF] Dubois | Informations bipolaires: une introduction[END_REF], the necessity of the point is dened as the impossibility of its complement. In the eld of humanities [START_REF] Granger | La science et les sciences[END_REF], seeking total determinisms appears futile, but this does not imply that there is no general impossibility in Ω × M (X) × M (Y ) and therefore no partial determinism. The fact that partial determinism may not have a utility value from the point of view of social or medical decision-making engineering has nothing to do with its fundamental scientic value. The subject of nomothetic research therefore appears in the form of a 'gap' in a descriptive reference system, this gap being theoretically interpreted as the eect of a general ontological impossibility. This is why in teaching, a methodology to support the nomothetic goal of training student researchers to `search for the impossible' is called for.

How to seek the impossible Discovery of a gap in the descriptive reference system involves the discovery of a general empirical fact, from which an empirical law is inferred by extending the set of observations Ω n to an unknown phenomenological eld Ω ⊃ Ω n (e.g. future events). A general empirical fact makes sense only with reference to the descriptive reference system M (X)×M (Y ). Practically speaking, dependent and independent variables are multivariate.

Let X = (X 1 , X 2 , . . . , X p ) be a series of p independent variables and M (X) the reference system of X ; M (X) is the Cartesian product of the p reference systems M (X i ), i = 1, • • • , p. Similarly, let Y = (Y 1 , . . . , Y q ) be a series of q dependent variables and M (Y) the reference system of Y. The descriptive reference system of the study is therefore

M [(X, Y)] = M (X) × M (Y) = M (X 1 ) × M (X 2 ) × • • • × M (X p ) × M (Y 1 ) × • • • × M (Y q ).
(3)

Thus the contingency table (the rows of which represent the multivariate values of X, and the columns the multivariate values of Y) can be dened. Observation readings are then carried out so that the cells in the contingency table are gradually lled in... or remain empty.

Two cases must be distinguished here. The rst corresponds to the situation in which the researcher is completely ignorant of what is happening in their observation reference system, in other words, they does not have any prior observations. They therefore has to carry out some kind of survey in order to learn more. Knowing what is happening in the reference system means knowing the frequency of each possible state. It does not involve calling on the notion of probability (the latter being rmly in the realm of mathematical mythology) since it would involve knowing the limit of the frequency of each cell in the contingency table as the number of observations (n) tends towards innity.

A nomothetic gap arises when there is at least one empty cell in at least one row of the contingency table, when the margin of the row (or rows) is well above the cardinality of M (Y). It is possible to identify all the gaps in the reference system only if its cardinality is well below the cardinality of Ω n , n. This empirical consideration sheds light on a specic epistemological drawback in Psychology: not only are its descriptive reference systems not given naturally, as emphasised by [START_REF] Danziger | Constructing the subject: Historical origins of psychological research[END_REF], 2 but in addition the depth of con- structible reality is such that its cardinality may be gigantic so much so that discussing what is happening in an observation reference system cannot be achieved in terms of sensible intuition. The fact is that the socio-technical norms which shape the presentation of the observation techniques used in empirical studies do not refer either to the notion of descriptive reference system or the necessity of plotting the cardinality card[M (X) × M (Y)] against the cardinality of the set of observations, card(

Ω n ) = n. If the quotient card[M (X) × M (Y)]/n
is not much lower than 1, planning to carry out an exhaustive examination of the nomothetic gaps in the descriptive reference system is unfeasible. This does not prevent the researcher from working on certain initial conditions α(X), but in such cases it must nonetheless be established that dividing the number of values of M (Y) by the cardinality of the class Cl Ωn/X [α(X)] of antecedents of α(X) in Ω n gives a result which is far less than 1.

Let us now present the second case, for which it is assumed that the researcher has been lucky enough to observe the phenomenon of a gap, whose 'coordinates' in the descriptive reference system of the study are [α(X), β(Y)]. The permanent nature of this gap constitutes a proper general hypothesis. This hypothesis should be tested using a targeted observation strategy. Indeed, accumulating observations in Ω is of interest from the point of view of the hypothesis if these observations are such that:

• X(ω) ∈ α(X), in which case we seek to verify that Y(ω ), in which case we seek to verify that X(ω) ∈ α(X).

) ∈ β(Y), • Y(ω) ∈ β(Y
This approach to observation is targeted, and indeed makes sense, in that it focuses on a limited number of states: the researcher knows exactly what they is looking for. It is the very opposite of blindly reproducing an experimental plan or survey plan.

When a counterexample is discovered, i.e. ω e exists such that X(ω e ) ∈ α(X) and Y(ω e ) ∈ β(Y), this observation falsies the general hypothesis. The researcher can then decide either to reject the hypothesis or to defend it. If they decides to defend it, they may restrict the set of conditions α(X), or try to nd a variable X p+1 which modulates verication of the rule. Formally speaking, this modulating variable is such that there is a strict non-empty subset of M (X p+1 ) let this be γ(X p+1 ) such that:

∀ ω ∈ Ω, [X(ω) ∈ α(X) and X p+1 (ω) ∈ γ(X p+1 )] ⇒ Y(ω) ∈ β(Y). (4)
Irrespective of how they revises the original hypothesis, they will have to restrict its domain of validity with respect to the implicit set of possible descriptive reference systems. A major consequence of revising the law by expanding the descriptive reference system of initial conditions is resetting the corroboration counter, since the world being explored has been given an additional descriptive dimension: this is the reference system Ω × M (X 1 ) × M (Y),

where X 1 = (X, X p+1 ).

Example

Without it being necessary to develop the procedure presented here in its entirety, we can illustrate it using the example of smokers' anxiety. The problem consists of restating the 2 But in terms of truth, scientic psychology does not deal with natural objects. It deals with test scores, evaluation scales, response distributions, series lists, and countless other items which the researcher does not discover but rather constructs with great care. Conjectures about the world, whatever they may be, cannot escape from this universe of artefacts (p. 2).

'general hypothesis' as a statement which is (i) general, properly speaking, as understood in (1) , and (ii) falsiable. We may proceed in two stages. Firstly, it is not necessary to talk in terms of reference systems to produce a general statement. Expressing the problem in terms of the dierence between two means is not relevant to what is being sought; however, the idea according to which any smoker undergoing cessation becomes more anxious may be examined, along the lines of the 'general hypothesis' described by [START_REF] Fernandez | La recherche en psychologie clinique[END_REF]. This idea is pre-referential inasmuch as we are unable to dene a smoker, a smoker undergoing cessation, or a person who is becoming more anxious.

Since we cannot claim to be able to actually settle these issues of denition, we shall use certain denitions for the purposes of convenience. Let U be a population of people and T a population of dates on which they were observed. Let Ω n be a subset of U × T × T such that, for any triplet ω = (u, t 1 , t 2 ), u is known on dates t 1 and t 2 in terms of their status as:

• a non-smoker, a smoker undergoing cessation or a non-cessation smoker • and their state of anxiety, for instance with reference to a set of clinical signs, of which the person is asked to evaluate the intensity on date t, using a standard `state-anxiety' questionnaire.

It can be noted that the set Ω n is a nite, non-virtual set, in that a person u whose smoker status is not known on date t 1 or t 2 for example, constitutes a triplet which does not belong to this set. According to our approach to the statistical population, it is not necessary for the observations to be the result of applying a specic random sampling technique. Since Ω n constitutes a set of known observations from the point of view of the descriptive reference system, it is a numbered set, to which new observations can be added over time; whence the notation Ω n (read "j-mat"), where n  stands for the cardinality of the most recent update to the set of observations. We can then dene the following variables X  and Y  , from the subset P  of Ω n , which includes the triplets (u, t 1 , t 2 ) such that t 2 -t 1 = d, where d is a transition time (e.g. 2 days). The variable X  matches any component of P  with an image in M (X  ) = {nf, f 1 , f 2 } × {nf, f 1 , f 2 }, where nf , f 1 and f 2 signify `non-smoker', `non-cessation smoker' and `smoker undergoing cessation' respectively. Let us call α(X  ) the subset of M (X  ) including all the pairs of values ending in f 2 which do not begin with f 2 and take an element p ∈ P  : the proposition `X (p) ∈ α(X  )' means that in the period during which they was observed, person u had been undergoing smoking cessation for two days whereas she/he has not been before.

3

The dependent variable Y  must now be dened. Let us assume that for any sign of anxiety, we have a description on an ordinal scale (i.e., a Likert scale). Anxiety can then be described as a multivariate state varying within a descriptive reference system A. Consider A × A; in this set a subset β(Y  ) can be dened which includes changes in states dened as a worsening of the state of anxiety. The variable Y  can then be dened, which, for each p ∈ P  , corresponds to a state in M (Y  ). The proposition 'Y  (p) ∈ β(Y  )' signies that in the period during which they was observed, person u became more anxious. Lastly, the general hypothesis can be formulated in terms which ensure that it may be falsied:

∀ p ∈ P  , X  (p) ∈ α(X  ) ⇒ Y  (p) ∈ β(Y  ).
(5)

We have just illustrated an apparently hypothetical-deductive approach; but in fact it is an exploratory procedure if the community is not aware of any database enabling a nomothetic gap to be identied. Let us assume that the work of the researcher leads to the provision of a database Ω 236 for the community and that sets α(X  ) and β(Y  ) are dened after the fact, such that at least one general fact may be stated. The community with an interest in the general fact revealed by this data may seek new supporting or falsifying observations in order to help update the database.

If a researcher nds an individual v, with q = (v, t v1 , t v2 ) and t v2 -t v1 = d, such that X  (q) ∈ α(X  ) and Y  (q) ∈ β(Y  ), this means that there is a smoker who has been undergoing cessation for two days, whose anxiety has not worsened. Let us assume that the researcher investigates whether the person was already very anxious; they may suggest that rule (5) should be revised so as to exclude people whose initial clinical state corresponds to certain values in the reference system A. This procedure usually consists in restricting the scope of validity of the general hypotheses.

Discussion

Operationalization in Psychology consists in restating a pre-referential proposition in order to enable the researcher to test a statistical null hypothesis, the rejection of which enables the `general hypothesis' to be credited with a certain degree of acceptability.

4 Using an example taken from [START_REF] Fernandez | La recherche en psychologie clinique[END_REF], we have shown that the aim of such a procedure is not the discovery of empirical laws, i.e. the discovery of nomothetic gaps in a reference system. We shall discuss two consequences of our radical approach to seeking empirical laws in an observation reference system Ω × M (X) × M (Y). The rst relates to the methodology for updating the state of knowledge in a eld of research, the second to the probabilistic interpretation of accumulated observations. The state of knowledge in a given eld of research can be apprehended in practical terms by means of a list of m so-called scientic publications. Let us call this set composed of specialist literature L m and let l i be an element in this list. The knowledge historian can then ask the following question: does text l i allow an observation reference system of the type Ω n × M (X) × M (Y) to be dened? Such a question can only be answered in the armative if it is possible to specify the following:

1. n > 0 pairs (u, t), 2. p > 0 reference systems enabling the description of the initial conditions aecting the n pairs (u, t), 3. q > 0 reference systems enabling the description of states aecting the n pairs (u, t) according to the initial conditions in which they are found. Specifying a descriptive reference system consists in identifying a nite set of mutually exclusive values. Not all the description methods used in Psychology allow such a set to be dened; for example, a close examination of the so-called Exner scoring system (1995) for verbatims which may be collected for any [START_REF] Rorschach | Psychodiagnostik[END_REF] test card did not enable us to determine the Cartesian product of the possible values. And yet, to nd a gap in a reference system, this reference system must be constituted, so as to form a stabilised and objective descriptive framework. Faced with such a situation, a knowledge historian would be justied in describing a scientic era in which research is based on such a form of descriptive methodology as being a pre-referential age.

With regard to the matter of the objectivity of a descriptive reference system, we shall conne ourselves to introducing the notion of score-objectivity. Let P = {p i , i = 1, . . . , z} be a set of Psychologists and ω

j ∈ Ω. (X, Y) i (ω j ) is the value of ω j in M (X) × M (Y)
as determined by the Psychologist p i . We may say that M (X) × M (Y) is score-objective relative to P if (X, Y) i (ω j ) depends only on j for all values of j. If a descriptive reference system is not score-objective, an event in Ω × M (X) × M (Y) which occurs in a gap cannot categorically be interpreted as a falsifying observation, since it may depend on a particular feature of the way the reporting Psychologist views it. Unless and until the descriptive denition of an event is regulated in a score-objective manner, the nomothetic aspiration appears to be premature, since it requires the objective world to be singular in nature. 5

Only once a descriptive reference system has been identied may the knowledge historian test its score-objectivity experimentally.

The historian might well discover that a eld of research is in fact associated with the use of divergent description reference systems. Their task would then be to connect these dierent elds of reality by attempting to dene the problem of the correspondence between the impossibilities identied in the eld R a and the impossibilities identied in the eld R b which assumes such identication is possible. Given a certain descriptive reference system of cardinality c, the historian may evaluate its explorability and perhaps note that certain description reference systems are inexplorable. Concerning explorable reference systems, they could perhaps try to retrieve data collected during the course of empirical studies, constitute an updated database, and seek nomothetic gaps in it. 6

Let us now move on to the second point of this discussion. If the reference system is explorable and assumed to be score-objective, it may be that each of its possible states has been observed at least once. In this case, the descriptive reference system is sterile from the nomothetic point of view and this constitutes a singular observation fact: everything is possible therein. In other words, given an object in a certain initial state, nothing can be asserted regarding its Y-state. This does not prevent the decision-making engineer from wagering on the object's Y-state based on the distribution of Y-states, conditioned by the initial conditions in which the object is found. These frequencies may be used to measure 'expectancies', but they do not form a basis on which to deduce the existence of a probability function for these states. Indeed, dening a random variable Y or Y|X requires the denition of a probability space on the basis of the possible states M (X) × M (Y). In order to be probabilistic, such a space requires a probability space established on the basis of Ω (e.g., [START_REF] Renyi | Calcul des probabilités[END_REF]. Since Ω is a virtual set, adding objective probabilities to it is wishful thinking: seeing (X, Y) as a pair of random variables constitutes an unfalsiable interpretation.

Since such an interpretation is nonetheless of interest for making decisions, the existence of a related law of probability being postulated, the probability of a given state may be estimated on the basis of its frequency. The higher the total number of observations, the more accurate this estimation will be, which is why a database established by bringing together the existing databases is of interest. With the advent of the internet, recourse to probabilistic mythology no longer requires the inferential machinery of null-hypotheses testers to be deployed; it rather requires the empirical stabilisation of the parameters of the mythical law.

We conclude this critical analysis with a reminder that scientic research in Psychology is also aimed at the discovery of empirical laws. This requires two types of objectives to be distinguished with care: practical objectives, which focus on decision amid uncertainty, and nomothetic objectives, which focus on the detection of empirical impossibilities. Has so-called scientic Psychology been able to discover any empirical laws, and if so, what are they? From our contemporary standpoint, this question is easy to answer in principle if not in practice.

It may be noted that an observation p such that X(p) = (nf, f2) is not plausible; this relates to the question of the denition of the state of cessation and does not aect the structure of the logic.

[START_REF] Meehl | Theory-testing in psychology and physics: A methodological paradox[END_REF] noted several decades ago that the greater the `experimental precision', i.e. sample size, the easier it is to corroborate the alternative hypothesis.

We cannot simply classify the sources of score-subjectivity as measurement errors in the quantitative domain[START_REF] Stigler | The history of statistics: The measurement of uncertainty before 1900[END_REF], since most descriptive reference systems in Psychology are qualitative; diverging viewpoints for the same event described in a certain descriptive reference system represent an error, not of measurement, but of denition.

This type of database, established by merging several databases, has nothing to do with the aggregation methodology of `meta-analyses' based on the use of statistical summaries (e.g.,[START_REF] Rosenthal | Meta-analysis: Recent developments in quantitative methods for literature reviews[END_REF].