Exploring Mediation Effects of Gait Speed, Body Balance, and Falls in the Relationship between Physical Activity and Health-Related Quality of Life in Vulnerable Older Adults

The present study aimed to examine whether gait speed (GS), body balance (BB), and falls mediated the relationship between physical activity (PA) and health-related quality of life (HRQoL) in community-dwelling older adults. This is a cross-sectional study that included 305 men and 314 women (69.5 ± 5.6 years), residing in the Autonomous Region of Madeira, Portugal. HRQoL and PA were assessed using the SF-36 and Baecke Questionnaires, respectively. While BB was obtained by the Fullerton Advance Balance (FAB) scale, GS by the 50-foot (15 m) walk test, and the frequency of falls was obtained by self-report. According to the analyses, when GS and BB were placed concomitantly as mediators, the direct effect revealed by the model revealed a non-significant relationship between PA and falls. Thus, in the context of falls, GS and BB partially mediated the association between PA and HRQoL in approximately 29.7%, 56%, and 49.2%, respectively. The total HRQoL model explained a variance of 36.4%. The results can help to understand the role that GS, BB, and falls play in the relationship between PA and HRQoL of the vulnerable older adult population.


Introduction
Physical activity (PA) and health-related quality of life (HRQoL) are two crucial components in determining the health status of an individual, especially during the aging process [1,2]. PA is defined as a set of activities performed by individuals in their daily household activities and participation in sports and leisure activities [3]. According to the latest guidelines on physical activity and sedentary behavior, issued by the World Health Organization [4], to benefit health substantially, older adults should do at least 150 min of moderate-intensity aerobic activity or 75 min of vigorous-intensity aerobic activity, or have an equivalent combination of both. In addition, perform muscle strengthening and

Sample and Study Design
This is a cross-sectional analytical observational investigation, which included 619 individuals (69.5 ± 5.6 years). Of these, 305 were men and 314 were women, residing in the Autonomous Region of Madeira, Funchal, Portugal. Participants were recruited in clubs, cultural and sports associations, older adult homes, street markets, and churches, as well as through publicity in local newspapers, radio, and television. Inclusion criteria were as follows: (1) age 60-89 years, (2) domicile in the local community, and (3) ability to walk independently. As exclusion criteria, we adopted (1) impediment to participating in the set of assessments and (2) medical contraindications to performing physical exercises with submaximal intensity [36]. The procedures were approved by the Scientific and Ethics Committee and the Department of Physical Education and Sports of the University of Madeira (UMa), in addition to receiving authorization from the Regional Secretariat of the Social Affairs Committees and had the support of the FCT (SFRH/BD29300/2006). Before carrying out the assessments, the participants were informed about the procedures and signed a consent form. Study procedures followed the Declaration of Helsinki. The evaluations were carried out in 2009 by researchers trained in the Human Physical Growth and Motor Development Laboratory at UMa.

Demographics and Health Profile
Sociodemographic information (i.e., age, sex), comorbidities, and daily medication consumption were collected through face-to-face interviews.

Falls
The participants' history of falls was obtained through face-to-face interviews. The questions asked were the following: (1) Have you suffered any falls in the last 12 months? (binary answer: yes or no); and (2) If yes, could you tell us the total number of falls in the last 12 months? In the present study, we assumed the first question for the formation of the faller and non-faller groups.

Anthropometry
Height and body mass were measured using a Welmy ® anthropometric scale (London, UK) with a stadiometer attached to 0.1 cm and 0.1 kg [37]. Afterward, the body mass index (BMI) was defined through the equation: weight (kg)/[height (m)] 2 .

Physical Activity
Physical activity was estimated through the modified version of the Baecke Questionnaire for older adults [38]. The instrument is used worldwide, presenting three sections that assess the rates of physical activity in the last 12 months: (1) household activities (PA-domestic work); (2) leisure time activities (PA-leisure); (3) sporting activities (PA-sport), including regular weekly activities performed for at least one hour. For the evaluations, the total score (PA-total) was used, composed of the sum of the scores between PA-housework, PA-sport and PA-leisure. In their validation study, a time interval of three months, performed with 90 healthy, independent individuals (age 63 to 80 years), analyzes showed correlation reliability indices of 0.88, 0.81, and 0.74 for PA-work, PA-sport, and PA-leisure, respectively. The relative validity verified between the questionnaire and two reference methods, physical activity recall and pedometer, indicated a Spearman correlation coefficient of 0.78 and 0.72, respectively [38].

Gait
GS was assessed using the 50 ft (15 m) walk test proposed by the Senior Fitness Test (SFT) battery [39]. Initially, participants were asked to walk at their preferred speed and performed the test three times. Finally, the best performance was computed for analysis.
This test showed high test-retest reliability for households (0.94), and women (0.88), as well as a coefficient of validity for men (0.79), and for women (0.80) [39].

Body Balance
The Fullerton Advanced Balance (FAB) battery was used to evaluate the performance of the BB [40]. Its protocol includes ten tasks, which allow for evaluating the performance of the older adult's dynamic and static balance. The tasks consist of: (1) standing with feet together, and eyes closed, (2) reaching out to pick up an object (pencil) at shoulder height with the arm extended, (3) performing left and right 360 • turn, (4) stepping up and down a six-inch bench, (5) walking in tandem, (6) standing on one leg, (7) with eyes closed, standing on foam, (8) perform a long jump, (9) walk and turn head to the side, and (10) recover from an unexpected loss of balance. Each task was scored on an ordinal scale of 4 points (0-4), with a maximum score of 40 points. Instructions on its application and equipment, including instructional video, were reported by Rose [39]. The FAB scale showed high test-retest reliability (0.96), as well as intra-examiner (0.92-1.00) and inter-examiner (0.91-0.95) reliability.

Health-Related Quality of Life
HRQoL was assessed using the 36-item Short-Form Health Survey (SF-36) [41]. This questionnaire has eight dimensions, distributed in two components, each with four domains: (1) Physical: physical functioning (PF), physical role (RP), bodily pain (BP), general health status (GH), and (2) Mental: vitality (VT), social functioning (SF), emotional role (ER), and mental health (MH). The scores for each specific domain range from 0 to 100. Thus, the higher the score, the better the HRQoL. In the present study, we adopted a global and continuous measure of HRQoL, obtained by adding the scores of the physical and mental components of the SF-36 questionnaire. The instrument presented validity in the range of 0.92-0.95, and acceptable reliability for the eight dimensions with Cronbach's alpha ranged from 0.62 to 0.94, in addition to test-retest coefficients between 0.43 and 0.90.

Covariates
The following variables were considered confounding factors: gender, age, number of medications consumed per day, vision, BMI, hypertension, and musculoarticular problems. Additionally, therefore, controlled in the serial analysis of mediation.

Statistical Analysis
Data distribution was analyzed using the Kolmogorov-Smirnov test. Considering that the data presented a normal distribution, continuous variables (i.e., age, medications, weight, height, number of falls over 12 months, BMI, GS, BB, and HRQoL) were presented as mean and standard deviation (SD). Categorical variables (i.e., sex, falls, and comorbidities) were presented by frequencies and percentages. Comparisons of significance levels between continuous variables were established using the unpaired Student's t-test for independent samples, while statistical differences between categorical variables were tested by the chi-square test with Fischer's correction. Although our study did not focus on drawing comparisons between groups, the main characteristics of the participants were presented in two groups for descriptive purposes: fallers and non-fallers (dichotomous variable). On the other hand, for serial analysis of parallel mediation (investigation goal), the mediator variable falls (M 3 ) was formed by the total number of falls reported by participants over the last 12 months (scalar variable).
To achieve the study's main objective, we conducted Parallel and Serial Mediation [42]. Before the mediation analyses, the assumptions of multiple regression were verified: the linear relationship between independent and dependent variables, mean of residuals equal to zero, normality of residuals, non-multicollinearity, non-autocorrelation of residuals, and homoscedasticity of residuals, or an equal variation [43]. Figure 1 illustrates the path model used, composed of 9 direct effects (paths a-i). The model included two parallel mediators (M 1 and M 2 ), preceded by a third mediator (M 3 ). This type of analysis broadens and qualifies the understanding of how an independent variable (PA) can directly influence a dependent variable (HRQoL) mediated in parallel series by two mediators (GS and BB), which in turn indirectly affect falls (M 3 ), and concluding the cycle, falls also influences the perception of HRQoL. Our analysis considered a complete mediation, if with the inclusion of GS and BB objectively measured (mediator variable), preceded serially by a third mediator (Falls), the size of the association between the independent variable (PA) and the dependent variable (HRQoL) did not remain significant, which would be indicated when the confidence interval included the value of zero [42]. On the other hand, a partial mediation would occur if the observed relationship between the independent variable (PA) and the dependent variable (HRQoL) became weaker after the inclusion of the mediating variables (M 1 , M 2 , M 3 ). uals, and homoscedasticity of residuals, or an equal variation [43]. Figure 1 illustrates path model used, composed of 9 direct effects (paths a-i). The model included two para mediators (M1 and M2), preceded by a third mediator (M3). This type of analysis broade and qualifies the understanding of how an independent variable (PA) can directly inf ence a dependent variable (HRQoL) mediated in parallel series by two mediators (GS a BB), which in turn indirectly affect falls (M3), and concluding the cycle, falls also influen the perception of HRQoL. Our analysis considered a complete mediation, if with the clusion of GS and BB objectively measured (mediator variable), preceded serially by third mediator (Falls), the size of the association between the independent variable (P and the dependent variable (HRQoL) did not remain significant, which would be in cated when the confidence interval included the value of zero [42]. On the other hand partial mediation would occur if the observed relationship between the independent v iable (PA) and the dependent variable (HRQoL) became weaker after the inclusion of mediating variables (M1, M2, M3). The effects represented by the regression coefficients were estimated using PROCE v4.0, a computational extension of the SPSS program (IBM, Chicago, IL, USA). For para multiple serial mediation analysis, we used Model 80 [42]. The coefficients (a-i) describ in the equation (Figure 2) were calculated using least squares regression analyses. T direct and indirect effects of X on Y of the model were estimated using four equatio one for each of the three mediators, and one for the final consequent Y, as follows: The effects represented by the regression coefficients were estimated using PROCESS v4.0, a computational extension of the SPSS program (IBM, Chicago, IL, USA). For parallel multiple serial mediation analysis, we used Model 80 [42]. The coefficients (a-i) described in the equation (Figure 2) were calculated using least squares regression analyses. The direct and indirect effects of X on Y of the model were estimated using four equations, one for each of the three mediators, and one for the final consequent Y, as follows: Y = iY + c X + b1M 1 + b2M 2 + b3M 3 + eY the equation did not include zero, specific indirect effects were assumed to be significa [44]. The following procedure was used to calculate the proportion of mediation effec subtraction of 1 minus the result of the division between the direct effect and the to effect [42]. The results illustrated in the figures correspond to the standardized paramet β. The significance level was set at 5%.

Participants' Characteristics
Among the 619 participants (Table 1), 314 were women (69.49 ± 5.57 years old) a 305 men (69.51 ± 5.69 years old) (p < 0.001). The observed frequency of falls was 1-10 e sodes. The analysis procedures of the complete model (see Figure 2 for better visualization) were composed of four submodels, namely: Models 1 and 2, which perform the regression of each of the parallel mediators (M 1 and M 2 ) in X; Model 3 processed the regression of M 3 simultaneously on X, M 1 and M 2 ; and Model 4 performed the regression from Y to X, M 1 , M 2 , and M 3 . In parallel, the complete model calculated specific indirect effects (SIE's). The principle used in this calculation was the product of the path coefficients in a sequence. The SIE's calculated between X and Y were: SIE1 = a*b, SIE2 = a*g*d, SIE3 = c*d, SIE4 = e*f, SIE5= e*h*d. Finally, the total indirect effect corresponded to the sum of all SIE's = SIE1 + SIE2 + SIE3 + SIE4 + SIE5. Our mediation hypothesis was estimated using a confidence interval (95% CI) with bias correction and acceleration (BCa) by the Bootstrapping method; we set the number of bootstrap samples at 5000. When the confidence interval of the equation did not include zero, specific indirect effects were assumed to be significant. [44]. The following procedure was used to calculate the proportion of mediation effects: subtraction of 1 minus the result of the division between the direct effect and the total effect [42]. The results illustrated in the figures correspond to the standardized parameters β. The significance level was set at 5%.

Serial and Parallel Mediation Analysis
The model was significant (Figure 2). The analysis of the three mediation variables proved them to be predictors of the relationship between PA and HRQoL: The proportion of the total effect that PA had on HRQoL mediated by GS and BB through falls was up to 36.4%. Regarding the mediation proportion, the variables GS, BB, and falls explained the variance of the association between PA and HRQoL at approximately 29.7%, 56%, and 49.2%, respectively.

Discussion
This study examined, in a large sample of community-dwelling older adults, whether GS, BB, and falls mediated the relationship between PA and HRQoL. A parallel-serial mediation analysis was performed, and the total HRQoL variance explained by the entire model was 36.4%. In this scope, our three hypotheses were confirmed. We found that GS and BB inversely affect falls and, in turn, falls inversely affect HRQoL. When GS and BB were placed as mediators simultaneously, controlling for covariates (i.e., sex, age, medication, vision, hypertension, musculoarticular problems, and BMI), the direct effect of the pathway between PA and HRQoL (x-y) became non-significant. Thus, it was found that GS, BB, and falls partially mediated the link between PA and HRQoL by up to 29.7%, 56%, and 49.2%, respectively. The results suggested, in percentage terms, the effect that high levels of PA have on motor skills such as GS and BB, which are crucial for the older adult population to reach and/or maintain appropriate levels of HRQoL. Moreover, when these levels are adequate, it is possible to reduce both the risk of falls and the negative impact they have on HRQoL. As far as we know, this study is the first to present results in proportional terms on the investigated topic.
After controlling for potential confounding factors (i.e., sex, age, medication, vision, hypertension, musculoarticular problems, and BMI), the serial mediation model showed a negative association between GS and BB with falls. Thus, reductions in GS of approximately 0.1 m/s in the standard deviation (SD) represented an increase in the risk of falling by up to 0.92% (M 1 -M 3 , path h). Bohannon [45] suggested normal GS performance values of 1.13 m/s and 1.26 m/s for healthy individuals aged 70 to 79 years (both sexes), respectively. Additionally, for those aged 80 to 89 years, the suggested values were 0.94 and 0.97 m/s, respectively. According to our analysis, the average performance of both groups for GS was 1.24 m/s, and the difference between them was relatively small (∆ = 0.08 m/s). The literature suggests the value of 1 m/s as a cutoff point in the GS exam to identify the risk of falling in older adults [46]. Thus, GS values below 1 m/s are considered idle speed. In turn, the relationship between M 1 -M 3 (path g) indicated that for each reduction in BB performance of 0.1 points in standard deviation (SD), the risk of falling increased by up to 0.05%. According to our analysis, members of the non-faller group had better postural control than those of the faller group. The difference between the groups was considerably large (∆ = 2.39 points). However, considering the ideal cutoff score of 25 out of 40 on the FAB scale, fallers and non-fallers indicated preserved postural control [40]. It is worth mentioning that falls are multifactorial events, determined by the joint action of extrinsic and intrinsic factors [47].
With aging, gait patterns (e.g., speed, cadence, stride width), coordination, muscle strength, respiratory endurance, and balance tend to deteriorate [48]. In the case of GS and BB, this process is caused by several factors, such as changes in cognitive functions [49,50], somatosensory damage [51], vestibular problems [52], as well as neuromuscular problems responsible for muscle weakness [53]. Thus, compared to young individuals, older adults move more slowly, which makes them more vulnerable to falls, especially in challenging situations, such as those that require the simultaneous processing of two or more motor and cognitive tasks [54,55]. Older adults also have difficulty performing postural corrections accurately and quickly in situations of imbalance caused by external disturbances [56,57]. In this perspective, our findings were in line with the literature suggesting the promotion of PA as a valuable strategy to increase the performance of GS and BB (physical functions), benefiting the reduction of the risk of falls [58].
In a meta-analysis study, Chase et al. [59] showed that PA might be able to improve the physical functions of older adults. Furthermore, it is known that there is a bidirec-tional relationship between PA and physical function [60]. Therefore, the improvement in physical functions reflects positively on PA levels, which comes from the perception of improvement in motor skills (i.e., GS and BB). This makes the individuals more motivated and willing for everyday activities and encourages them to remain physically active [9]. As a result, the individual perceives an improvement in the general state of his health, which consequently benefits his HRQoL [61]. In our analysis, the SIE1 and SIE4 pathways showed the benefits of increasing GS and BB (physical functions) in the link between PA and HRQoL in dependence on falls (see Figure 1). We found that an increase in the standard deviation (SD) of 0.1 m/s in the GS performance represented an increase in HRQoL of up to 13.75%. At the same time, an increase in the standard deviation (SD) of 0.1 m/s in the execution of the BB, meant an increase in HRQoL of up to 0.65%.
Studies have reported that a high GS is able to increase the perception of HRQoL in the older adult population [35,62], helping to maintain levels of independence [63]. An improvement in GS can promote beliefs about one's own abilities to deal with the environment in which one lives, which is important for strengthening self-confidence and generating new perspectives on life during aging [64]. Experimental studies have also shown the effects of BB training on HRQoL in community-dwelling older adults [65,66]. Regarding the relationship between PA and HRQoL, with BB as one of the mediators, other factors must be considered as mediators or moderators. A current study pointed out that in the relationship between PA and HRQoL, BB and lower limb strength mediated the relationship by approximately 47% and 39.6%, respectively [30]. Moreover, unipedal support and lower limb strength were identified in older adults (75 years) as mediators in the relationship between walking habits and HRQoL [67]. The outcomes attest that one or two variables cannot explain falls, in addition to the fact that the association between PA and HRQoL is widely considered. Another point to highlight in the relationships among PA, GS, BB, and falls is the association between HRQoL and fear of falling (FOF). FOF is considered a psychological risk factor for intrinsic falls, which is combined with the others (i.e., GS and BB) related to falls [68]. It is known that after a fall, the older adult develops the fear of falling again [69], becoming more cautious about walking and performing ADLs. Thus, due to the intentional reduction of the GS or BB, the ability of the older adult person to execute movements quickly due to external mechanisms (i.e., collisions with objects and people, tripping and slipping) is limited, increasing their chances of falling [70]. A systematic review study showed a negative relationship between FOF and HRQoL of individuals aged ≥60 years [71], particularly the discredit in physical beliefs. In our study, 44.4% of fallers were recurrent. Thus, some participants may have developed FOF, and this feeling has reduced GS [72] and BB control [73], co-participating in the occurrence of new fall events, in turn reducing HRQoL [67]. Our findings also corroborate a previous investigation that pointed to GS, unipodal support, and lower limb strength in older adults (75 years old) as mediators in the relationship between walking habits and HRQoL [67], as well as an increase in HRQoL due to increased PA levels in the bilateral relationship with an improvement in physical functions, which includes GS and BB [30,34].
Several limitations of the current study are important to note. First, the use of a cross-sectional design did not allow us to attribute causalities in mediation analyses. Thus, it is suggested that future investigations adopt longitudinal designs or experimental studies to generalize the results presented here and, in turn, expand our understanding of these study variables during the aging process. Second, it should be considered that the main characteristic of the sample (older adult inhabitants of Madeira Island) may have influenced the general findings. Thus, we suggest caution in generalizing the results. Third, it should be considered that the participants in this study were recruited from different locations, including sports clubs and associations: It is possible that the PA levels of these older adults were higher than those of the other participants. Fourth, it should be considered that, although the Baeck questionnaire is used worldwide to measure PA levels in older adults, there are instruments with better validity and reliability scores, such as the Physical Activity Scale for the Elderly (PASE) [74]. This fact does not detract from our results; however, it serves as a suggestion for future investigations. Our study has a strong point. It is the first to investigate the mediating role of GS, BB, and falls in the association between PA and HRQoL, bringing to light information about the proportion of this mediation. Moreover, we encourage the development of new investigations that evaluate the association between PA and HRQoL, mediated by GS, BB, and falls, considering potential moderators such as fear of falling, sex, and age to determine differences.

Conclusions
Our results suggested that the association between PA and HRQoL in vulnerable older adults was partially mediated by GS, BB, and the frequency of fall events. Based on parallel serial analysis mediation procedures, we detailed in proportional terms the role that each of the three mediating variables plays in the association between PA and HRQoL, in addition to the proportion of the total effect of PA on HRQoL. Moreover, the parallel-serial mediation pathway model indicated that total PA played a crucial role in improving physical functions (i.e., GS and BB), counteracting the negative effects related to age, capable of increasing the risk of falling, benefiting, in turn, the perception of HRQoL. From this perspective, when it comes to falls in the older adult population, the results can provide useful information to professionals in the clinical area, helping them to identify and monitor levels of PA and HRQoL.