Marie Herr
email: marie.herr@spr.aphp.fr

Jean-Jacques Arvieu

Joël Ankri

Jean-Marie Robine

Running head: Life expectancy in frailty WHAT IS THE DURATION OF LIFE EXPECTANCY IN THE STATE OF FRAILTY? ESTIMATES IN THE SIPAF STUDY

Keywords: pre-frailty, frailty, disability, health expectancy, Sullivan's method

The screening of frailty can trigger interventions aiming to delay disability in older people.

Whereas the prevalence, the consequences and the factors associated with frailty are well described, little is known about the duration of the state of frailty. This study aimed to estimate the time spent in the state of frailty in men and women using the Sullivan method.

Data used were the age and sex-specific prevalence of frailty found in SIPAF study ("Système d'Information sur la Perte d'Autonomie Fonctionnelle de la personne âgée") and statistics of mortality from the Human Mortality Database. The SIPAF study included 2,350 individuals aged 70 and over and living in France. Participants were interviewed at home by trained nurses. Frailty was defined as impairment in three domains or more among nutrition, energy, physical activity, strength, and mobility. People requiring assistance in basic activities of daily living were considered in a separate category. Mean age of the study sample was 83.3+/-7.5 years, with 59.4% of women. Overall, the prevalence of pre-frailty, frailty and dependency was 39.1%, 17.0% and 15.4% respectively. Life expectancy at age 70 was 18.3 years for women of which 7.4 years (95%CI: 6.9-7.9) were pre-frail, 3.4 years (95%CI: 3.0-3.8) frail and 2.4 (95%CI: 2.1-2.7) with disability. In contrast LE for men at 70 was 14.8 years, of which pre-frail, frail and disabled years were 6.0 years (95%CI: 5.5-6.5), 1.2 years (95%CI: 1.0-1.5), and 1.2 (95%CI: 1.0-1.5) respectively. In conclusion, frailty is a transition state that is relatively limited in time compared to pre-frailty that may represent a larger time window for prevention.

Introduction

Frailty is defined as an ageing-related state, resulting from a decrease in physiological reserves of multiple systems, which increases vulnerability to stressors [START_REF] Clegg | Frailty in elderly people[END_REF].

Based on this theoretical basis, multiple operational definitions of frailty have emerged, the most famous being the frailty phenotype [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF]) and the Frailty Index (FI) [START_REF] Rockwood | A global clinical measure of fitness and frailty in elderly people[END_REF]. The former is based on a set of five criteria exploring physical strength, physical activity, nutrition, mobility and energy, while the latter is a count of up to 70 deficits including the presence and severity of current diseases, ability in activities of daily living and physical signs from clinical and neurologic exams [START_REF] Cesari | The frailty phenotype and the frailty index: different instruments for different purposes Age[END_REF]. Whatever the definition of frailty, it is a predictor of adverse health outcomes, such as falls, institutionalisation, and mortality [START_REF] Shamliyan | Association of frailty with survival: a systematic literature review[END_REF]).

As such, frailty has become a major issue in the prevention of functional decline and disability in aged populations [START_REF] Bergman | Frailty: an emerging research and clinical paradigm--issues and controversies[END_REF]. The range of possible interventions is large and includes improvements in the management of chronic conditions, increased physical activity, and nutritional skills [START_REF] Morley | Frailty consensus: a call to action[END_REF]. The great majority of the experts now agree on the relevance of detecting frailty as early as possible in order to implement corrective and/or preventive actions to delay disability in the frail old population [START_REF] Rodriguez-Manas | Searching for an operational definition of frailty: a Delphi method based consensus statement: the frailty operative definition-consensus conference project[END_REF].

In this context, times issues are essential. How large is the window for action, i.e. the period of time during which frailty can be detected and corrective/preventive actions implemented? The few longitudinal studies with repeated measures of frailty over time do not answer this question, either because they describe the gradual evolution of old people over time with FI derived from repeated geriatric evaluations [START_REF] Marshall | Cohort differences in the levels and trajectories of frailty among older people in England[END_REF][START_REF] Mitnitski | Improvement and decline in health status from late middle age: modeling age-related changes in deficit accumulation[END_REF]; Yang and Lee 2010), or because time intervals between phenotypic frailty measures are too long, at best 18 months [START_REF] Dapp | Long-term prediction of changes in health status, frailty, nursing care and mortality in community-dwelling senior citizens-results from the Longitudinal Urban Cohort Ageing Study (LUCAS)[END_REF][START_REF] Gill | Transitions between frailty states among community-living older persons[END_REF][START_REF] Lee | Transitions in frailty states among community-living older adults and their associated factors[END_REF][START_REF] Shardell | Serum 25-hydroxyvitamin D, transitions between frailty states, and mortality in older adults: the Invecchiare in Chianti Study[END_REF]Xue et al. 2008).

In the absence of longitudinal data about frailty with very close intervals between measures that would allow the estimation of the duration of frailty, Romero-Ortuno et al suggested to calculate life expectancy in the state of frailty by using the Sullivan method [START_REF] Romero-Ortuno | Cross-national disparities in sex differences in life expectancy with and without frailty Age[END_REF]. Health expectancy is the number of remaining years, at a particular age, which an individual can expect to live in a healthy or unhealthy state [START_REF] Robine | The joint action on healthy life years (JA: EHLEIS) Archives of public health[END_REF]. Although longitudinal information is theoretically required to estimate the incidence of health states and thus calculate health expectancies, the Sullivan method is of particular practical interest as it is usable in cross-sectional designs. Data required are the sexand age-specific prevalence of each health state in the population and mortality information [START_REF] Jagger | Health Expectancy Calculation by the Sullivan Method: A Practical Guide[END_REF]). The Sullivan method has been used to analyse health priorities and notably to estimate disability-free life expectancy [START_REF] Manton | Frailty and Forecasts of Actice Life Expectancy in the United States[END_REF]. Of note, the Sullivan method does not require assumption of a linear progression from frailty to functional disability.

Applying the Sullivan method to the data from the Study on Health, Retirement, and Ageing (SHARE), life expectancy in frailty at age 70 years was estimated to be 1.8 years on average for women and 0.7 year for men [START_REF] Romero-Ortuno | Cross-national disparities in sex differences in life expectancy with and without frailty Age[END_REF]). To our knowledge, this first calculation of life expectancy in the state of frailty has not been replicated in other settings.

Using the Sullivan method, this study aimed to calculate the time spent in each frailty state (robust, pre-frail, frail, and dependent) in men and women included in the SIPAF study, an observational study including a large proportion of very old people in France.

Methods

Study design and sample

This work is part of a cross-sectional study carried out to characterize health and functional independence among people aged 70 and older (SIPAF study, French acronym for "Système d'Information sur la Perte d'Autonomie Fonctionnelle de la personne âgée").

Subjects were selected at random among participants in a supplementary pension fund, AG2R La Mondiale (Paris, France). The French pension system is composed of three levels: the basic pension, supplementary pension, and private pension. The system is based on solidarity between generations; active employees contribute to pay the pensions of their elders. In return, they are eligible for an old age pension. The supplementary pension is the second level of the pension system. Like the basic pension, it is mandatory and operates on the principle of "pay-as-you-go" [START_REF] Herr | Contribution of socioeconomic position over life to frailty differences in old age: comparison of lifre-course models in a French sample of 2,350 old people[END_REF].

The selection of a random sample to be surveyed was centralized and performed by the actuary of AG2R La Mondiale. Using information about the geographic area of residence, the sampling method was designed to ensure the inclusion of participants from all regions of France excluding overseas territories, in rural as well as in urban areas. The sample selection was stratified by age group in order to include a larger proportion of oldest old aged 90 years and over than expected with a simple random drawing. Recruitment took place across France from 2008 to 2010, in 21 survey areas that were representative of all regions and sizes of cities in mainland France. Participants were interviewed at home by trained nurses. In 16.6% of the cases, a close relative was present to confirm or complete the answers of the participants. Information about non-participants included age, gender, and department of residence. Tertiles of departmental statistics were used in the analysis of participation: density of population, proportion of people aged 65 years and over, and median income in the population (www.insee.fr). The research protocol was approved by an independent ethics committee (permission n°060316).

Data collection

The interviews followed a standard procedure, starting with a questionnaire and ending by physical measurements.

Information was collected about self-rating of health, and chronic diseases. Chronic diseases were identified by reported diagnosis or treatment of 14 diseases, including asthma, allergies, diabetes, cataract, high blood pressure, heart attack, stroke/cerebral haemorrhage, chronic bronchitis/emphysema, rheumatoid arthritis/osteoarthritis, osteoporosis, gastric or duodenal ulcer, malignant tumour, migraines/frequent headaches, and chronic anxiety/depression. The number of drugs prescribed was determined from the prescriptions that the participants had at home. Polypharmacy was defined as 5 medications or more and excessive polypharmacy as 10 medications or more.

The geriatric assessment included measured height and weight and a question about unintentional weight loss (of 10% of body weight during the past 6 months), difficulty to walk up and down stairs, and difficulty to lift a bag weighing 5 kg. Cognitive impairment was defined as a Mini-Mental State Examination score of 26 or less [START_REF] Folstein | Mini-mental state". A practical method for grading the cognitive state of patients for the clinician[END_REF]). The evaluation of activity limitations examined five activities of daily living (ADL) included in the Katz index [START_REF] Katz | Studies of Illness in the Aged. The Index of Adl: A Standardized Measure of Biological and Psychosocial Function[END_REF], i.e. bathing, dressing, toileting, transferring, continence and feeding, as well as instrumental activities of daily living (IADL) such as food preparation, the ability to use a telephone, housekeeping, shopping and the ability to manage one's finances [START_REF] Lawton | Assessment of older people: self-maintaining and instrumental activities of daily living[END_REF]. Dependency was defined as the need of assistance with at least one ADL. Emotional status was assessed with the 15-item Geriatric Depression Scale (GDS-15) (Yesavage et al. 1982).

The level of physical activity was assessed with the International Physical Activity Questionnaire (IPAQ) and three levels of activity were distinguished (low, moderate and high) according to time spent walking and doing moderate (for instance, carrying light loads, leisure bicycle ride, tennis) and vigorous activity (for instance, carrying heavy loads, digging, lifting a pack of 6 bottles or speed bicycle) during the past 7 days [START_REF] Hurtig-Wennlof | The International Physical Activity Questionnaire modified for the elderly: aspects of validity and feasibility[END_REF]. The GDS-15 provided information about the renunciation of activities participants used to do ("Have you dropped many of your activities and interests"). Variables dealing with social support dealt with emotional features (lack of support when needing to talk, when needing an advice or when needing affection) and practical features (lack of support when bedridden, when needing to be accompanied to a medical appointment or when needing help to prepare meals). People were also invited to report elements of their environment that limit their activity (open question).

In addition to health variables, socio-demographic information was collected: age, gender, marital status, and level of occupation during midlife. Three levels of occupation were defined: low (blue-collar workers), intermediate (intermediate white-collar workers, employees, shopkeepers), and high (high-level white-collar workers). When possible, we assigned to housewives and people who had never worked the level of occupation of the spouse (4.2% of the study sample).

Frailty definition

Frailty was defined according to the construct derived from the Cardiovascular Health Study (CHS) [START_REF] Fried | Frailty in older adults: evidence for a phenotype[END_REF], in order to differentiate people in different categories of phenotypic frailty. Due to variations in health assessment between the SIPAF study and the CHS, some components of our operational measurement of frailty differ from the original definition. In particular, measures of grip strength and slow walking speed were replaced by self-reported variables, as previously done in other epidemiological settings [START_REF] Castrejon-Perez | Oral health conditions and frailty in Mexican community-dwelling elderly: a cross sectional analysis[END_REF]Theou et al. 2013). The five frailty components were defined as follows:

-Nutrition: unintentional weight loss or body mass index £18.5 kg/m 2 ; -Energy: positive answer to the question "Do you feel weak now?" or negative answer to the question "Do you have a lot of energy?"; -Physical activity: low level of activity according to the IPAQ questionnaire; -Physical strength: difficulty lifting a bag weighing 5 kg; -Mobility: difficulty walking up and down stairs.

Frail persons were identified as having 3 or more of the 5 components. Persons having one or 2 of the 5 components were considered pre-frail. Because frailty is a precursor and etiologic factor in disability [START_REF] Bergman | Frailty: an emerging research and clinical paradigm--issues and controversies[END_REF][START_REF] Cesari | The frailty phenotype and the frailty index: different instruments for different purposes Age[END_REF], persons requiring assistance with at least one ADL were considered in an additional category. In cases where people met both the criteria for frailty and dependency, precedence was given to dependency.

Statistical analysis

Life expectancy in each state of frailty was calculated using the Sullivan's method.

Information about the prevalence of frailty came from the interviews that were conducted between 2008 and 2010 in the SIPAF study whereas information about mortality in France in 2009 was taken from the Human Mortality Database (Human Mortality Database). Health expectancies were calculated using an abridged life table (five-year intervals, from 70-74 years to 95 years and over) and standard errors of health expectancies were calculated according to the guidelines available on the Eurohex website [START_REF] Jagger | Health Expectancy Calculation by the Sullivan Method: A Practical Guide[END_REF]). The variance of mortality rates was ignored as it is classically negligible compared to the variance of the prevalence rates.

Analyses were performed using Stata® software (version 13.0) and Microsoft Excel®.

Results

Participation and characteristics of the study sample

A total of 2,350 people agreed to participate in the study (participation rate: 18.9%).

The main reasons for non-participation were the lack of interest in the study (28.3% of the non-participants), followed by a self-reported state of frailty (10.8%) and the refusal of a close relative (7.3%). At the departmental level, participation was better in low-populated areas and in departments where the population was ageing or had a lower standard of living. At the individual level, participation was higher among males and younger persons. The socioeconomic profile of the participants was comparable to national statistics, with about 12% of executives and higher intellectual professions within the national workforce in 1999 as in the SIPAF study (www.insee.fr).

The study sample consisted of 1,395 women (59.4%) and 955 men (40.6%), of mean age 83.3 +/-7.5 years. Among the 2,286 participants with data on all five dimensions of frailty (i.e. no missing) or with sufficient information to classify them in the frail category (i.e. those having deficits in at least 3 criteria for frailty), 654 (28.9%) were robust, 893 (39.1%) were pre-frail, 388 (17.0%) were frail, and the remaining 351 (15.4%) were considered dependent because they needed help with at least one ADL. Notice that 84.0% of dependent people also met the criteria for frailty, in line with our hypothesis that frailty often precedes disability.

Table 1 describes the characteristics of the subjects according to their frailty state.

More than three quarters of the frail individuals reported a lack of energy, difficulty lifting a bag weighing 5 kg or a low level of physical activity. Lack of energy and low level of physical activity already affected 58.9% and 36.5% of the pre-frail individuals respectively.

As expected, there was a gradient between poor health and increasing frailty in different domains: self-perceived health, cognition, mood, functional abilities, chronic diseases, and polypharmacy. Social support also diminished with increasing frailty. When asked about elements of their environment that limit their activity, participants often mentioned inappropriate bath facility and stairs.

Time spent in each frailty state

Table 2 displays health expectancies by five-year age intervals with 95%CI. On average, life expectancy at age 70 was 18.3 years for women and 14.8 years for men, including 87% of life expectancy without dependency for women and 92% for men. The expected duration of frailty was 3.4 years (95%CI: 3.0-3.8) for women and 1.2 years (95%CI:

1.0-1.5) for men. Life expectancy in pre-frailty was 7.4 years (95%CI: 6.9-7.9) for women and 6.0 years (95%CI: 5.5-6.5) for men. Women were likely to spend 2.2 years more frail and 1.4 years more pre-frail than men. Pre-frailty lasted longer than frailty in men of every age and in women before age 90 years (up to five times the duration of frailty in men aged 70 to 74 years). Although men had shorter life expectancy than women, they were expected to live longer in a robust state compared to women.

The relative importance of each state over time is presented graphically in Figure 1. Of note, this figure illustrates how years spent dependent and frail concentrate at the end of life, whereas periods of pre-frailty and robustness are larger in younger ages, for both women and men.

Discussion

Using the Sullivan's method, this study combined cross-sectional health data with period life tables to estimate age-and sex-specific life expectancy in each state of frailty. At age 70 years, women were expected to live 3.4 years in frailty (95%CI: 3.0-3.8) and men 1.2 year (95%CI: 1.0-1.5). Before that, they were expected to stay pre-frail much longer, 7.4 years (95%CI: 6.9-7.9) for women and 6.0 years (95%CI: 5.5-6.5) for men.

Applying the Sullivan method to the data from the SHARE study, Romero-Ortuno et al estimated life expectancy in frailty at age 70 years to 1.8 year for women and 0.7 year for men on average (Romero-Ortuno et al. 2014). Although higher, our estimates still stand within the range of values found across the different European countries included in the SHARE study, i.e. 0.4 to 5.5 years for women and 0.1 to 1.8 years in men. Furthermore, the ratio of the duration of frailty between women and men was comparable between the two studies: 2.6 in SHARE and 2.8 in SIPAF. In accordance with Romero-Ortuno et al, we distinguished disabled people from frail people. However, we defined disability as the need of help in at least one ADL whereas Romero-Ortuno et al identified disabled people as those reporting severe activity limitation. Our definition of disability may be more objective but also more stringent, explaining why we found lower life expectancies in disability compared to the SHARE study (2.4 versus 5.7 years for women and 1.2 versus 3.6 years for men at age 70). Furthermore, our results concerning life expectancy without dependency were consistent with those from previous studies in France, which reported that life expectancy at age 65 without severe disability represented 86% to 91% of total life expectancy for men and 80% to 86% for women [START_REF] Cambois | Trends in disability-free life expectancy at age 65 in France: consistent and diverging patterns according to the underlying disability measure[END_REF]).

Our estimate of the time spent in the pre-frailty state was about 40% of total life expectancy for both women and men, which is largely higher than previous estimates from the SHARE study where life expectancy in the pre-frail state represented 22% of total life expectancy at age 70 years for women and 13% for men. The Sullivan method is sensitive to the definition of health states and our results should be interpreted with regards to the definition of frailty we used. Differences in the assessment of frailty may explain why we had a higher estimate of the years spent in pre-frail state in our study sample, at the cost of the estimated years lived robust. in our study sample. The SIPAF study assessed the same five dimensions as the SHARE study but involved trained nurses and used different tools to estimate the prevalence of each criterion. Notably, the wording of the questions we used to asses exhaustion may explain why this criterion was highly prevalent (almost half of the study sample). Furthermore, the use of self-reported difficulties climbing stairs or carrying a heavy bag instead of performance measurement may overestimate the prevalence of deficits in the strength and mobility criteria in the SIPAF study.

We confirm the sex differences in health expectancy observed in the SHARE study.

Frailty is known to be more prevalent in women than men; in the meta-analysis by Shamliyan et al [START_REF] Shamliyan | Association of frailty with survival: a systematic literature review[END_REF], the pooled prevalence of the frailty phenotype was 13% in women and 7% in men. The fact that women live longer whereas they bear a larger burden of health deficits than men is designated as the "male-female health-survival paradox" [START_REF] Oksuzyan | Gender gap in health expectancy[END_REF], Explanatory factors involve social, behavioural, and biological factors, whose influence may vary throughout life [START_REF] Alvarado | Life course social and health conditions linked to frailty in Latin American older men and women[END_REF].

From a public health perspective, frailty is a useful outcome to target comprehensive assessment and geriatric interventions. Our results highlight the potential interest of pre-frailty in terms of prevention. First, the pre-frailty state offers a larger time window for action compared to the frailty state. Second, our results indicate that a number of pre-frail subjects are already characterised by polypharmacy, lack of energy or depressed mood. Furthermore, a significant proportion of both robust and pre-frail subjects reported lack of social support and renunciation of some activities. Furthermore, previous studies stressed that prevention may be more effective at the early stages of frailty [START_REF] Gill | A program to prevent functional decline in physically frail, elderly persons who live at home[END_REF][START_REF] Puts | Static and dynamic measures of frailty predicted decline in performance-based and self-reported physical functioning[END_REF].

Main strengths of this study are its large assessment of geriatric health problems performed by trained nurses and the recruitment of a large number of people aged 90 years and over (n=512). In addition, participants were randomly selected among the 2,100,000 recipients of a supplementary pension fund with a sampling method designed to ensure the representativeness of the study sample with regard to regions of France. Nevertheless, we cannot exclude a participation bias due to the low participation, where participants were more likely to be healthy than persons who refused to participate in the study. Our comparative approach to the results of the SHARE study was limited by the fact that we did not use the algorithm developed to determine the frailty phenotype in men and women in the SHARE study [START_REF] Romero-Ortuno | A frailty instrument for primary care: findings from the Survey of Health, Ageing and Retirement in Europe (SHARE)[END_REF]). This algorithm uses coefficients which give different weights to the five dimensions of frailty. Because they were determined using close but different questions and in a younger population (mean age 64 years, i.e. approximately 20 years lower compared to the SIPAF study), the use of these coefficients was inappropriate in the SIPAF study. The Sullivan method is recommended for its relative accuracy compared to longitudinal measures. If the transition rates between health states are stable or gradually change over time, the Sullivan method provides fair estimates of the life expectancy in the various health states [START_REF] Mathers | How good is Sullivan's method for monitoring changes in population health expectancies?[END_REF]. Errors could have affected the results if the transition rates between the frailty states had suddenly changed before the SIPAF survey (in the sense of an overestimation if the rates had increased and in the sense of underestimation if the rates had decreased). However, nothing in the literature suggests, in France as well as globally, a sudden change in the transition rates between the frailty states. A limitation of the Sullivan method is that it does not describe transitions between states and hence,does not allow the identification of risk factors for functional decline.

In conclusion, this work provides elements to answer a fundamental question in ageing research, which is whether the extension of life expectancy is made up of healthy life expectancy or not. Although women have a longer life expectancy, they also spend more time in a frail state compared to men. Our results also show that the state of pre-frailty last longer than the state of frailty itself, thereby providing an important opportunity to identify those at risk of subsequent frailty and disability for targeted preventative interventions.

  Theou O, Brothers TD,Mitnitski A, Rockwood K (2013) Operationalization of frailty using eight commonly used scales and comparison of their ability to predict all-cause mortality J Am Geriatr Soc 61:1537-1551 doi:10.1111/jgs.12420 Xue QL, Bandeen-Roche K, Varadhan R, Zhou J, Fried LP (2008) Initial manifestations of frailty criteria and the development of frailty phenotype in the Women's Health and Aging Study II J Gerontol A Biol Sci Med Sci 63:984-990 Yang Y, Lee LC (2010) Dynamics and heterogeneity in the process of human frailty and aging: evidence from the U.S. older adult population The journals of gerontology Series B, Psychological sciences and social sciences 65B:246-255 doi:10.1093/geronb/gbp102 Yesavage JA, Brink TL, Rose TL, Lum O, Huang V, Adey M, Leirer VO (1982) Development and validation of a geriatric depression screening scale: a preliminary report Journal of psychiatric research 17:37-49

Table 1 . Characteristics of the subjects included in the SIPAF study according to their frailty state

 1

	Tables
	Variables	Robust	Pre-frail	Frail	Dependent
		N=654	N=893	N=388	N=351
	Socio-demographic information
	Women (%)	298 (45.6)	514 (57.6)	293 (75.5)	250 (71.2)
	Age (mean +/-SD)	79.5 +/-6.4 82.5 +/-6.9 86.3 +/-7.0	88.5 +/-6.8
	Married or living as a couple (%)	359 (55.0)	401 (45.0)	107 (27.7)	106 (30.2)
	Level of former job (%)
	High	106 (16.2)	116 (13.0)	33 (8.5)	22 (6.3)
	Intermediate	319 (48.4)	423 (47.5)	187 (48.2)	155 (44.3)
	Low	229 (35.0)	351 (39.4)	168 (43.3)	173 (49.4)
	Frailty variables
	Unintentional weight loss or low BMI	0	72 (8.1)	84 (21.7)	53 (15.5)
	(%)
	Lack of energy (%)	0	526 (58.9)	321 (82.7)	270 (79.0)
	Low-level of physical activity (%)	0	326 (36.5)	301 (78.8)	289 (83.3)
	Difficulty lifting a bag weighing 5 kg	0	202 (22.6)	324 (83.9)	284 (82.8)
	(%)
	Difficulty walking up and down stairs	0	128 (14.3)	286 (74.5)	264 (76.3)
	(%)
	Other health and social variables
	Self-rating of health (%)
	Good	473 (72.4)	402 (45.2)	97 (25.0)	88 (25.2)
	Fair	171 (26.2)	407 (45.8)	208 (53.6)	160 (45.9)
	Poor	9 (1.4)	80 (9.0)	83 (21.4)	101 (28.4)
	Need of help in IADL	42 (6.4)	209 (23.4)	255 (65.7)	337 (96.3)
	Cognitive impairment (MMSE score of	49 (7.6)	103 (11.7)	71 (18.8)	96 (30.2)
	26 or less) (%)
	Depression (Geriatric Depression Scale
	15 items) (%)
	No (<5)	643 (98.3)	732 (82.0)	248 (63.9)	203 (59.0)
	Probable (5-9)	11 (1.7)	151 (16.9)	121 (31.2)	128 (37.2)
	Severe (10 or greater)	0	10 (1.1)	19 (4.9)	13 (3.8)
	Number of comorbidities (%)

Notes: BMI: Body Mass Index; IADL: Instrumental Activities of Daily Living; MMSE: Mini-Mental State Evaluation

Table 2 . Life expectancy by frailty state in women and men by 5-year age group in the SIPAF study

 2

	Gender	Age at start	N	Total life	Robust		Pre-frail		Frail		Dependent
		of the interval		expectancy
					Life expectancy	% of total	Life expectancy	% of total	Life expectancy	% of total	Life expectancy	% of total
					in years with	life	in years with	life	in years with	life	in years with	life
					95%CI	expectancy	95%CI	expectancy	95%CI	expectancy	95%CI	expectancy
	Women	70	197	18.34	5.12 [4.63-5.60]	27.9	7.41 [6.89-7.94]	40.4	3.40 [3.02-3.79]	18.5	2.41 [2.11-2.71]	13.1
		75	261	14.27	3.24 [2.87-3.61]	22.7	5.59 [5.16-6.02]	39.2	3.02 [2.68-3.36]	21.2	2.42 [2.12-2.71]	17.0
		80	299	10.53	1.64 [1.37-1.91]	15.6	4.00 [3.65-4.35]	38.0	2.62 [2.32-2.93]	24.9	2.27 [1.99-2.54]	21.6
		85	288	7.35	0.74 [0.56-0.93]	10.1	2.53 [2.25-2.82]	34.4	2.00 [1.73-2.26]	27.2	2.08 [1.82-2.34]	28.3
		90	209	5.04	0.28 [0.15-0.40]	5.6	1.42 [1.17-1.67]	28.2	1.49 [1.24-1.74]	29.6	1.85 [1.59-2.12]	36.7
		95	141	3.34	0.15 [0.03-0.27]	4.5	0.60 [0.28-0.82]	18.0	1.12 [0.86-1.39]	33.5	1.47 [1.19-1.75]	44.0
	Men	70	178	14.76	6.35 [5.85-6.86]	43.0	5.97 [5.47-6.47]	40.4	1.21 [0.97-1.46]	8.2	1.23 [0.98-1.48]	8.3
		75	227	11.35	4.16 [3.75-4.57]	36.7	4.73 [4.32-5.15]	41.7	1.25 [1.00-1.50]	11.0	1.21 [0.96-1.45]	10.7
		80	221	8.33	2.69 [2.35-3.03]	32.3	3.50 [3.13-3.86]	42.0	1.06 [0.82-1.29]	12.7	1.08 [0.84-1.31]	13.0
		85	167	5.80	1.40 [1.11-1.69]	24.1	2.33 [2.00-2.66]	40.2	1.09 [0.83-1.35]	18.8	0.98 [0.74-1.22]	16.9
		90	111	4.00	0.81 [0.55-1.06]	20.3	1.62 [1.30-1.93]	40.5	0.57 [0.35-0.79]	14.3	1.00 [0.72-1.27]	25.0
		95	51	2.73	0.63 [0.30-0.95]	23.1	0.91 [0.55-1.28]	33.3	0.51 [0.21-0.82]	18.7	0.68 [0.35-1.02]	24.9

Life expectancy by frailty state in women and men by 5-year age group in the SIPAF study

This work was supported by AG2R La Mondiale (data collection) and Université Versailles St-Quentin-en-Yvelines (data analyses).


Aditi Chakrabarti

Amir Porat

Elie Raphaël

Thomas Salez

Manoj K Chaudhury

Elie Raphael

Elastowetting of Soft Hydrogel Spheres

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

INTRODUCTION

Contact mechanics is an important field that involves the study of how elastic solids deform when they are brought into contact with each other. While the Hertz model 1 forms the basis to characterize infinitesimal deformations of nonadhesive stiff spheres, Johnson-Kendall-Roberts' (JKR) theory [START_REF] Johnson | Surface Energy and the Contact of Elastic Solids[END_REF][START_REF] Johnson | Contact Mechanics[END_REF] describes situations in which adhesion becomes important, e.g., for soft objects such as elastomers [START_REF] Chaudhury | Direct measurement of interfacial interactions between semispherical lenses and flat sheets of poly (dimethylsiloxane) and their chemical derivatives[END_REF] and cells. [START_REF] Chu | Kendall Roberts theory applied to living cells[END_REF] However, there is yet another regime involving much softer materials, such as hydrogels, where surface tension also contributes to their mechanics, [START_REF] Mora | Capillarity Driven Instability of a Soft Solid[END_REF] thus implying that their contact behavior should fundamentally differ from that of stiffer materials. In this regime, we speculate that a soft elastic particle, when contacted with a rigid hydrophilic substrate, would undergo a large deformation with effects of both surface tension and elasticity. This so called elastowetting of soft hydrogel spheres on rigid substrates can be considered to be an elastic perturbation to the classical Young-Dupréwetting of drops of liquid. [START_REF] De Gennes | Wetting: Statics and Dynamics[END_REF] The contact mechanism of soft particles is expected to depend on hysteresis, phase separation, [START_REF] Jensen | Wetting and phase separation in soft adhesion[END_REF][START_REF] Liu | Osmocapillary phase separation[END_REF] and specific material properties. [START_REF] Rivetti | Elastocapillary levelling of thin viscous films on soft substrates[END_REF] By studying the wetting behavior of such soft materials, we expect to gain a better understanding of cell migration, [START_REF] Lo | Cell Movement Is Guided by the Rigidity of the Substrate[END_REF][START_REF] Joanny | Motion of an adhesive gel in a swelling gradient: a mechanism for cell locomotion[END_REF][START_REF] Schwarz | Physics of adherent cells[END_REF][START_REF] Fischer Friedrich | Quantification of surface tension and internal pressure generated by single mitotic cells[END_REF] nanoparticle adhesion, [START_REF] Champion | Role of target geometry in phagocytosis[END_REF] mechanical properties of nanomateri als, [START_REF] Cuenot | Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy[END_REF] and behavior of pressure sensitive adhesives, [START_REF] Newby | Macroscopic evidence of the effect of interfacial slippage on adhesion[END_REF] and it may have important implications in the design of new approaches for atomic level characterization. [START_REF] Luan | The breakdown of continuum models for mechanical contacts[END_REF][START_REF] Erath | Characterization of adhesion phenomena and contact of surfaces by soft colloidal probe AFM[END_REF] The specific geometry of a rigid sphere contacting a soft elastic substrate, in the presence of adhesion and solid-air surface tension, has been studied in detail recently, both experimentally and theoretically. [START_REF] Rimai | Adhesion induced deformations of polymeric substrates: Particle size dependence of the contact area[END_REF][START_REF] Rimai | Adhesion induced deformations of a highly compliant elastomeric substrate in contact with rigid particles[END_REF][START_REF] Rimai | The adhesion of dry particles in the nanometer to micrometer size range[END_REF][START_REF] Style | Surface tension and contact with soft elastic solids[END_REF][START_REF] Chakrabarti | Elastocapillary Interaction of Particles on the Surfaces of Ultrasoft Gels: A Novel Route To Study Self Assembly and Soft Lubrication[END_REF][START_REF] Hui | Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion[END_REF][START_REF] Butt | Forces between a stiff and a soft surface[END_REF][START_REF] Karpitschka | Surface tension regularizes the crack singularity of adhesion[END_REF][START_REF] Andreotti | Soft wetting and the Shuttleworth effect, at the crossroads between thermodynamics and mechanics[END_REF][START_REF] Ina | From Adhesion to Wetting: Contact Mechanics at the Surfaces of Super Soft Brush Like Elastomers[END_REF] These works assume geometrically small elastic deformations, which is only valid for a sufficiently low work of adhesion. Finite element simulations allowed to extend this framework to larger deformations through a neo Hookean approach. [START_REF] Xu | Effects of surface tension on the adhesive contact of a rigid sphere to a compliant substrate[END_REF] In contrast, the dual geometry of a very soft elastic sphere placed atop a flat rigid substrate has only been scarcely addressed, despite its obvious similarity with the natural configuration of liquid droplet wetting and cell adhesion. On the experimental side, the spreading of latex particles on rigid substrates was studied using atomic force microscopy (AFM). [START_REF] Lau | Spreading of latex particles on a substrate[END_REF] However, there are two limitations in this preliminary work. First, due to the very small particle size (∼0.1 μm), it was only possible to image them in plan view. Therefore, instead of directly measuring the vertical deformation, the contact radius of the particles was used to estimate itbased on an assumed spherical cap shape. Second, latex is a glassy material that can flow if the contact stresses exceed its yield point. On the theoretical side, there are currently only global scalings to describe the elastowetting of soft spheres, [START_REF] Carrillo | Adhesion of nanoparticles[END_REF][START_REF] Salez | From adhesion to wetting of a soft particle[END_REF] which again assume a spherical cap shape. What we expect in reality is a scenario where the adhesion driven wetting of the elastic sphere gives rise to a gradient of shear deformation, from the highest value closest to the contact region and decaying with the distance from the substrate. Finally, we note that the problem of spreading of a semicylindrical polymer gel placed on a flat rigid substrate was studied theoretically, [START_REF] Joanny | Gels at interfaces[END_REF] in which an equilibrium shape was envisioned with a foot due to a positive spreading parameter S. The foot length was further predicted to be independent of the cylinder radius and to scale only with the ratio of the spreading parameter and the shear modulus μ, as ∼ S/μ. We note that a similar footlike feature was also observed in the dual geometry of a rigid sphere in contact with a soft substrate. [START_REF] Jensen | Wetting and phase separation in soft adhesion[END_REF][START_REF] Jensen | Strain dependent solid surface stress and the stiffness of soft contacts[END_REF] In view of the above state of art, we chose cross linked polyacrylamide hydrogel as the material with which to study the elastowetting phenomenon. One could easily modulate the associated shear modulus by varying the monomer concen tration, while the gel-air surface tension γ G always remained close to that of water in air. [START_REF] Chakrabarti | Vibrations of sessile drops of soft hydrogels[END_REF] We explored the arrested wetting behavior of soft hydrogel spheres when placed upon smooth silanized silicon wafers of varying surface energies, as characterized through the work of adhesion W. In all cases, the elastocapillary length γ G /μ and the elastoadhesive length W/μ were in the submillimeter range, so that solid capillary and adhesion effects could be directly visualized through optical microscopy techniques. Moreover, the radii of the gel spheres were chosen to be smaller than their capillary length to avoid the effect of gravity. Our main objective was to measure the equilibrium contact angle θ* of the soft elastic spheres on the various substrates, as a function of the gel shear modulus μ, sphere radius R, and work of adhesion W, in order to quantify how they deviate from the pure wetting case. During our investigations, we found the presence of a localized contact foot of length in the arrested wetting configuration of these gel spheres. This is in essence the scenario envisioned by Joanny et al. [START_REF] Joanny | Gels at interfaces[END_REF] but with different geometry and material. To rationalize our experimental observations, we develop a minimal analysis involving energy minimization, volume conservation, and scaling arguments.

EXPERIMENTS

In order to synthesize spherical hydrogel beads of different shear moduli, [START_REF] Chakrabarti | Vibrations of sessile drops of soft hydrogels[END_REF] we first prepared pregel solutions by diluting varying concentrations (<10%) of the monomer N (hydroxymethyl) acrylamide (48% solution in water, Sigma Aldrich) in deionized water. Upon degassing the monomer solutions by purging them with bubbles of pure nitrogen gas, we dissolved potassium persulfate (99.99% trace metals basis, Sigma Aldrich; 0.25% weight basis) and N,N,N′,N′ tetramethylethylenediamine (TEMED, ≥99.5%, purified by redistillation, Sigma Aldrich; 0.3% weight basis) into the solution that would initiate the polymerization of the polyacrylamide hydrogel roughly 10 min after mixing the TEMED. The hydrogel spheres were prepared by suspending drops of the pregel solution in a beaker containing a vertical liquid density gradient created by introducing a heavy silicone oil (poly[dimethylsiloxane co methylphenylsiloxane], Sigma Aldrich, density ρ = 1.05 g/cm [START_REF] Johnson | Contact Mechanics[END_REF] ) at the bottom of the beaker and a lighter n octane (99% pure, Acros Organics, ρ = 0.71 g/cm [START_REF] Johnson | Contact Mechanics[END_REF] ) at the top gently using a pipet. The interface between these two oils was allowed to be well diffused by waiting for about 30 min to attain a uniform composition in the mixed zone. The ratio of the volumes of silicone oil to octane used in these experiments was around 2:1. Drops of pregel solution of different volumes were released gently into the octane layer. They sank to the diffused interface of octane/silicone oil until they were neutrally buoyant. Each pregel drop assumed a spherical shape at the interface, and care was taken to allow enough space in between each drop to avoid coalescence. Even though the two liquids used in creating the density gradient had slightly different surface tensions with water, the broad thickness of the diffused zone ensured uniform curvature of the spheres. The drops of pregel solution cured into spherical elastic beads in about 2 h at room temperature. As was reported earlier, [START_REF] Chakrabarti | Vibrations of sessile drops of soft hydrogels[END_REF] when these hydrogel spheres are placed atop a rigid substrate subjected to random vibration in the vertical direction, they exhibit surface harmonic modes which marginally differ from those of pure water drops. For liquids, surface modes are related to the surface tension and mass of the drops. For the surface modes of gels, the same scaling with surface tension and mass was observed, while the slight deviation of the values could be accounted for by the effect of elasticity. It was concluded that the surface tension of hydrogels with air is similar to that of water with air. The elastic shear modulus of these gels was measured (μ ranging from 61 to 789 Pa) using an oscillatory shear rheology technique that is described in more detail in the same previous study. [START_REF] Chakrabarti | Vibrations of sessile drops of soft hydrogels[END_REF] While preparing a batch of gel spheres of a particular monomer concentration, we cured a small amount of the same pregel solution into a rectangular slab of gel confined between two rigid plates, which was then set to horizontal vibration and the shear modulus was estimated from the slab's resonant mode.

For preparing the rigid substrates, silicon wafers were cut into small pieces of about 2 cm 2 each and were flame treated to remove all organic contaminants, rendering them hydrophilic. After cooling, they were placed in a chamber underneath a horizontal silane source, which rested upon spacers that were 13 mm tall. The silane source was prepared by attaching a flat sheet of filter paper to a glass slide with double sided tape and depositing few drops of dodecyltrichlorosilane (Gelest Inc.) uniformly on the filter paper, wiping off any excess with tissue paper. The wafers were treated by the diffusing silane vapor in the chamber, at room temperature of 20 °C and relative humidity of 35% for different times. An exposure time of about 2 min in our system led to surfaces with ∼60°contact angle for water, while an exposure time of about 12 min led to complete grafting of the surfaces, giving ∼106°contact angle for waterthe untreated surfaces being the most hydrophilic, where water spread as thin films. This resulted in the work of adhesion W, estimated from the Young-Dupréequation for the different hydrogel-substrate systems, ranging from ∼50 to ∼144 mN/m, corresponding to water contact angles of ∼106°to ∼0°, respectively (Figure 1a, top).

After curing, each hydrogel sphere was gently taken out from the liquid environment where they were prepared, using a plastic pipet with a smooth hydrophobic tip, and rinsed in pure n heptane (Fisher Chemicals) repeatedly followed by moderate drying in air. The inner walls of the glass containers, which were used to house the heptane for cleaning, were also hydrophobized with vapors of dodecyl trichlorosilane to prevent the gel spheres from sticking to the walls, thereby avoiding any possible damage to their surfaces. A treated silicon wafer was then placed on a weighing balance, and the cleaned gel sphere was deposited upon it. This was the most critical step in our protocole as the pipet tip holding the gel sphere had to be held just above the wafer while slowly releasing the sphere on the latter to allow for uniform radial spreading. From the measured weight on the balance, the initial radius R of the droplet was estimated (ranging from 1.2 to 3.8 mm) assuming a spherical shape. The gel drop on substrate system was immediately photographed with a CCD camera (Sony XC 75). Each experimental measurement was completed in a few minutes, within which there was no observable loss in volume of the gel due to evaporation. On removing gel drops from hydrophilic substrates after a few minutes, we observed very thin and annular patches of liquid concentrated at the edge of the former contact region. However, the thickness of these annular films was always much smaller than the height of the foot region, thus ensuring that the measured macroscopic deformation of the gel-air interface, which gave us the modified contact angle θ* and the foot length , was not due to the traces of exuded liquid. These experiments being very sensitive to the smoothness of the gel surface, utmost care was taken while handling the spheres by pipet aspiration such that only a very small fraction was inside its tip. Furthermore, each gel sphere was used for the corresponding measurement only once as its surface got slightly damaged upon removing it from contact.

In sharp contrast with classical wetting of liquid droplets, the hydrogel spheres spread to their equilibrium configurations on the hydrophilic substrates by protruding a localized axisymmetric foot at the edge of the contact region, while maintaining their undeformed spherical shape far away from contact (Figure 1a). Note that there was no such foot observed on the hydrophobic substrates. We estimated the length of the foot from the 2D side view in the following way (Figure 5a). A circle with the radius R of the undeformed sphere was fitted to the upper periphery of the deformed gel sphere. A horizontal line along the reflection plane at the rigid substrate was drawn by joining the left and right triple phase contact points (2D projection of the triple phase contact line). The distance between one of these two triple phase contact points and the nearest intersection of the fitted circle with the horizontal line defines the foot length , and we used the averaged value from both the left and right sides. To measure the contact angle, the entire deformed gel-air interface was fitted with a spline curve in ImageJ via the DropSnake [START_REF] Stalder | A snake based approach to accurate determination of both contact points and contact angles[END_REF] plugin. An automatic algorithm then determined the contact angle θ* at the triple phase contact points (Figure 2a), and we used the average value from both the left and right sides.

The contact angle θ* of the hydrogel droplets on the silanized wafers decreases with increasing work of adhesion W (Figures 1a and2b), as for pure water, with a general trend reminiscent of the Young-Duprélaw (Figure 2c). However, interestingly, θ* increases with the shear modulus μ of the gel (Figures 1b and2b, inset), while being mostly independent of the droplet radius R within our experimental range which was rather narrow by design in order to stay below the capillary length. Besides, as μ increases, the deformation and thus the foot length decrease (Figure 1b). The observation of a localized contact foot is the first verification of the prediction by Joanny et al. [START_REF] Joanny | Gels at interfaces[END_REF] Nevertheless, our systematic study with gels involving different elastic moduli and radii, as well as substrates with varying wetting properties, reveals an even richer scenario. The latter will become more obvious below, as we attempt to recast the main experimental features within a theoretical framework involving energy minimization, volume conservation, and scaling arguments.

DISCUSSION

The equilibrium profiles of hydrogel spheres placed on hydrophilic substrates suggest that elasticity, surface tension, and adhesion are intimately coupled and that there are two essential observables: the modified contact angle θ* and the foot length . In the following, we discuss those two quantities successively with minimal arguments. Specifically, for the contact angle, we consider an energy functional minimization and focus on the boundary term, while for the foot length, we avoid the detailed analysis of the resulting Euler-Lagrange equation and instead resort to simple scaling arguments.

Contact Angle. The system and notations are defined in Figure 3. Removing the constant bare substrate surface energy, and including volume conservation, we consider the following energy functional:

∫ ∫ ∫ ∫ γ γ π πγ λ π π πμ πμ = - + +′+ - + - - + - ′ -′ δ δ δ δ - - - - ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ E r z r z r r R z r z r r r r r z r r r r [ ( )] ( ) (0) 2 d 1 4 3 d 3 2 d ( ) 2 d ( )( ) R R R R SG SV 2 G 0 2 2 3 0 2 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 (1)
where the prime indicates the derivative with respect to z. The first term describes the energy of the gel-substrate interface, where γ SG and γ SV denote the substrate-gel and substratevapor interfacial tensions, respectively. The second term describes the energy of the gel-vapor interface. The third term ensures volume conservation through a Lagrange multiplier λ with the dimension of a stress. The last two terms are ad hoc approximations for the elongational and shear elastic contributions, respectively, that assume incompressibility and enforce the strain to be localized in the foot region.

Minimizing the energy functional with respect to the function r(z), one obtains a Euler-Lagrange equation as well as two boundary conditions: one at z = 2R -δ and one at z = 0. We only consider the latter, which reads

θ γ γ γ μ γ * = - - - ′ -′ r a r r r cos 2 (0) (0) [ (0) (0)] SV SG G G 2 2 0 (2)
with the notation a = r 0 (0) (Figure 5a), and where we introduced the contact angle θ* (Figure 5b) geometrically defined by θ* = -′ + ′ r r cos (0)/ 1 (0) 2 . In the absence of elasticity (μ = 0), this condition reduces to the Young-Dupreĺ aw:

θ γ γ γ = - cos SV SG G (3)
where θ* = θ is the classical contact angle of the liquid case. In contrast, when μ ≠ 0, θ* is impacted by elasticity and thus different from θ, and the boundary condition can be approximated by

θ θ μ γ θ α - *≃ *+ cos cos (cot cot ) G (4)
at first order in /a, with the foot length defined as = r(0)a (Figure 5a) and where we introduced the inner angle α of the foot region (Figure 5b). Figure 4 shows that the general trend of the experimental data is consistent with eq 4. The observed ∼1/10 prefactor might result from the fact that the experimental measurements provide only macroscopic angles instead of the actual microscopic ones, while the scattering of the data possibly indicates that a more realistic shear energy integral is needed. Nevertheless, an important outcome of the above analysis is that the contact angle θ* depends on elasticity only through the shear deformation of the gel, but not through its elongational deformation.

Foot Length. The superposition of the image of the gel in the undeformed spherical state and that resulting from the wetting induced deformation (Figure 5a) shows that the upper portion of the gel remains essentially undeformed, whereas the lower region undergoes a footlike deformation. Such an Figure 3. Schematics of the system. A gel sphere with initial radius R undergoes an axisymmetric deformation when placed on a rigid hydrophilic substrate (z = 0), and r(z) describes the radial distance of the gel-air interface in that deformed state as a function of z. As a reference, we introduce the radial distance r 0 (z) of the gel-air interface in the undeformed spherical shape (dashed circle). The entire contact radius (including the foot) is denoted by r(0) and the vertical indentation depth by δ.

observation deviates from classical contact mechanics of elastic objects, in which the elastic sphere essentially maintains a spherical cap shape (Figure 6b). [START_REF] Johnson | Surface Energy and the Contact of Elastic Solids[END_REF][START_REF] Johnson | Contact Mechanics[END_REF] The base radius a Maugis of the latter was analyzed by Maugis [START_REF] Maugis | Extension of the Johnson Kendall Roberts theory of the elastic contact of spheres to large contact radii[END_REF] within the framework of JKR theory [START_REF] Johnson | Surface Energy and the Contact of Elastic Solids[END_REF][START_REF] Johnson | Contact Mechanics[END_REF] and found to scale as a Maugis ∼ R[W/(μR)] m , with m being close to 1/4 at geometrically large deformations. [START_REF] Rimai | Adhesion induced deformations of polymeric substrates: Particle size dependence of the contact area[END_REF] Volume conservation due to the incompressibility of the elastic material also imposes that a Maugis is geometrically related to the inner contact radius a of the (shifted) undeformed sphere (Figure 6c), as

= - + - + - ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ( ) ( ) a R 8 1 1 3 1 1 a R a R Maugis 2 3 2 (5)
We now focus on the situation where 0 < a/R < 0.9, which corresponds to the range of our experiments and which already contains geometrically large deformations. In that situation, the error one makes by replacing the right hand side of eq 5 by a/R is inferior to 20%, which is acceptable given the wide range of parameters studied in the experiments. Therefore, combining the above ingredients, one gets the following reasonable approximation:

μ ≈ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ a R W R 1/4 (6)
While we do not expect the real contact radius r(0) of our experiments to be given by a Maugis , as already explained above, that approximation for the inner contact radius a is valid, as shown in Figure 5c, with the missing prefactor being close to unity.

As a consequence of the previous analysis, we are led to propose the following elastowetting scenario with a schematic decomposition in two steps: first, the sphere undergoes a Maugis like elastic deformation (Figure 6b) inducing a spherical cap shape characterized by its contact radius a Maugis and the inner contact radius a (or equivalently the indentation depth δ); second, from that intermediate reference stage, the local capillary action near the triple phase contact line extracts a foot, but at constant volume and inner contact radius (or equivalently indentation depth δ), leading to a reorganization of the shape near contact (Figure 6c). To further characterize the foot length , we balance the volume πδ 2 (3R -δ)/3 of the fictive spherical cap below the substrate (Figure 5b) and the volume ∼ πa h of the axisymmetric foot at lowest order in /a. Indeed, to a fair approximation, the cross section of the latter can be considered to be triangular, with base and height h, such that = h (cot θ* + cot α). Combining those ingredients, we obtain

δ δ θ α ≈ - *+ R a (3 )(cot cot ) 3 2 (7)
This relation agrees well with experiments, as shown in Figure 7, with the missing prefactor being close to unity.

As a final remark, while two central relations (eqs 4 and 7) have been obtained and checked, they in fact involve five constitutive variables: θ*, , α, a, and δ. Thus, three other independent relations are needed to relate each of these variables only to the physical parameters of the problem: the initial radius R of the sphere, the shear modulus μ of the gel, the work of adhesion W between the gel and the substrate in air, and the gel-air surface tension γ G . Those three other relations are eq 6 (Figure 5c), δ = - -R R a 2 2 (Figure 5a), and cot α = (R -δ)/a (Figure 5b), thus bringing closure to the problem.

CONCLUSION

We presented novel experimental results on how soft hydrogel spheres deform when in contact with rigid substrates of varying surface energies. On hydrophilic surfaces, these spheres protrude an axisymmetric foot in the contact region, while maintaining a global undeformed spherical shape. Furthermore, while the contact angle of these gel spheres decreases with increasing substrate's wettability, as expected, it is found to increase with the elastic modulus of the gel. We rationalized these observations with a minimal analysis based on energy minimization, volume conservation, and scaling arguments. In future work, nonlinearities ensuing from both materially and geometrically large deformations of the gel should be incorporated within the framework of the Euler-Lagrangian equation introduced here. Along with this possible theoretical refinement, more precise experiments, with e.g. confocal microscopic techniques, [START_REF] Style | Surface tension and contact with soft elastic solids[END_REF] would as well be of paramount importance.

Among possible applications, one could use the finite contact angle of soft gel spheres on hydrophilic substrates to estimate the surface energies of those substrates, when liquids usually spread as thin films debarring them as suitable candidates for that task. Additionally, our results on elasticity dependent contact angles of gels could be applied to characterize the viscoelastic foot that is observed in the peeling of pressure sensitive adhesives from a substrate. While the role of the shear stress in the contact angle and length of such viscoelastic foots was implied in previous studies, [START_REF] Newby | Macroscopic evidence of the effect of interfacial slippage on adhesion[END_REF][START_REF] Newby | Effect of interfacial slippage on viscoelastic adhesion[END_REF] it is our hope that the current work will bring more attention to such a matter. Last but not least, the associated dynamic processes, involving friction and the possible slippage of those viscoelastic foots, represent important extensions of the present problem.

Figure 1 .

 1 Figure 1. (a) Comparison between equilibrium profiles of water drops (top) and gel spheres (shear modulus μ = 61 Pa) (bottom) on silanized silicon wafers, for various works of adhesion W (decreasing from left to right). (b) Equilibrium profiles of gel spheres on cleaned untreated silicon wafers, for various shear moduli μ (increasing from left to right). (c) Equilibrium profiles of gel spheres (μ = 93 Pa) on silicon wafers where water contact angle is 60°, for various sphere radii R (increasing from left to right). Scale bars of 1 mm depict calibrations for each row.

Figure 2 .

 2 Figure 2. (a) Snapshot of the equilibrium profile of a gel sphere (μ = 61 Pa) on a rigid substrate (W = 144 mN/m). The highlighted region at the three phase contact line is magnified on the right to show the measured contact angle θ* that is obtained from a spline fitting of the entire gel-air interface. 37 (b) Contact angle θ* as a function of work of adhesion W between the gel and the silanized silicon wafer in ambient air, for different shear moduli μ of the gel as indicated. Inset: contact angle as a function of shear modulus μ of the gel, for a substrate characterized by the work of adhesion W = 144 mN/m. For comparison, on this substrate the contact angle of pure water is close to 0°. (c) Same data as depicted in (b), but plotted according to the Young-Duprélaw, where the contact angle θ* is used and where γ G ≈ 72 mN/m in ambient air. The classical liquid reference is represented by the y = x solid black line.

Figure 4 .

 4 Figure 4. Experimentally measured difference between the cosines of the contact angle (θ) of water and the contact angle (θ*) of hydrogel, plotted according to eq 4. The shear moduli are indicated in the legend.

Figure 5 .

 5 Figure 5. (a) Two equilibrium profiles of gel spheres on hydrophilic substrates: one (top: μ = 61 Pa, W = 0.144 N/m) with larger foot length and the other (bottom: μ = 93 Pa, W = 0.11 N/m) with smaller foot length. The undeformed spherical shapes (radius R) are depicted by the white dashed circles. The horizontal lines represent the reflection plane at the silicon wafer. The foot length is measured from the intersection of the dashed circle with the horizontal line to the triple contact line, while δ denotes the indentation depth (i.e., the depth of the dashed circle underneath the horizontal line), and a denotes the inner contact radius (i.e., half the length of the horizontal line that is inside the dashed circle). (b) 3D schematic highlighting the volume conservation (gray) during the deformation of the incompressible gel: the volume of the fictive spherical cap below the substrate, with depth δ and base radius a, is redistributed in the axisymmetric triangular like foot, with base , height h, outer contact angle θ* and inner angle α. (c) Experimentally measured inner contact radius a (a) as a function of a combination of the relevant physical parameters, according to eq 6. The shear moduli are indicated in the legend.

ACKNOWLEDGMENTS The authors thank Basile Audoly and Animangsu Ghatak for helpful discussions. A.P. was financially supported by LabEx ENS ICFP: ANR 10 LABX 0010/ANR 10 IDEX0001 02 PSL. T.S. acknowledges funding from the Global Station for Soft Matter, a project of Global Institution for Collaborative Research and Education at Hokkaido University, as well as Howard Stone for hosting him in his group during part of this project. M.K.C. thanks the Chair Total ESPCI Paris for financial support.

AUTHOR INFORMATION

Corresponding Author *E mail: mkc4@lehigh.edu (M.K.C.).

Notes

The authors declare no competing financial interest.


Marie Herr
email: marie.herr@uvsq.fr

Helene Grondin

Stéphane Sanchez

Didier Armaingaud

Caroline Blochet

Antoine Vial

Philippe Denormandie

Joël Ankri

Polypharmacy and potentially inappropriate medications: a cross-sectional analysis among 451 nursing homes in France Running head: Suboptimal prescribing in nursing homes

Keywords: aged, frail elderly, inappropriate prescribing, information system, nursing homes, polypharmacy

Purpose: The quality of drug therapy is an important issue for nursing homes. This study aimed to assess the prevalence of polypharmacy and potentially inappropriate medications (PIMs) in a large sample of nursing home residents by using the data recorded during the preparation of pill dispensers.

Methods: This is a cross-sectional study that included 451 nursing homes across France.

Information about the medications received by the 30,702 residents (73.8% women) living in theses nursing homes was extracted from the system that assists the preparation of pill dispensers in pharmacies. The anonymized database included age, sex, and medications prescribed to residents, as well as nursing home characteristics (capacity, legal status). Factors associated with excessive polypharmacy (≥10 different drugs) and PIMs according to the Laroche list were studied using multilevel regression models.

Results: The average number of drugs prescribed was 6.9 +/-3.3 and excessive polypharmacy concerned 21.1% of the residents (n=6,468). According to the Laroche list, 47.4% of residents (n=14,547) received at least one PIM. Benzodiazepines (excessive doses, long-acting benzodiazepines, and combination of benzodiazepines) and anticholinergic medications (hydroxizine, cyamemazine, alimemazine) accounted for a large part of PIMs. Individual characteristics (age, gender) influenced the risk of receiving PIMs whereas nursing home characteristics (capacity, legal status) influenced the risk of excessive polypharmacy.

Conclusions: This study shows that polypharmacy and PIMs remain highly prevalent among nursing home residents. Main PIMs concerned psychotropic and anticholinergic medications.

Introduction

As people live longer, they accumulate health problems and drug prescriptions. The addition of medications increases the risk of adverse drug effects and of drug-drug and drug-disease interactions [START_REF] Fialova | Medication errors in elderly people: contributing factors and future perspectives[END_REF][START_REF] Field | Risk factors for adverse drug events among older adults in the ambulatory setting[END_REF]. Polypharmacy was shown to be the main determinant of iatrogenic effects of medications [START_REF] O'mahony | Optimizing pharmacotherapy in older patients: a European perspective[END_REF][START_REF] Gurwitz | Incidence and preventability of adverse drug events among older persons in the ambulatory setting[END_REF]. In addition, age-associated changes in body composition (sarcopenia) and organ function (decrease in renal and metabolic clearance) can cause changes in the pharmacokinetic/pharmacodynamics properties of medications, and hence modify the safety profile of medications [START_REF] Shi | The clinical implications of ageing for rational drug therapy[END_REF].

In order to avoid adverse drug reactions in older people, the benefit-risk balance of each drug should be considered, as well as the risk of interactions. Lists of Potentially Inappropriate Medications (PIMs) were published to help adapt the drug regimen in older people, notably the Beers' criteria, which were first published in 1991 to assess medication appropriateness in nursing homes [START_REF] Beers | Inappropriate medication prescribing in skilled-nursing facilities[END_REF]. Reasons for inappropriateness include an unfavorable benefit-risk ratio, the absence of clear indication or efficacy [START_REF] Connor | Inappropriate prescribing: criteria, detection and prevention[END_REF]. This list had been updated several times [START_REF]American Geriatrics Society updated Beers Criteria for potentially inappropriate medication use in older adults[END_REF][START_REF] Counsell | 2015 updated AGS Beers Criteria offer guide for safer medication use among older adults[END_REF] and other lists have been developed, notably to have guidelines that take into account the national specificities in terms of commercialized drugs and practices. In France, Laroche et al published a French list of PIMs in 2007 [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF]. This list included 34 general criteria and 5 additional criteria where the PIM is related to an underlying condition.

Studies that compared drug regimen between institutionalized people and old people living in community have shown higher rates of polypharmacy and PIMs among institutionalized people [START_REF] Barnett | Prevalence and outcomes of use of potentially inappropriate medicines in older people: cohort study stratified by residence in nursing home or in the community[END_REF][START_REF] Halvorsen | Prescribing quality for older people in Norwegian nursing homes and home nursing services using multidose dispensed drugs[END_REF][START_REF] Haasum | Institutionalization as a risk factor for inappropriate drug use in the elderly: a Swedish nationwide register-based study[END_REF]. Inappropriate drug use was shown to increase the risk of adverse health outcomes (hospitalizations, emergency department visits, death) in nursing home residents [START_REF] Perri | Adverse outcomes associated with inappropriate drug use in nursing homes[END_REF][START_REF] Ruggiero | Potentially inappropriate drug prescriptions and risk of hospitalization among older, Italian, nursing home residents: the ULISSE project[END_REF][START_REF] Lau | Hospitalization and death associated with potentially inappropriate medication prescriptions among elderly nursing home residents[END_REF]. The quality of drug therapy is an important issue for nursing homes and the use of psychotropic medications and polypharmacy have been proposed as indicators of quality of care in nursing homes [START_REF] Frijters | The calculation of quality indicators for long term care facilities in 8 countries (SHELTER project)[END_REF][START_REF] Zimmerman | Improving nursing home quality of care through outcomes data: the MDS quality indicators[END_REF]. Indicators of the quality of drug therapy should be monitored regularly to identify areas for improvement and evaluate the efficacy of interventions. Data about drug therapy in nursing homes can be retrieved from medical records but also from insurance claims and pill dispenser systems. These last options should develop with the increasing willingness of stakeholders involved in health and quality of care to share their data for quality purposes.

In this context, this study aimed to describe the drugs' prescriptions of old people living in nursing homes in terms of polypharmacy and PIMs, by using the data collected during the preparation of pill dispensers.

Material and methods

Study design and population

This is a cross-sectional study that analyzed the drugs prescribed to the 30,702 persons living in the 451 nursing homes that used a pill dispenser supplied by the company Medissimo (Poissy, France) at the time of the analysis. The pill dispenser contains 28 days of treatment, with as many compartments as drugs and time of administration. It is prepared by qualified staff in pharmacy. During the preparation, information about the individuals and their prescriptions is entered in specific software to ensure traceability. Although the pharmaceutical forms that cannot be placed in the pill dispenser (sachets, creams, drops, etc.) are given in their original packaging, information about these drugs are still recorded in the information system. Data from March 25 th to March 31 st 2014 were extracted from the information system and communicated anonymously to the UMR 1168 for analysis.

Medissimo received the approval of the National Commission for Data Protection and Liberties (CNIL, authorization n°1067312).

Data

The database included the following information:

-Residents: sex, month and year of birth; -Drugs: Anatomical Therapeutical Classification (ATC) code, dosage, time and date of administration; -Nursing homes: legal status (public, private not-for-profit, private for-profit) and capacity (number of places).

Indicators of suboptimal prescribing

The number of drugs prescribed was determined for each day of the week. In order to take into account drugs administered weekly (for instance bisphosphonates), the assessment of polypharmacy considered the day of the week where the number of medications was the most important. Polypharmacy was defined as five medications or more and excessive polypharmacy as 10 medications or more. This definition included systemic drugs, as well as topical ones.

PIMs were those listed in the Laroche list [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF]. Briefly, the French panel consensus list is based on the 2003 Beers criteria but several drugs or therapeutic drug classes were not selected, because they were not available on the French market (such as mataxalone, guanabenz, barbiturates, except phenobarbital) or because the drugs were not judged inappropriate by the French experts (such as amiodarone and nonsteroidal anti-inflammatory drugs, except indometacine). Conversely, some criteria were added to the Beers criteria, notably the concomitant use of two (or more) nonsteroidal anti-inflammatory drugs and the concomitant use of two (or more) psychotropic drugs from the same therapeutic class. The drugs or the drug-classes proposed in this list are to be avoided when possible in the elderly, because of questionable efficacy and/or of unfavorable benefit-risk ratio. We excluded the 5 criteria that required information about underlying conditions because the database did not include clinical information.

Statistical analyses

Indicators of suboptimal prescribing were described in terms of prevalence. Factors related to excessive polypharmacy and to the fact of receiving at least one PIM were investigated among variables related to residents (age and sex) and nursing homes (legal status and capacity) by using Chi-2 test. Multilevel logistic regression models were used to study the independent effect of each variable, with an individual level and a nursing home level in order to take into account the correlation between subjects of a same nursing home. Indeed, the intraclass correlation coefficient obtained in empty models indicated that 8.0% and 3.4% of the total variance of excessive polypharmacy and of at least one PIM was explained by the nursing home level respectively. Analyses were performed using Stata® software v13 and the level of significance was set at 5%.

Results

Population

Of the 451 included nursing homes, 57.7% were private-for-profit (n=260), 29.9% were private-not-for-profit (n=135), and 12.4% were public facilities (n=56). The mean number of places per nursing home was 85 +/-33. Residents included 22,655 women (73.8%) and 8,047 men (26.2%). After exclusion of 904 potentially erroneous values of age considering the context (i.e. age <60 or >110), the mean age was 87.4 +/-7.6. The mean number of drugs prescribed was 6.9 +/-3.3. The most prescribed drugs are listed in the Table 1.

Polypharmacy, PIMs, and anticholinergic drugs

Polypharmacy (5 to 9 medications) and excessive polypharmacy (³10 medications) concerned 54.9% (n=16,854) and 21.1% (n=6,468) of the residents respectively. Potentially inappropriate prescribing was found in 14,547 residents (47.4%). PIMs and their rationale are listed by order of frequency in the Table 2. Additional information about drugs participating in the different PIMs is given in Appendix 1. Psychotropic medications were a leading cause of PIMs, because of inappropriate dosage, molecule or association. Notably, 2,876 residents (9.4%) received at least two different benzodiazepines during the study period. The prescription of drugs with anticholinergic properties was another frequent PIM. Considered together, drugs with anticholinergic properties were prescribed in 12.2% of the residents (n=3,738). Among them, hydroxyzine was largely prescribed, in 3.4% of the residents (n=1,217). Other notable PIMs involved antihypertensive drugs (4.6% of the residents, n=1,415), cerebral vasodilators and muscle relaxants, especially baclofene.

Factors associated with suboptimal prescribing

Factors associated with suboptimal prescribing are described in Table 3. Men and older residents were at lower risk of PIMs. Private for-profit nursing homes had lower levels of excessive polypharmacy compared to public nursing homes, as well as intermediate-size compared to small-size nursing homes. Overall, individual characteristics influenced the risk of receiving PIMs whereas nursing home characteristics influenced the risk of excessive polypharmacy.

Discussion

Main findings

Taking advantage of technologies used to secure the administration of drugs in nursing homes, indicators of quality of drug therapy could be calculated in a large population of nursing home residents. Excessive polypharmacy and PIMs concerned a large part of the study population, 21.1% and 47.4% respectively. Areas for improvement mostly concerned psychotropic and anticholinergic medications.

Polypharmacy

The prevalence of excessive polypharmacy found in this study was close to the estimate of the SHELTER study. Among voluntary nursing homes in 7 European countries + Israel, the prevalence of excessive polypharmacy was 24.3% [START_REF] Onder | Polypharmacy in nursing home in Europe: results from the SHELTER study[END_REF]. The health outcomes associated with polypharmacy in old people living in community have been extensively studied. Risks associated with polypharmacy include falls, hospitalizations, and mortality [START_REF] Fried | Health outcomes associated with polypharmacy in community-dwelling older adults: a systematic review[END_REF][START_REF] Herr | Polypharmacy and frailty: prevalence, relationship, and impact on mortality in a French sample of 2350 old people[END_REF]. In the context of nursing homes, polypharmacy has been recognized as a major cause of adverse drug events [START_REF] Nguyen | Polypharmacy as a risk factor for adverse drug reactions in geriatric nursing home residents[END_REF], notably falls [START_REF] Morley | Inappropriate drug prescribing and polypharmacy are major causes of poor outcomes in long-term care[END_REF]. The increased risk of adverse drug events associated with polypharmacy may be explained by the increased risk of receiving psychotropic medications and PIMs. In addition, polypharmacy increases medication regimen complexity and the risk of errors during the preparation and dispensation of medications [START_REF] Witticke | Opportunities to reduce medication regimen complexity: a retrospective analysis of patients discharged from a university hospital in Germany[END_REF].

PIMs

The prevalence of PIMs was relatively high compared to studies in community that reported a prevalence of PIMs about 20% [START_REF] Tommelein | Potentially inappropriate prescribing in community-dwelling older people across Europe: a systematic literature review[END_REF][START_REF] Opondo | Inappropriateness of medication prescriptions to elderly patients in the primary care setting: a systematic review[END_REF]. Comparison with other studies that assessed PIMs in nursing homes is complicated by methodological differences between studies regarding the PIMs criteria and data source. The literature shows that the prevalence of PIMs in nursing homes varies widely between studies, from 15% to 89% [START_REF] Blozik | Reduction of inappropriate medications among older nursing-home residents: a nurse-led, pre/post-design, intervention study[END_REF][START_REF] Grace | A comparison of beers and STOPP criteria in assessing potentially inappropriate medications in nursing home residents attending the emergency department[END_REF]. Two studies previously used the Laroche list [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF] in the context of nursing homes and reported prevalence of PIMs about 22% [START_REF] Cool | Potentially inappropriate drug prescribing and associated factors in nursing homes[END_REF][START_REF] Kolzsch | Potentially inappropriate medication for the elderly: adaptation and evaluation of a French consensus list[END_REF]. Our higher estimate (47.4%) can be explained by differences in the number of criteria considered. Indeed, the prevalence reported by Cool et al in 175 nursing homes in the South region of France refers to medications with unfavorable benefit-risk ratio only, PIMs due to questionable efficacy being considered separately [START_REF] Cool | Potentially inappropriate drug prescribing and associated factors in nursing homes[END_REF]. In the German study by Kolzsch et al, the authors could not identify overdosing of benzodiazepines and concomitant use of drugs from a same therapeutic class, whereas these criteria accounted for a large part of the PIMs in our study population [START_REF] Kolzsch | Potentially inappropriate medication for the elderly: adaptation and evaluation of a French consensus list[END_REF]. More generally, our estimate is in line with a recent review of literature that estimated the prevalence of PIMs in nursing homes at 49.8% (all criteria of PIMs considered, studies published since 2005) [START_REF] Morin | Prevalence of Potentially Inappropriate Medication Use in Older Adults Living in Nursing Homes: A Systematic Review[END_REF].

Psychotropic and anticholinergic medications accounted for a large part of PIMs in this study.

Though there are clear national and international recommendations to avoid the use of longacting benzodiazepines in old people [START_REF]Benzodiazépine à demi-vie longue chez le sujet âgé[END_REF][START_REF]American Geriatrics Society updated Beers Criteria for potentially inappropriate medication use in older adults[END_REF][START_REF] Lang | STOPP-START: adaptation of a French language screening tool for detecting inappropriate prescriptions in older people][END_REF][START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF], they were still prescribed in 7.2% of the residents in the present study. Among benzodiazepine users, those receiving long-acting molecules were shown to be at increased risk of falls [START_REF] Ray | Benzodiazepines and the risk of falls in nursing home residents[END_REF][START_REF] Landi | Psychotropic medications and risk for falls among community-dwelling frail older people: an observational study[END_REF]. Furthermore, long-acting benzodiazepines would increase the risk of onset of dementia assumed in benzodiazepine users [START_REF] Pariente | The Benzodiazepine-Dementia Disorders Link: Current State of Knowledge[END_REF]. The use of excessive doses of short-or intermediate-half-life benzodiazepines, as well as the prescription of multiple benzodiazepines, was another worrying result. Though to a lower extent compared to long-acting molecules, short-and intermediate-half-life benzodiazepines also increase the risk of adverse effects such as cognitive impairment, delirium, drowsiness, and falls [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF][START_REF]The American Geriatrics Society 2012 Beers Criteria Update Expert Panel. American Geriatrics Society Updated Beers Criteria for Potentially Inappropriate Medication Use in Older Adults (2012)[END_REF]. Moreover, the combination of several psychotropics does not necessarily ameliorate the symptoms, and may increase the risk of interactions and side-effects [START_REF] Gulla | Multi-psychotropic drug prescription and the association to neuropsychiatric symptoms in three Norwegian nursing home cohorts between 2004 and 2011[END_REF].

Using data from reimbursement of medications in 2012, Beuscart et al reported that 22.3% of people living in nursing homes in the North region of France received anticholinergic drugs, hydroxyzine in two third of the cases [START_REF] Beuscart | Potentially inappropriate medications (PIMs) and anticholinergic levels in the elderly: a population based study in a French region[END_REF]. Though anticholinergic drugs were far less prescribed in our study (12.2%), hydroxyzine was still the most prescribed anticholinergic drug, probably because it is considered an alternative to benzodiazepines in the treatment of anxiety. However, drugs with anticholinergic properties can cause peripheral side effects such as dry mouth and constipation, as well as central side effects, namely falls, dizziness, delirium, and cognitive decline [START_REF] Gerretsen | Drugs with anticholinergic properties: a current perspective on use and safety[END_REF].

Factors associated with suboptimal prescribing

The increased risk of PIMs observed in women is quite surprising. Indeed, gender had no influence on PIMs in any of the 11 studies that studied this relationship [START_REF] Halvorsen | Prescribing quality for older people in Norwegian nursing homes and home nursing services using multidose dispensed drugs[END_REF][START_REF] Hosia-Randell | Exposure to potentially inappropriate drugs and drug-drug interactions in elderly nursing home residents in Helsinki, Finland: a cross-sectional study[END_REF][START_REF] Kolzsch | Potentially inappropriate medication for the elderly: adaptation and evaluation of a French consensus list[END_REF][START_REF] Stafford | Inappropriate prescribing in older residents of Australian care homes[END_REF][START_REF] Chen | Evaluation of potentially inappropriate medications among older residents of Malaysian nursing homes[END_REF][START_REF] Mann | Prevalence and associations of potentially inappropriate prescriptions in Austrian nursing home residents: secondary analysis of a cross-sectional study[END_REF][START_REF] Cool | Potentially inappropriate drug prescribing and associated factors in nursing homes[END_REF][START_REF] Lao | Potentially inappropriate prescribing and drug-drug interactions among elderly Chinese nursing home residents in Macao[END_REF][START_REF] Vieira De Lima | Potentially inappropriate medications used by the elderly: prevalence and risk factors in Brazilian care homes[END_REF][START_REF] Perri | Adverse outcomes associated with inappropriate drug use in nursing homes[END_REF][START_REF] Zuckerman | Potentially inappropriate prescribing before and after nursing home admission among patients with and without dementia[END_REF]. This result may reflect the fact that women live longer, but with a heavier burden of comorbidity, and hence medications. Though we did not confirm the inverse association between excessive polypharmacy and age previously found in the SHELTER study [START_REF] Onder | Polypharmacy in nursing home in Europe: results from the SHELTER study[END_REF], we observed a significant decrease in the prevalence of PIMs with advanced age, consistently with previous studies in nursing homes [START_REF] Halvorsen | Prescribing quality for older people in Norwegian nursing homes and home nursing services using multidose dispensed drugs[END_REF][START_REF] Bergman | Evaluation of the quality of drug therapy among elderly patients in nursing homes[END_REF][START_REF] Niwata | Prevalence of inappropriate medication using Beers criteria in Japanese long-term care facilities[END_REF][START_REF] Kolzsch | Potentially inappropriate medication for the elderly: adaptation and evaluation of a French consensus list[END_REF][START_REF] Ruggiero | Potentially inappropriate drug prescriptions and risk of hospitalization among older, Italian, nursing home residents: the ULISSE project[END_REF][START_REF] Mann | Prevalence and associations of potentially inappropriate prescriptions in Austrian nursing home residents: secondary analysis of a cross-sectional study[END_REF]. This phenomenon may be explained by the reduction of pharmacotherapy in people with limited life expectancy, especially in demented people who are less likely to receive PIMs according to the literature [START_REF] Perri | Adverse outcomes associated with inappropriate drug use in nursing homes[END_REF][START_REF] Ruggiero | Potentially inappropriate drug prescriptions and risk of hospitalization among older, Italian, nursing home residents: the ULISSE project[END_REF][START_REF] Lau | Hospitalization and death associated with potentially inappropriate medication prescriptions among elderly nursing home residents[END_REF][START_REF] Cool | Potentially inappropriate drug prescribing and associated factors in nursing homes[END_REF][START_REF] Gerretsen | Drugs with anticholinergic properties: a current perspective on use and safety[END_REF][START_REF] Chen | Evaluation of potentially inappropriate medications among older residents of Malaysian nursing homes[END_REF][START_REF] Vieira De Lima | Potentially inappropriate medications used by the elderly: prevalence and risk factors in Brazilian care homes[END_REF].

Contrary to the results published by Beers et al in 1992 that reported an increased risk of

PIMs among large nursing homes [START_REF] Beers | Inappropriate medication prescribing in skilled-nursing facilities[END_REF], we found that intermediate-size nursing homes had lower rates of polypharmacy and PIMs compared to small ones. In addition, private-for-profit nursing homes had lower rates of polypharmacy compared to public nursing homes. These results indicate that organizational factors can play a role in the quality of drug prescribing. In a qualitative study in long-term aged care, Tariq et al actually identified multiple systemrelated factors that could influence the risk of prescribing errors [START_REF] Tariq | Underlying risk factors for prescribing errors in long-term aged care: a qualitative study[END_REF]. They were related to communication systems, team coordination and staff management. Organizational differences between nursing homes should be further investigated in order to identify levers to reduce PIMs. Emphasis should be given to the communication between staff and doctors who come to visit their patients in the nursing home and to the implementation of comprehensive geriatric evaluation and multidisciplinary medication review [START_REF] Burns | Prescribing in care homes: the role of the geriatrician[END_REF].

Strengths and limitations of the study

The main strength of this study is the size of the study population, covering 6.6% of the total number of places in nursing homes in France [START_REF]Les soins en EHPAD en 2013 : le financement de la médicalisation et le bilan des coupes Pathos[END_REF]. All the nursing homes using the pill dispenser Mono28® were included in this study. This is hence a real life evaluation of the quality of drug therapy, as opposed to studies in samples of nursing homes willing to participate where a selection bias can be expected. Nevertheless, the included nursing homes were not representative of French nursing homes in terms of legal status. Indeed, the proportion of private-for-profit nursing homes was higher in our study sample compared to national statistics (58% versus 43%) and the proportion of public nursing homes was lower (12% versus 26%). The mean capacity of the included nursing homes was comparable to national statistics (85 places versus 83 places).

The use of multi dose systems to assess medications in nursing homes can restrict information to tablets and capsules that can be placed in the multi dose system [START_REF] Halvorsen | Prescribing quality for older people in Norwegian nursing homes and home nursing services using multidose dispensed drugs[END_REF]. Because information was collected during the preparation of all the medications prescribed in the pharmacy, this study overcame this limitation and provided information about other formulations than tablets and capsules (inhalers, sachets, drops, syrups, injectable, etc.). Moreover, information was sufficiently detailed to allow the assessment of PIMs based on inappropriate dosage. Nevertheless, we did not have information about the health and diseases of the residents. This prevented us from studying drug-disease interactions. However, an underestimation of the overall prevalence of PIMs in this study because of the exclusion of drug-disease interactions is unlikely because most of the criteria of the Laroche list [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF] that consider drug-disease interactions deal with the prescription of anticholinergic drugs (e.g. drugs with anticholinergic properties in patients with prostate closed-angle glaucoma or chronic constipation), which are also considered in other criteria.

Though the choice to use the Laroche list [START_REF] Laroche | Potentially inappropriate medications in the elderly: a French consensus panel list[END_REF] was the most relevant with regards to the French context, this list has not been updated since its publication in 2007. Many drugs had been withdrawn from the market since then and maybe some other recommendations could be added. For instance, several studies have recently been published concerning the adverse effects of prolonged use of proton-pump inhibitors (fractures, pneumonia, death) [START_REF] Maggio | Proton pump inhibitors and risk of 1-year mortality and rehospitalization in older patients discharged from acute care hospitals[END_REF], resulting in their inclusion in the 2015 update of the Beers criteria [START_REF] Counsell | 2015 updated AGS Beers Criteria offer guide for safer medication use among older adults[END_REF]. Considering the high prevalence of use of proton-pump inhibitors in the study population (esomeprazole was used by 17% of the included residents), a part of misuse is likely.

Because data were collected during the routine process of preparation of the pill dispensers by the pharmacy staff and not by trained investigators, we registered about 2.9% of abnormal values of age. These individuals had to be excluded from multivariate analyses. Nevertheless, they did not differ from the rest of the study population in terms of mean number of medications prescribed. Errors regarding medications are very unlikely because the pill dispenser once prepared is checked by a pharmacist.

Conclusion

By using the data collected in routine during the preparation of pill dispensers for nursing homes, this study shows that excessive polypharmacy and inappropriate prescribing concern a large part of nursing home residents. Further studies are required 1/ to understand individual and organizational factors associated with suboptimal prescribing and 2/ to assess the consequences of each criteria of suboptimal prescribing, in terms of adverse health outcomes and subsequent costs, in order to refine the list of indicators of quality of drug therapy and operationalize their monitoring.

Table 2 . Prevalence of potentially inappropriate medications (PIMs) in the 30,702 residents included in the study

 2

	PIM	Reason	N (%)
	Dose of short-or intermediate-half-life	Questionable efficacy and increased	5,371 (17.5)
	benzodiazepines > half the dose given in	risk of cognitive impairment,
	young subjects	delirium, drowsiness, falls
	Use of two or more psychotropic drugs from	Questionable efficacy and increased	4060 (13.2)
	the same therapeutic class during the study	risk of adverse effects
	period
	Long-acting benzodiazepines	Increased risk of cognitive	2,199 (7.2)
		impairment, delirium, drowsiness,
		falls
	Anticholinergic histamines	Anticholinergic effects	1,256 (4.1)
	Short-acting calcium-channel blockers	May cause postural hypotension,	1044 (3.4)
		myocardial infarction, and stroke
	Anticholinergic antipsychotic drugs	Anticholinergic effects, second choice	891 (2.9)
		drugs
	Anticholinergic antidepressants	Anticholinergic effects, potential for	639 (2.1)
		cardiotoxicity, second-choice drugs
	Anticholinergic hypnotic drugs	Anticholinergic effects	614 (2.0)
	Anticholinergic antispasmodic drugs	Anticholinergic effects	531 (1.7)
	Cerebral vasodilators	Questionable efficacy	442 (1.4)
	Centrally acting antihypertensives	Sedation, hypotension, bradycardia,	412 (1.3)

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Cimetidine

Confusion, drug-drug interactions 4 (0.0) Reserpine Drowsiness, depression, gastrointestinal disorders 0