**2. Methods**

#### *2.1. Study Overview*

The 3C-study is a French population-based prospective study initiated in 1999–2000 to study the vascular risk factors of dementia [32]. Its protocol was approved by the Consultative Committee for the Protection of Persons participating in Biomedical Research at Kremlin-Bicêtre and all participants gave written informed consent. Participants were randomly sampled from electoral rolls from three French cities (Bordeaux, Dijon, and Montpellier). Eligible participants had to be 65 years and older at the time of recruitment and not institutionalized. Among the 9294 participants included at baseline, 2104 were from the Bordeaux center, which completed the initial data collection in 2001–2002 (wave 1). A comprehensive dietary survey of 1597 participants was also performed. This dietary survey served as the baseline for the present study, where DP frequency of consumption and frailty were assessed.

#### *2.2. Assessment of Dairy Products*

Dietary data were obtained from a semi-quantitative Food Frequency Questionnaire (FFQ) administered during face-to-face interviews by dietitians. This allowed the assessment of the daily frequency of consumption of 148 foods and beverages (with frequencies assessed in 11 classes, from "never or less than once a month" to "7 times per week") during each of the six meals/snacks of the day, as previously detailed [33]. Data from the FFQ was validated against a 24-h dietary recall in an independent subsample of the 3C-study [34]. DP consumption was considered using the frequency of consumption of milk, fresh DP, and cheese. The milk consumption variable included the consumption of "milk", "coffee with milk", "tea with milk", "chocolate", "chicory", and "natural milk or with cereal". Consumption of "yogurt and cottage cheese" was classified as fresh DP

while frequency of consumption of "cheese" was considered as the cheese category. As already described by Pellay et al. (2020), we considered the DPs' frequency of consumption as four main exposures, including total DP, milk, fresh DP, and cheese [31]. For each DP component, three categories were created based on the quartile distribution of consumption (low frequency: first quartile; intermediate frequency: quartiles 2 and 3; high frequency: fourth quartile). This classification ensured the differentiation between the most infrequent and frequent consumers, as previously described [31].

#### *2.3. Assessment of Frailty*

At baseline and at the 10-year follow-up, frailty was defined following the Cardiovascular Health Study frailty index [4], the tool recommended by the International Conference of Frailty and Sarcopenia Research [35]. Nevertheless, minor modifications were made to adapt this tool to the available data in our cohort study, as already published [17,18]. Briefly, (1) weight loss was defined as self-reported unintentional loss of 3 kg or more or, if missing, as a body mass index (BMI) <21 kg/m2; (2) exhaustion was evaluated using the following statements from the Center for Epidemiologic Studies-Depression scale (CES-D): "I felt that everything I did was an effort" and "I could not ge<sup>t</sup> going". Participants were considered frail for this criterion when they answered "a moderate amount of the time" or "most of the time" to either of these statements [36]; (3) walking speed was determined based on a 6-m walking test, adjusting for height and gender. Participants in the highest quintile were considered slow. When this information was missing, participants were considered frail for this criterion when they reported being unable to walk between 500 m and 1 km or to walk up and down a flight of stairs based on the Rosow–Breslau scale [37]. This proxy has been shown to be strongly associated with walking [38]; (4) weakness was identified in different ways at baseline and at the 10-year follow-up, depending on availability of data. At the 10-year follow-up, weakness was identified using the handgrip strength quartiles stratified by sex and BMI, as recommended [4]. At baseline, weakness was identified using the chair standing method, shown to be a good proxy for handgrip strength [39]; (5) physical activity was assessed in a face-to-face interview via an open-ended questionnaire. Low physical activity was defined as less than 1 h of sports activities or less than 3.5 h of leisure activities per week, as previously described [17,18].

Older adults with three or more criteria out of five were considered as frail, otherwise they were considered as non-frail. Prevalent frail participants at baseline were excluded for the prospective analyses.

The FRAIL scale was also used to define frailty in sensitivity analyses [40]. The FRAIL scale includes five self-reported components: Fatigue, Resistance, Ambulation, Illnesses and Loss of weight. Fatigue and weight loss were evaluated similarly to those of the frailty index. Resistance and Ambulation were evaluated using the Rosow–Breslau scale, as recommended. Resistance was assessed by asking participants if they could walk up and down a flight of stairs and Ambulation by asking if they could walk between 500 m and 1 km; "no" responses were each scored as 1 point. Lastly, Illnesses was scored 1 for respondents who reported 5 or more chronic conditions out of 13 including hypertension, diabetes, hypercholesterolemia, cardio- and cerebro-vascular diseases (myocardial infarction or cardiac and vascular surgery, or arteritis or stroke), Parkinson's disease, cognitive decline and dyspnea. Cancer was considered when reports were available, i.e., at the 10-year follow-up. The FRAIL score ranged from 0–5, with those scoring three or more considered as frail and those scoring two or less as non-frail.

#### *2.4. Assessment of Disability*

Dependency in basic Activities of Daily Living (ADLs) was assessed using the five following items of the Katz scale: bathing, dressing, toileting, transferring from bed to chair, and eating [41]. An individual was considered dependent if they could not perform at least one activity without a given level of assistance, as defined in the original instrument. All

identified dependent participants at baseline and at 10-year follow-up were excluded from the analyses because frailty is considered as risk factor for dependency [35].

## *2.5. Covariates*

The covariates included age, sex, marital status, education, smoking status, polypharmacy (dichotomous variable with 6 medications/d as a cut-off), multimorbidity (dichotomous variable with 2 chronic diseases or more as a cut-off point), and global cognitive performances using the Mini-Mental State Examination (MMSE) [42] (0–30 points; higher scores indicate better cognitive status). A diet quality score was also computed. This score included seven components: pulses, raw fruits, raw vegetables, cooked fruits and vegetables, fish, alcohol and olive oil. Each component was dichotomized into meeting the current dietary recommendations versus not. The total score of 7 was also dichotomized into having a good diet quality (score > 3) versus not (score ≤ 3). Finally, total protein intake was evaluated from a single 24-h dietary recall that was administered at home in addition to the FFQ [43].

#### *2.6. Statistical Analysis*

Baseline demographic, clinical and dietary characteristics were compared between prevalent frail and non-frail (i.e., sample used in the cross-sectional analysis) and incident frail and non-frail (i.e., sample used in the longitudinal analysis) older adults using the student's *t*-test or chi-square test, depending on the type of the variables.

Logistic regression models were used to estimate odds ratio (OR) and 95% confidence intervals (95% CI) for the association between consumption of total DP or DP sub-type (milk, fresh DP, or cheese) and frailty, both cross-sectionally and prospectively. For each DP exposure, intermediate frequency consumption (quartiles 2 and 3) and high frequency consumption (quartile 4) were compared to the reference category of low frequency consumption (quartile 1).

Model 1 was adjusted for age, sex, education and marital status. Model 2 was additionally adjusted for smoking status, multimorbidity, polypharmacy, diet quality score, total protein intake and global cognitive performances. Finally, two sets of sensitivity analyses were performed. First, we assessed frailty using the FRAIL scale and the same multivariate models were applied, except excluding multimorbidity as a covariate from model 2 as this variable is a component of the FRAIL scale. Second, we retained all ADL dependent individuals as we assumed that those who are ADL dependent might already be frail, both in the cross-sectional analysis and the prospective one. All statistical analyses were performed with the SAS Statistical package (Version 9.4 SAS Institute) and statistical significance was set at *p* < 0.05.
