Understanding Frailty: Probabilistic Causality between Components and Their Relationship with Death through a Bayesian Network and Evidence Propagation
by
, , and
Ricardo Ramírez-Aldana
1,
Juan Carlos Gomez-Verjan
2
,
Carmen García-Peña
2,
Luis Miguel Gutiérrez-Robledo
2 and
Lorena Parra-Rodríguez
2,* 1
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City 3000, Mexico
2
Research Department, Instituto Nacional de Geriatría, Mexico City 10200, Mexico
*
Author to whom correspondence should be addressed.
Electronics 2022, 11(19), 3001; https://doi.org/10.3390/electronics11193001
Submission received: 27 July 2022
/
Revised: 7 September 2022
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Accepted: 19 September 2022
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Published: 22 September 2022
(This article belongs to the Special Issue Data Analytics and Visualization in Health Informatics)
Abstract
Identifying relationships between components of an index helps to gain a better understanding of the condition they define. The Frailty Index (FI) measures the global health of individuals and can be used to predict outcomes as mortality. Previously, we modelled the relationship between the FI components (deficits) and death through an undirected graphical model and a social network analysis framework. Here, we model the FI components and death through an averaged Bayesian network obtained through a structural learning process and resampling, in order to understand how the FI components and death are causally related. We identified that components are not similarly related between them and that deficits are related according to their type. Two deficits were the most relevant in terms of their connections, and two others were directly associated with death. We obtained the strength of the relationships in order to identify the most plausible, identifying clusters of deficits. Finally, we propagated evidence and studied how FI components predict mortality, obtaining a correct assignation of almost 74% and a true positive rate (TPR) of 56%. Values were obtained after changing the model threshold (via Youden’s Index maximization) whose possible values are represented in a Receiving Operating Characteristic (ROC) curve (TPR vs. 1-True Negative Rate). The greater number of deficits included for the evidence, the best performances; nevertheless, the FI does not seem to be quite efficient to correctly differentiate between dead and living people.
1. Introduction
Frailty is a term widely used to denote a state of poor homeostatic resolution (vulnerability) after a stressor event and is a consequence of loss of homeostatic reserve across multiple physiological systems, which occurs across the lifetime [1]. Frailty appears to be a valid construct, since it can be used to identify older adults who are at increased risk of mortality and functional decline when they are hospitalized [2], but a consensus has yet to be reached on how exactly to define and determine it so we could make this term useful for clinics.
One approach to measure frailty is to count deficits in health (symptoms, signs, diseases, disabilities or laboratory, radiographic, or electrocardiographic abnormalities) on the grounds that the more deficits a person has, the more likely that such individual could be frail [3,4]. The frailty index (FI) is often expressed as a ratio of deficits present to the total number of deficits considered [4].
Variables included in the FI satisfy that they are associated with health status and that their prevalence must generally increase with age, but do not become too prevalent at a younger age. The deficits that make up the FI cover a range of systems; if a single FI is used serially on the same people, the items that make up the FI need to be the same from one iteration to the next [4]. A robust FI requires a significant number of individual items (between 30 and 40), which are utilized to record deficit accumulation, and are recorded as a score or index. In this sense, the FI is strongly associated with the risk of death, institutionalization, and worsening health status, especially when at least 30 variables are included [5].
Interestingly, the FI approach does not assume that the deficits that make up frailty are statistically independent [6], and usually includes comorbidity (the concurrent presence of two or more medically diagnosed diseases) and disability (difficulty or dependency in performing activities of daily living) variables [7]. It is still unclear whether disabilities and comorbidities themselves should be a domain to define frailty or if they already constitute adverse health outcomes [8,9]. Additionally, more research is needed to understand how health deficits connect and interact with each other and how the FI is associated with death.
There is an urgent need for a deeper understanding of the components of frailty to develop newer approaches that lead to better solutions for the care of frail older people. The interplay of interactions between deficits may lead to targeted interventions if some components are more closely causally related to death. For this reason, several theoretical complex network models have been proposed. These models try to better understand how changes in health are captured by the FI [10] by simulating a network for each individual according to the theoretical connections that all deficit and dead nodes could have [11]. Thus, they try to explain how damage propagates through a network and what makes FI components informative of mortality [12], study how damage propagates through a complex network of interconnected elements [10], demonstrate the patterns of frailty and mortality that influence the health trajectories of individuals [13], and explore the effects of interactions between deficits, deficit damage, and repair processes, as well as the connection between the FI and mortality [14]. These studies analyze frailty through simulation methods, with social network analysis models; thus, analyzing frailty using real data seems to be a priority to validate such models.
On the other hand, a Bayesian network is a complex model that allows one to identify independences and causal relationships between variables, considering all variables at the same level, in the sense that there is not necessarily a division between explanatory and response variables. Additionally, we can see how a subset of variables are affected conditionally to values provided to other subset of variables, also known as evidence propagation. Thus, this methodology simultaneously allows us to perform explanatory and predictive analyses. Markov chains can be seen as a particular case of a dynamic Bayesian network whose graph corresponds to a directed path; as such, interactions of more than two variables are not possible, whereas using the Bayesian network this can be easily done.
In this context, we have already presented probabilistic graphical models using real data through a Markov network [15], an undirected graphical model. Our previous research showed that not all deficits are equally related, since clusters of strongly related deficits and non-connected deficits were obtained, which might be considered in the construction of the FI score [15]. However, in the present study, we consider directionality. We assigned values to some variables (evidence) and derived through algorithms the probabilities associated with other variables conditional to such assignation (evidence propagation), as well as the strength of the relationships. Such considerations will help to have a better understanding of how frailty and its components are working together and how they relate with death.
The main purposes of this work are: (1) to obtain in non-simulated data, through a Bayesian network, causal inference (probabilistic causality) concerning the deficits defining the FI and death (seeing whether all variables are similarly related or whether some variables are more related than others); (2) to identify how the variables are related between themselves and with death, considering the strength of the relationships, and (3) to determine how the probability of death is modified in each individual according to assignation of values (evidence) in certain variables, and to evaluate whether dead and living people can be correctly separated using an adequate cut-off value for the probability and different sets of variables providing evidence.
2. Materials and Methods
2.1. Data
The analysis is derived from the longitudinal data from the third and fourth waves (2012 and 2015) of the Mexican Health and Aging Study (MHAS) [16]. The overall goal of the study is to examine the aging process and its disease and disability burden in a large representative panel of older Mexicans living in urban and rural areas. MHAS involves human data, whose access is granted after registration. The owners of this information declare that the MHAS study protocol and instruments were approved by the Institutional Review Board or Ethics Committee of the University of Texas Medical Branch, the Instituto Nacional de Estadística y Geografía (INEGI), and the Instituto Nacional de Salud Publica (INSP) in Mexico. MHAS baseline was nationally representative of Mexicans born prior to 1951. A set of questionnaires (socio-demographic, health-related, cognitive performance, and functional status, among others) was applied to older Mexican adults over five waves (2001, 2003, 2012, 2015, and 2018). We built all frailty deficits from the 2012 wave. Mortality was obtained using information from the 2015 wave and corresponds to deaths which occurred between 2012 and 2015. In the 2012 wave, 15,723 participants were assessed, including 9827 follow-up participants and 5896 from a refresh sample (including spouses of the chosen individuals, regardless of age). 1209 deaths were reported by 2015.
For this study, we used a sample of 14,872 individuals, since participants younger than 50 years old were eliminated. Independence between individuals is assumed in the models; thus, correlation analyses were performed finding that correlation between couples was low for all variables, thus couples were included in all analyses. We discarded second or third wives or husbands (165 cases) to avoid problems concerning marital status transitions through time. Though missing data imputation is possible using Bayesian networks, we preferred to discard cases with missing values in any variable to avoid any masking of the sensitivity and specificity associated with the evidence propagation. Hence, from 14,707 cases, a final sample of 10,983 was retained for the present analysis.
2.2. Frailty
A set of 35 variables or deficits, all self-reported, was included as determined by Searle et al. [4]. Variables included concern functional status, chronic diseases, self-rated health, cognitive status, and depressive symptoms. The variables were obtained, categorized, and named as shown in Table A1. They are explained with more detail in [15], where we showed frequencies, calculated the FI for each individual, and showed tables concerning tertiles associated with the index.
2.3. Analytic Plan
Bayesian networks (BNs) are discrete probabilistic graphical models [17], which use several concepts defined in graph theory [18]. All variables correspond to vertices in a set V, and the arcs (directed edges) belong to a set A, obtaining a directed graph or digraph D (V,A), which, in BNs, should be a directed acyclic graph (DAG). The network represents a factorization of the joint probability distribution (probability associated with all variables) corresponding to the random variables associated with each vertex, depending on the graph structure and the Markov properties. These properties state conditional independence relationships between sets of variables. Due to the concept of d-separation, cycles are not allowed, which permits determination of conditional independences and, to use the belief propagation algorithm explained below, depends on this property. In BNs, the factorization depends on the probability density associated with each variable conditional to the parent nodes (nodes having any directed edge pointing to a vertex v). BNs are also used to represent probabilistic causality between sets of variables.
The graph structure that best represents some data or structural learning process is obtained through algorithms (e.g., [19]). Some of them are based on optimizing scores, for instance, the hill-climbing algorithm. There are instances in which the same conditional independence structure can be represented by more than one digraph, thus having the same score, and in this case, causal relationships could be randomly chosen. Hence, to improve the robustness of the structural learning process, we used a resampling technique, the bootstrap method, to learn a set of 100 network structures to use for model averaging [20]. Additionally, to avoid illogical directions between variables, we restricted the structural learning process to avoid arcs from death to any other node (blacklist of directions). We obtained the network structure from each bootstrap sample with a hill-climbing search using the Bayesian Information Criterion as a score and an empty graph (graph without edges) as an initial model. Then, a strength (probability) associated with the presence and direction of each arc was obtained from the bootstrap method. Thus, the strength corresponds to the probability of observing an arc between nodes A and B in all bootstrap replicates, i.e., the strength is a measure between 0 and 1 corresponding to how frequently an arc can be observed independently of the data. A similar measure is obtained for the direction.
An average network can be derived by defining a threshold for the strength of both the presence and direction of the arcs. To determine the presence of the arcs, we decided to use a threshold that the algorithm chooses as the one that best represents the data (which in our data was close to 0.5) and to define the direction, we used the most probable direction (strength above or equal to 0.5). Since there are instances in which an arc can have both directions (Stairs to Effort and Effort to Stairs), thus obtaining a network with both directed and undirected edges, we chose the model whose associated DAG pertains to the same equivalence class of the model with the graph having directed and undirected edges. Hence, there could be arcs with a direction strength lower than 0.5 (three in our case, one from Meds to Meals, another from Toilet to Walk, and a last one from Effort to Lift, which originally were in the opposite direction). The DAG associated with the chosen model was drawn using different colours, graphically representing which relationships are stronger.
The parameters (conditional probabilities of a node given its parents) associated with the chosen model were estimated from the data. After that, the network was compiled and since there were no undefined probabilities, evidence propagation was possible [21,22]. Evidence propagation means that values are provided to a subset of variables, evidence e, and its effect over another subset of variables n is derived by obtaining the conditional probability of the variables in n given the evidence, P(n|e).
We used the values associated with all variables except death as evidence, and propagated them over the death variable, obtaining the probability of death under the model conditional to each combination of values that the other variables can take. Then, individuals can be assigned, according to the model and evidence, into dead or alive, by defining a threshold associated with the probability of dying. The default threshold of 0.5 was not appropriate in our data since all probabilities were under 0.5; thus, classifying all dead people as alive. Consequently, we decided to obtain a Receiving Operating Characteristic (ROC) curve, a plot representing for different thresholds the associated true positive rate (TPR, sensitivity, or recall), dead people assigned as such in our model, and specificity (1-TNR, with TNR = True Negative Rate), alive people assigned as such in our model. We examined the area under ROC curve and chose the threshold maximizing both measures by optimizing the sum of sensitivity and specificity, i.e., maximizing the Youden’s J statistic. In order to see whether all deficits defining frailty were relevant to determine an accurate probability of death, a similar analysis was performed, but using as evidence only the values associated with two variables: difficulty walking a block and self-rating of health. These nodes were chosen since they were the most relevant nodes (most central nodes using degree, betweenness, and closeness) according to an analysis based on a Markov network [15]. A similar analysis was performed using the nine most connected nodes in the Bayesian network. Finally, the FI by itself was also used to classify dead people.
All analyses were performed in R-studio (R-version 3.5.1) through the bnlearn package [23] to implement the structural learning process, with the bootstrap method and hc algorithm, and for evidence propagation. On the other hand, the pROC [24] package was used to obtain ROC curves and analyze sensitivity and specificity after evidence propagation.
3. Results
Of the total sample, (n = 10,983), 43.8% were women (n = 4810). The mean age of individuals was 64.6 years (SD = 9.3, R = 50–102). The number of deaths between 2012 and 2015 was 574 (5.23%). The FI, considering all observations, was 0.18 (SD = 0.131, R = 0–0.8). Deficits with the higher percentage of participants were physical inactivity = 60.52%, feel tired within the past week = 58.29, and feel without energy = 51.34%. The most prevalent deficits related to mobility were helping in/out of a chair = 29.72%, help up/down one flight of stairs = 23.62%, and help lifting ten pounds = 23.28%. Components of the depression scale resulted in high percentages (feel depressed = 33.7%, feel lonely = 29%). Hypertension and diabetes diagnosis was reported in 43.04% and 21.80% of the individuals. The description of the total sample is shown in Table 1.
The network associated with the frailty components and death is shown in Figure 1. Nodes are coloured according to the following classification: Black: Dead; Yellow: AS (Affective Status: No_Happy, Lone, No_energy, Depressed, Tired, and Effort); Light Blue: Symptoms (Anorexia, Bed, and Lost_weight); Gray: SRH (Self-rated health: Health and H_change); Green: ADL-IADL (activities of daily living and instrumental activities of daily living: In_out_chair, Stairs, Shop, Dress, Walk, Eat, Groom, Meals, Meds, Finance, and Toilet); Orange: Physical Health (Grip, Exercise, Lift, and Walk_out); Pink: Comorbidities (CLD, Stroke, Cancer, CHF, Arthritis, Heart_Attack, Diabetes, and High_BP); Navy Blue: Cognition (Memory).
Arcs are colored according to the strength of the relationship as a color gradient from yellow (less strength) to dark blue (more strength). We can see that all variables are connected, except Cancer, which is an isolated vertex, since there are no edges with enough strength considering the cut-off values used. Thus, Cancer was found to be marginally independent from the other variables.
We observed that only two deficits are directly linked with the Dead node: Lost_weight and Shop, being Shop the node with the strongest relationship with Dead with a value of 0.85, whereas the value for Lost_weight is 0.69. There are four nodes pointing to Shop, the variable with the strongest relationship with Dead, which are Stairs, Dress, Lift, and Walk_out; thus, the probability associated with the Dead variable conditional to values provided to other variables not only depends on the Shop node. In fact, the set of ancestors of the Dead node, nodes from which there are directed paths to Dead, is formed by 14 nodes (Figure 2).
We observed that the variables with the greatest outdegree, with more arcs from the variable to any other variable, are In_out_chair, with a value of ten, and Lift and Effort, with a value of eight. On the other hand, the variables with the greatest indegree, with more arcs pointing to them, are Grip and H_change. It is noticeable that In_out_chair has an indegree of zero, though it has the greatest outdegree of all variables. When considering both arcs that begin or end into a variable, the variables with the greatest number of arcs are H_change with eleven arcs; In_out_chair, Lift, and Shop with ten arcs each; and Health, Walk_out, Effort, Depressed, and Grip with nine arcs (Table 2).
When considering the arcs with the highest strength, greater than or equal to 0.8 for both the presence of an arc and its direction (Figure 3 and Table A2), we observe direct relationships from the following nodes: from Depressed to Anorexia, Lone, and No_Happy; from Diabetes to Lost_weight; from Effort to Health, Depressed, and Lone; from Grip to Arthritis and Memory; from Groom to Toilet; from H_change to Bed and Memory; from Health to No_Happy, Diabetes, and H_change; from Heart_attack to CHF; from High_BP to Diabetes and Heart_attack; from In_out_chair to Health, Memory, and Arthritis; from Lift to High_BP and Grip; from Meals to Eat; from Meds to Finance; from Shop to Dead, Meds, Finance, and Meals; from Stairs to Grip; from Tired to Depressed; from Lone to No energy; and from Walk_out to Toilet and Walk. Of course, there are indirect relationships, for instance from Effort to No_Happy through the Depressed node.
After evidence associated with all nodes, except Dead, was propagated over the Dead node, we obtained the probability of death under the model for every individual. The corresponding ROC curve is shown in Figure 4a with an Area Under the Curve (AUC) of 0.6732. A new cut-off for assigning an individual to the dead class of 0.051 was obtained (individuals with probability greater than or equal to that number are assigned to the dead category), obtaining through this cut-off value a sensitivity (death correctly assigned) of 56.1%, a specificity of 74.6%, and a total percentage of correct assignation or accuracy of 73.58%.
When the values associated with the Walk_out and Health nodes are used as evidence and this evidence is once again propagated over the Dead node, we obtain the probability of death under the model and evidence provided by the two nodes. The associated ROC curve under the evidence is shown in Figure 4b with an AUC of 0.63. A new cut-off of 0.061 is obtained with an associated sensitivity of 37.98%, a specificity of 84.76%, and an accuracy of 82.31%. When the values associated with the nine most connected nodes in the network in this paper are used (H_change, In_out_chair, Lift, Shop, Health, Walk_out, Effort, Depressed, and Grip), the AUC of the ROC curve (not shown) is the same (0.63) with a cut-off value of 0.055, sensitivity and specificity of 38.15% and 87.27%, respectively, and accuracy of 84.7%, obtaining almost the same numbers as those obtained above using two nodes.
By only using the FI to separate between dead and living people, the FI being the average number of deficits by individual, and following a similar process of obtaining the associated ROC curve and optimum cut-off value, we obtained an AUC of 0.707, slightly better than the values obtained before, a cut-off value of 0.214 with an associated sensitivity of 60.97%, a specificity of 68.90%, and an accuracy of 68.49%.
4. Discussion
In the present study, we obtained a Bayesian network associated with frailty components and death, observing that not all nodes are similarly related between them. Some have more arcs originating from them than others (outdegree), the same applies when considering arcs pointing to them (indegree). Interestingly, these unequal relationships were also found in our previous paper [15]. Additionally, we identified arcs, or, in other words, probabilistic causality through the network, with more plausibility present, those arcs having the greatest strength. This indicates which relationships between the frailty components are more likely to occur and which nodes have a direct impact on death. In this work, we also provided values for all variables except death in order to calculate the probability of death for each individual, and analyzed whether living and dead people can be correctly separated using these variables. The same process was repeated using the values corresponding to other variables as evidence, and the results were compared.
As expected, variables of the same type are more likely to be linked together. For instance, there are arcs between comorbidities: from Heart_Attack to CHF and Stroke and from High_BP to Diabetes, Heart_Attack, and Stroke. Similarly, there are arcs between Affective Status (AS); for instance, from Depressed to Lone and No_Happy; from Effort to Depressed, Lone, and Tired; from Lone to No_Happy, from the latter to No_Energy; and, finally, from Tired to Depressed, Lone, and No_Energy. There are also arcs between ADL and IADLs, for instance, from Meds to Meals and Finance. There are also arcs linking physical activities, one from Grip to Exercise, and others from Lift to Grip and Walk_out, and another linking self-report of health, from Health to Health_change. On the other hand, there are arcs between variables of different types; for instance, there are arcs pointing to symptoms: from Diabetes (comorbidity) and Depressed (AS) to Lost_weight or from Depressed (AS) to Anorexia. There are also arcs from Self-report of health variables to comorbidities and symptoms, for instance from Health to CLD, Diabetes, and High_BP (comorbidities) and from H_change to Anorexia, Bed, and Lost_weight (symptoms). Similarly, there are AS variables linked to physical health, for instance from Lift to Depressed. These allow us to perceive the complexity of the relationships within all components forming the frailty index.
As stated before, some nodes seem to be more relevant than others, and such importance should be considered in the index calculation, since they are all taken together as if they have the same impact. Apart from the highest number of connections (indegree, outdegree, and their sum) and the analysis of arcs with the highest strength to be present and in its direction, the identification of nodes that are connected to death can be used to determine the most relevant items comprising the FI.
The node with the highest number of arcs (in or out) is a report of current health compared to two years ago. Global health status, as measured by self-assessment, is a robust predictor of mortality and chronic morbidity, as well as a very inclusive measure of health, reflecting aspects relevant to survival which are not covered by other health indicators [25,26,27,28].
Functional impairment has long been an essential measure of disability in aging studies and in clinical practice to assess care needs. It is commonly measured using Activities of Daily Living (ADLs) and Instrumental Activities of Daily Living (IADLs). ADLs functions are essential for an individual’s self-care, whereas IADLs functions are more concerned with self-reliant functioning in each environment [29].
From the directed graph induced by the set of ancestors of the Dead node (Figure 2), we identified that the node corresponding to difficulty getting in or out of a chair, which is an ADL, has the highest outdegree of all the variables and is the initial node in all the directed trajectories to the Dead node. This feature agrees with the fact that the act of transferring is basic and critical in ADLs [30]. Many of the ADLs and IADLs, such as eating, toileting, shopping, and cooking require an initial act of transfer to or from a sitting position before the performance of the activity. This importance is recognized in many scales including the Barthel Index [31] and its modifications [32] whereby a higher weightage is given to transfers compared to the other ADLs. In other instruments, such as the Functional Independence Measure [33], there are 13 motor items, of which there are three types of transfers: transfer to bed/chair, transfer to a shower/bathtub, and transfer to a toilet; and thus, the ADL ‘transfer’ is triple the weightage of other ADLs.
On the other hand, several studies have shown that self-rating of health is a strong predictor of mortality, especially in the elderly [25,34,35], therefore, it is not surprising that this node belongs to the set of ancestors of the Dead node. The importance of self-rated health for morbidity has also been studied due to its relation to mental health, chronic cardiovascular diseases, and diabetes [36,37,38], which are major contributors to morbidity and mortality worldwide. Hence, as expected, depression, high blood pressure, and diabetes also belong to the set of ancestors of the Dead node.
High blood pressure has long been recognized as an independent risk factor for fatal and nonfatal vascular events [39], leading to heart disease, stroke, and kidney failure. If left uncontrolled, hypertension can lead to a heart attack, an enlargement of the heart, and eventually heart failure [40,41]. In Mexico, cardiovascular disease is the most important cause of death; it is responsible for approximately 162,000 deaths a year, nearly 23% of the total. Of these, complications of high blood pressure account for more than 80,000 deaths every year [42]. Therefore, as seen in Figure 1, there were arcs from high blood pressure to heart attack and stroke. Similarly, heart attack was linked to chronic heart failure, which can be understood since all participants who reported CHF in this study also suffered a heart attack [43].
Diabetes is also associated with an increased risk of complications including retinopathy, kidney disease, limb amputation, heart disease, and stroke [44,45]. In Mexico, diabetes is responsible for 9% of deaths each year [42]. High blood pressure and diabetes are associated with each other, but whether a direct causal effect links the two is unclear. Some studies have shown that diabetes is causal for hypertension, but the impact of hypertension on the development of diabetes has provided conflicting findings [46,47,48]. Interestingly, according to our network, there is an arc from high blood pressure to diabetes with strength above 0.8. Hypertension and diabetes have etiological aspects in common [49], and often co-exist in the same individual [50]; diabetes is more frequent in hypertensive than normotensive subjects [48,51,52]. For our study, 3252 individuals reported having only hypertension, 1475 reported having both conditions, and 919 participants reported having only diabetes. Therefore, there is rationale to suspect that hypertension may cause incident diabetes, but further investigation is needed.
As shown in Figure 2, depression, worsening health status in the last two years, and diabetes are linked to unintentional weight loss (Lost_weight). Unintentional weight loss is common among elderly people and is associated with adverse outcomes and age-related diseases such as sarcopenia [53]. Among several physiologic, psychological, and social risk factors for involuntary weight loss, depression and intake of medications for cardiac and endocrine illnesses have been associated with it [54].
Only Shop and Lost_weight point directly to the Dead node (Figure 1 and Figure 2). Since there are several arcs pointing to these two variables, this does not mean that they only determine the probabilities associated with death when we provide values to other variables. However, probabilistically, it means that the Dead variable is conditionally independent to all other variables except Shop and Lost_weight (non-descendants) given Shop and Lost_weight; in other words, the other variables are linked to Dead through Shop and Lost_weight. Considering the relationship between weight loss and death, unintentional weight loss may reflect disease severity or undiagnosed illness [53]. Weight loss of 4–5% or more of body weight within one year, or 10% or more over 5–10 years or longer, is associated with increased mortality, morbidity, or both [53,54]. In frail elderly populations, even small weight loss (e.g., 1 kg [55], or 3% of body weight [56]), may be significant. The relationship between the Shop and Dead nodes is discussed below.
As seen in Figure 3, when considering the arcs with the highest strength, greater than or equal to 0.8 for both the presence of an arc and its direction, three independent clusters emerge. Of course, 0.8 was an arbitrary value and results could vary using other values. However, we thought this could be a valid value to identify the most plausible arcs, since at least 80% of the networks derived from each bootstrap sample include these arcs. In cluster B, all the nodes linked with Dead (directly or indirectly) are IADLs (nodes in the arcs going from difficulty shopping to the nodes representing difficulty taking medications, managing finances, and preparing hot meals) and ADLs (nodes in the arc from difficulty preparing hot meals to difficulty eating).
In this sense, many ADLs and IADLs are conventionally scored by summing up the responses to individual items on the scale to yield a total score. Despite the popularity of this method, some issues make it difficult to interpret [57], since the total-score method weights each item equally, which assumes that all items represent equal levels of severity. It has been suggested [58] that the eight items in the IADL scale could be placed on a hierarchy of ‘difficulty’, with ‘shopping’ the most discriminatory item differentiating well between patients of different levels of ability. ‘Shopping’, ‘food preparation’, and ‘medicine’ were found to be the most ‘difficult’ abilities to continue performing after a disease in patients with dementia and therefore those lost earliest. When ADLs are combined with IADLs, they better describe the spectrum of disability for a broader range of people [59] and it was also found that when combined [60,61], ‘Shopping’ is placed second in the difficulty hierarchy (first place was taken by ‘Do Heavy Cleaning’ or ‘Cutting Toenails’, which were not available in the data set we used to obtain the FI); thus, its direct relationship with the Dead node makes sense.
Cluster C in Figure 3 relates ‘difficulty walking a block’ (physical activity) with ADLs (nodes in the arcs going from the physical activities ‘difficulty walking a block’ to ‘difficulty using the toilet’ and ‘walking around a room’) and ADL’s (arc going from ‘difficulty grooming’ to ‘difficulty using the toilet’). Clusters B and C contain 8 of the 11 ADLs and IADLs included in the FI.
On the other hand, Cluster A, which is the largest, contains two ADLs: ‘difficulty getting in/out of a chair’ (which is the node with the highest outdegree, linked with 10 nodes) and ‘difficulty up/down one flight of stairs’. The node corresponding to ‘difficulty dressing’ is the only one of the included ADLs and IADLs not appearing within the arcs with the highest strength (though it is weakly linked to Groom, Shop, Stairs, In_out_chair, Lift, and Walk_out). It is also noticeable that in this cluster, the self-rated health nodes (Health and H_change) connect the affective status nodes with all the rest (i.e., in the underlying graph of the digraph, Health and H_change form a set of vertices separating affective status from the other nodes).
Surprisingly, Cancer was found to be marginally independent to all other variables. When analyzing the network structure before considering any threshold, i.e., before obtaining the average network, there were arcs to and from Cancer. In particular, the arc with the highest strength, for both presence and direction, was from ‘help dressing’ (Dress) to Cancer with values of 0.4 and 0.925, respectively. Thus, if we had used a threshold of 0.4 for the presence of an arc, it would have appeared. In fact, the direct association between Cancer and Dead was quite low, though significant (Pearson or Phi correlation of 0.060, p-value < 0.001), thus indicating that perhaps at most an indirect relationship with the Dead node could exist, even though this relationship likely exists through variables not considered for our analyses.
Of course, the network structure should be carefully evaluated. For each bootstrap sample, a different network structure was obtained, but in the end, only one was chosen after eliminating arcs and directions appearing less frequently. In this sense, this process allowed us to obtain more reliable relationships between variables, decreasing at the same time over-parametrization. Even so, we performed a 5-fold cross-validation with different network structures: the Bayesian network obtained through the bootstrap process, a network obtained without the bootstrap process, an empty graph, and a random digraph, obtaining an expected log-likelihood loss (the lower value, the better) of 11.53, 11.48, 13.38, and 13.12, respectively. Hence, we obtained one of the best performances, at least as good as the one corresponding to a network with more arcs, with the advantage that the bootstrap network is more representative of true relationships.
When considering evidence provided by all nodes except Dead, people that died were more correctly assigned using all nodes than when only two nodes, Walk_out and Health, or even the nine most connected nodes, were used. This means that the information provided by all deficits is important for identifying the characteristics that people who died possessed.
However, since the sensitivity obtained through our model is 56%, it means that we are not completely characterizing what separates dead from living people, at least using the chosen deficits, which could mean that there are other important deficits that could be taken into account, though this could be relevant to our data set only. It is noticeable that when the FI by itself is used, the sensitivity increases by almost 5%, which is surprising considering that it is just an average, but FI has proved to be successful to separate dead and living people when compared with other models [62,63,64]. This does not mean that the FI is the best available form to distinguish between dead and living people, but that with the defined deficits and in our population, the FI had slightly better results in terms of sensitivity. Even so, identifying barely 56% or 60% of dead individuals can seem not to be as accurate as desired, and in any case, a classifier considering other aspects is needed. When a network was fitted with only arcs from each variable to the dead node (naïve Bayes), we observed that in our selected model there was higher accuracy (72.7% vs. 74.6%), higher specificity (73.3% vs. 74.6%), and lower sensitivity (61.8% vs. 56.1%). Since, in our model, only a few variables directly point to the dead node, this result indicates that the relationship between all nodes is relevant, even obtaining slightly better results than those derived from a model in which all nodes point only to the dead node. In this sense, if we wanted to create a classifier, we probably should include other type of variables, e.g., socio-economic, molecular, or demographic. In terms of Bayesian networks, we could possibly generate arcs guided more closely by experts instead of depending on algorithms, and work in the framework of supervised learning (creation of classifiers), i.e., using training and test sets, comparing with different classification models, using k-fold validation methods, etc. This analysis is out of the scope of this work and corresponds to further research. On the other hand, the relationships and relevance of certain nodes in terms of their connection and probabilistic causality, identified in this and our previous paper, could serve to improve the FI by modifying it as a weighted average, but this also requires further analyses.
Using samples concerning different populations, subpopulations (e.g., men and women), and time could also help to foster a better understanding of the real phenomenon, not only in terms of which causal relationships are or are not present between deficits in different populations, but also in terms of which variables composing the FI should be used when trying to separate dead and living people. This is also future work.
One limitation of our work is that we are not considering possible censoring as in survival analysis. We are only considering survival at a fixed time point (2015); thus, we are not considering that death occurs at different time points and that survival time could add relevant information. Additionally, all variables are self-reported, and thus some information could be inaccurate. A bootstrap process was used to improve the robustness of the structural learning process; even so, causality should be carefully interpreted, since some arbitrary directions or arcs could be obtained that do not represent how variables are related in the real world. In this sense, digraphs should be acyclic, which could have some effects on our final results; for instance, obtaining a directed edge in a specific direction or not allowing the presence of an arc in one direction only to satisfy this property. Even so, this effect perhaps could be reduced after obtaining networks from each bootstrap sample. Additionally, without cycles, feedback is not allowed, eliminating effects that can be increased when a variable is part of a directed cycle. Of course, our results could also depend on the sample size, since as the sample size increases, the presence of new arcs or different relationships between variables could occur. Finally, we used a group of variables as components forming the FI, those recommended by the creators of the index; however, if we had used others, we do not know whether the results could have been different.
5. Conclusions
By using averaged Bayesian networks, we were able to identify causal relationships between deficits comprising the FI. We derived that not all deficits are similarly related. For instance, a report of current health compared to two years ago was the most connected node. Difficulty getting in or out of a chair was the node with the greatest number of arcs parting from it, and the node from which all directed trajectories to the Dead node start. When considering the strength of the relationships derived from a resampling process, arcs with a strength in their presence of 0.8 and over, we identified three clusters of nodes, two of them mostly involving ADL and IADLs. Only two nodes point directly to the Dead node, difficulty shopping and weight loss, though there are several directed trajectories joining some nodes (14 nodes) to the Dead node. All of these results seem plausible from a clinical perspective. Dead people are identified in at most 61%, independently or not of the use of the Bayesian network with evidence propagation and the variables used in the model. This suggests that the FI is not a good classifier, at least in our data set, even though the FI has been found to be relevant to explaining mortality, this feature having a different task than classification. The latter suggests that other variables should be considered in order to obtain a good classifier, improving the correct classification of dead people. Finally, it might be useful to fit similar models into other populations and subpopulations to determine whether the results are consistent.
Author Contributions
Conceptualization, R.R.-A.; methodology, R.R.-A.; software, R.R.-A.; validation, R.R.-A. and L.P.-R.; formal analysis, R.R.-A.; investigation, R.R.-A. and L.P.-R.; resources, R.R.-A. and L.P.-R.; data curation, R.R.-A. and L.P.-R.; writing—original draft preparation, R.R.-A. and L.P.-R.; writing—review and editing, R.R.-A., J.C.G.-V., C.G.-P., L.M.G.-R. and L.P.-R.; visualization, R.R.-A., J.C.G.-V. and L.P.-R.; supervision, R.R.-A.; project administration, R.R.-A.; funding acquisition, L.P.-R. All authors have read and agreed to the published version of the manuscript.
Funding
The publication of this paper was supported by Instituto Nacional de Geriatría, México.
Data Availability Statement
Conflicts of Interest
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
Appendix A
Table A1.
Syntaxis to create each variable used in this study.
| Variable Description (Name) | MHAS Variable | Coding of the Variable | Syntaxis to Generate Variables |
|---|---|---|---|
| Help dressing (Dress) | h13_12 Because of health problems, difficulty dressing self | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF | Dress = h13_12_d_2 1 Yes if h13_12 = 1|h13_12 = 6|h13_12 = 7 0 No if h13_12 = 2 |
| Help getting in/out of a chair (In_out_chair) | h5_12 Because of health problems, difficulty getting up from chair | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF | In_out_chair = h5_12_d_2 1 Yes if h5_12 = 1|h5_12 = 6|h5_12 = 7 0 No if h5_12 = 2 |
| Help walking around the room (Walk) | h15a_12 Because of health problems, difficulty walking | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Walk = h15d_12_d 1 Yes if (h15a_12 = 1|h15a_12 = 6|h15a_12 = 7) & h15d_12 = 1 0 No if h1_12 = 2 & h4_12 = 2 & h5_12 = 2 & h8_12 = 2 & h9_12 = 2 & h10_12 = 2 & h11_12 = 2 & h12_12 = 2 & h13_12 = 2|h15a_12 = 2|h15d_12 = 2 |
| h15d_12 Someone helps you walk across room | 1 Yes 2 No 8 RF 9 DK | ||
| Help eating (Eat) | h17a_12 Because of health problems, difficulty eating or cutting | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Eat = h17d_12_d 1 Yes if (h17a_12 = 1|h17a_12 = 6|h17a_12 = 7) & h17d_12 = 1 0 No if h1_12 = 2 & h4_12 = 2 & h5_12 = 2 & h8_12 = 2 & h9_12 = 2 & h10_12 = 2 & h11_12 = 2 & h12_12 = 2 & h13_12 = 2 OR h17a_12 = 2 OR h17d_12 = 2 |
| h17d_12 Does someone help you eat your food? | 1 Yes 2 No 8 RF 9 DK | ||
| Help grooming (Groom) | h16a_12 Because of health problems, difficulty bathing | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Groom = h16d_12_d 1 Yes if (h16a_12 = 1 | h16a_12 = 6 | h16a_12 = 7) & h16d_12 = 1 0 No if h1_12 = 2 & h4_12 = 2 & h5_12 = 2 & h8_12 = 2 & h9_12 = 2 & h10_12 = 2 & h11_12 = 2 & h12_12 = 2 & h13_12 = 2 OR h16a_12 = 2 OR h16d_12 = 2 |
| h16d_12 Does someone help you to bathe or shower? | 1 Yes 2 No 8 RF 9 DK | ||
| Help using toilet (Toilet) | h19a_12 Because of health problems, difficulty going to the bathroom | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Toilet = h19d_12_d 1 Yes if (h19a_12 = 1 | h19a_12 = 6 | h19a_12 = 7) & h19d_12 = 1 0 No if h1_12 = 2 & h4_12 = 2 & h5_12 = 2 & h8_12 = 2 & h9_12 = 2 & h10_12 = 2 & h11_12 = 2 & h12_12 = 2 & h13_12 = 2 OR h19a_12 = 2 OR h19d_12 = 2 |
| h19d_12 Does someone help you use the toilet, get on/off? | 1 Yes 2 No 8 RF 9 DK | ||
| Help up/down 1 flight of stairs (Stairs) | h6_12 Because of health problems, difficulty with flights of stairs | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Stairs = h7_12_d_2 h7_12_d = 1 if h7_12 = 1 h7_12_d = 0 if h6_12 = 2 | h7_12 = 2 1 Yes if h7_12_d = 1 | h7_12 = 6 0 No if h7_12_d = 0 |
| h7_12 Because of health problems, difficulty with 1 flight of stairs | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | ||
| Help lifting 10 pounds (Lift) | h11_12 Because of health problems, difficulty carrying objects | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Lift = h11_12_d_2 1 Yes if h11_12 = 1 | h11_12 = 6 0 No if h11_12 = 2 |
| Help shopping groceries (Shop) | h27a_12 Difficulty shopping | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Shop = h27c_12_d_2 h27c_12_d = 1 if h27c_12 = 1 h27c_12_d = 0 if h27a_12 = 2|h27c_12 = 2 1 Yes if h27c_12_d = 1|h27a_12 = 6| h27a_12 = 7 0 No if h27c_12_d = 0 |
| h27c_12 Does anyone help you shop for groceries? | 1 Yes 2 No | ||
| Help with preparing hot meal (Meals) | h26a_12 Difficulty preparing hot food | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF | Meals = h26c_12_d_2 h26c_12_d = 1 if h26c_12 = 1 h26c_12_d = 0 if h26a_12 = 2 | h26c_12 = 2 1 Yes if h26c_12_d = 1 | h26a_12 = 6 | h26a_12 = 7 0 No if h26c_12_d = 0 |
| h26c_12 Does anyone help you prepare a hot meal? | 1 Yes 2 No 8 RF 9 DK | ||
| Help taking medication (Meds) | h28a_12 Difficulty taking medications | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF | Meds = h28c_12_d_2 h28c_12_d = 1 if h28c_12 = 1 h28c_12_d = 0 if h28a_12 = 2 | h28c_12 = 2 1 Yes if h28c_12_d = 1 | h28a_12 = 6 | h28a_12 = 7 0 No if h28c_12_d = 0 |
| h28c_12 Does anyone help you take medications? | 1 Yes 2 No | ||
| Help with finances (Finance) | h29a_12 Difficulty managing money | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Finance = h29c_12_d_2 h29c_12_d = 1 if h29c_12 = 1 h29c_12_d = 0 if h29a_12 = 2 | h29c_12 = 2 1 Yes if h29c_12_d = 1 | h29a_12 = 6 | h29a_12 = 7 0 No if h29c_12_d = 0 |
| h29c_12 Does anyone help you manage your money? | 1 Yes 2 No 8 RF 9 DK | ||
| Compared to 2 years ago: Unintentional change in weight (Lost_weight) | c64_12 Compared to 2 years ago: respondent’s change in weight | 1 Has increased 5 kilos/more 2 Has decreased 5 kilos/more 3 Has remained more/less the same 8 RF 9 DK | Lost_weight = c64_12_d 1 Yes if c64_12 = 2 & c65_12 = 2 0 No if c64_12 = 1 | c64_12 = 3 |
| c65_12 Compared to 2 years ago: respondent’s change in exercise or diet | 1 Yes 2 No 8 RF 9 DK | ||
| Self-rating of health (Health) | c1_12 Global self-reported quality of health | 1 Excellent 2 Very good 3 Good 4 Fair 5 Poor 8 RF 9 DK | Health = c1_12_d 1 Yes if c1_12 = 5 0 No if c1_12 = 1 | c1_12 = 2 | c1_12 = 3 | c1_12 = 4 |
| Compared to 2 years ago: Report your current health (H_change) | c2a_12 Compared to 2 years ago: report your current health | 1 Much better 2 Somewhat better 3 More or less the same 4 Somewhat worse 5 Much worse 9 DK | H_change = c2a_12_d 1 Yes if c2a_12 = 4 | c2a_12 = 5 0 No if c2a_12 = 1 | c2a_12 = 2 | c2a_12 = 3 |
| Last 12 months: Number of days in bed… due to sickness/injury (Bed) | c73_12 Last 12 months: Respondent’s number of days in bed… due to sickness/injury | Bed = c73_12_d 1 Yes if c73_12 >= 1 & c73_12 <= 365 0 No if c73_12 = 0 | |
| Within the past week: Felt tired (Tired) | c49_8_12 Within the past week: Respondent felt tired | 1 Yes 2 No 8 RF 9 DK | Tired = c49_8_12_d 1 Yes if c49_8_12 = 1 0 No if c49_8_12 = 2 |
| Difficulty walking a block (Walk_out) | h1_12 Because of health problems, difficulty walking blocks | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | Walk_out = h3_12_d_2 h3_12_d = 1 if h3_12 = 1 h3_12_d = 0 if h1_12 = 2 | h3_12 = 2 1 Yes if h3_12 = 6 | h3_12 = 7 | h3_12_d = 1 0 No if h3_12_d = 0 |
| h3_12 Because of health problems, difficulty walking a block | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | ||
| Feel everything is an effort (Effort) | c49_2_12 Within the past week: respondent experienced difficulty performing | 1 Yes 2 No 8 RF 9 DK | Effort = c49_2_12_d 1 Yes if c49_2_12 = 1 0 No if c49_2_12 = 2 |
| Feel depressed (Depressed) | c49_1_12 Within the past week: respondent was depressed | 1 Yes 2 No 8 RF 9 DK | Depressed = c49_1_12_d 1 Yes if c49_1_12 = 1 0 No if c49_1_12 = 2 |
| Feel happy (No_happy) | c49_4_12 Within the past week: respondent was happy | 1 Yes 2 No 8 RF 9 DK | No_happy = c49_4_12_d 1 Yes if c49_4_12 = 2 0 No if c49_4_12 = 1 |
| Feel lonely (Lone) | c49_5_12 Within the past week: respondent was lonely | 1 Yes 2 No 8 RF 9 DK | Lone = c49_5_12_d 1 Yes if c49_5_12 = 1 0 No if c49_5_12 = 2 |
| Feel energetic (No_energy) | c49_9_12 Within the past week: respondent was energetic | 1 Yes 2 No 8 RF 9 DK | No_energy = c49_9_12_d 1 Yes if c49_9_12 = 2 0 No if c49_9_12 = 1 |
| Hypertension/high blood pressure (High_BP) | c4_12 Has a physician diagnosed hypertension/high blood pressure? | 1 Yes 2 No 8 RF 9 DK | High_BP = c4_12_d 1 Yes if c4_12 = 1 0 No if c4_12 = 2 |
| Heart attack (Heart_attack) | c22a_12 Has a physician ever told respondent of a heart attack? | 1 Yes 2 No 8 RF 9 DK | Heart_attack = c22a_12_d 1 Yes if c22a_12 = 1 0 No if c22a_12 = 2 |
| Heart failure (CHF) | c25b_12 Has a physician ever told respondent of a heart failure? | 1 Yes 2 No 9 DK | CHF = c25b_12_d 1 Yes if c25b_12 = 1 0 No if c22a_12 = 2 | c25b_12 = 2 |
| Stroke (Stroke) | c26_12 Ever/last 2 years: has a physician told respondent of a stroke? | 1 Yes 2 No 8 RF 9 DK | Stroke = c26_12_d 1 Yes if c26_12 = 1 0 No if c26_12 = 2 |
| Cancer (in the last 10 years) (Cancer) | c12_12 Has a physician diagnosed respondent cancer (last 10 years)? | 1 Yes 2 No 8 RF 9 DK | Cancer = c12_12_d 1 Yes if c12_12 = 1 last 10 years 0 No if c12_12 = 2 last 10 years |
| Diabetes (Diabetes) | c6_12 Has a physician diagnosed respondent with diabetes? | 1 Yes 2 No 8 RF 9 DK | Diabetes = c6_12_d 1 Yes if c6_12 = 1 0 No if c6_12 = 2 |
| Arthritis/rheumatism (Arthritis) | c32_12 Has a physician diagnosed respondent with arthritis/rheumatism? | 1 Yes 2 No 8 RF 9 DK | Arthritis = c32_12_d 1 Yes if c32_12 = 1 0 No if c32_12 = 2 |
| Respiratory illness (CLD) | c19_12 Has a physician diagnosed respondent with respiratory illness? | 1 Yes 2 No 8 RF 9 DK | CLD = c19_12_d 1 Yes if c19_12 = 1 0 No if c19_12 = 2 |
| Compared to 2 years ago: respondent reports his/her memory quality (Memory) | e1b_12 Compared to 2 years ago: respondent reports his/her memory quality | 1 Better 2 About the same 3 Worse 8 RF 9 DK | Memory = e1b_12_d 1 Yes if e1b_12 = 3 0 No if e1b_12 <= 2 |
| Respondent’s dominant hand strength (Grip) | c69a_12 Respondent’s dominant hand strength | 1 Very strong 2 Somewhat strong 3 Somewhat weak 4 Very weak 8 RF 9 DK | Grip = c69a_12_d 1 Yes if c69a_12 = 3 | c69a_12 = 4 0 No if c69a_12 <= 2 |
| Anorexia: Last 2 years: Loss of appetite (Anorexia) | c70_12 Last 2 years: Respondent’s loss of appetite | 1 Often 2 Sometimes 3 Rarely 8 RF 9 DK | Anorexia = c70_12_d 1 Yes if c70_12 = 1 0 No if c70_12 = 2 | c70_12 = 3 |
| Exercise: Last 2 years: Exercise or hard physical work >= 3 times a week (Exercise) | c50b_12 Last 2 years: Respondent’s exercise or hard physical work >= 3 times a week | 1 Yes 2 No 8 RF 9 DK | Exercise = c50b_12_d 1 Yes if c50b_12 = 2 0 No if c50b_12 = 1 |
| Died between 2012 and 2015 (Dead) | fallecido_15 Died between 2012 and 2015 | 1 Yes 0 No | Dead 1 Yes if fallecido_15 = 1 0 No if fallecido_15 = 0 |
| * Filter participants aged 50 or more years old Variable for age 2012 is age_12, then age_12_cat = 1 if age_12 >= 50, age_12_cat = 0 if age_12 < 50 Filter: age_12_cat = 1 | |||
| ** Eliminate second or third wives or husbands Variable for subject identification is np, np = 10 original subject, np = 20 original spouse Filter: np = 10 | np = 20 | |||
| *** The following variables have the same coding: h1_12 Because of health problems, difficulty walking blocks h4_12 Because of health problems, difficulty staying seated h5_12 Because of health problems, difficulty getting up from chair h8_12 Because of health problems, difficulty sitting up h9_12 Because of health problems, difficulty lifting arms h10_12 Because of health problems, difficulty pushing or pulling h11_12 Because of health problems, difficulty carrying objects h12_12 Because of health problems, difficulty picking up a coin h13_12 Because of health problems, difficulty dressing self | 1 Yes 2 No 6 Can’t do 7 Doesn’t do 8 RF 9 DK | ||
Abbreviations refer to: don’t know (DK) and refused (RF).
Appendix B
Table A2.
Arcs and strength, for both the presence and direction, corresponding to the averaged Bayesian network concerning frailty components and death.
Table A2.
Arcs and strength, for both the presence and direction, corresponding to the averaged Bayesian network concerning frailty components and death.
| Arc from | Arc to | Strength (Presence) | Strength (Direction) | Arcs with Greatest Strength (Value = 1 if Presence and Direction >= 0.8) |
|---|---|---|---|---|
| Depressed | Anorexia | 0.91 | 1.00 | 1 |
| Depressed | Lone | 1.00 | 0.94 | 1 |
| Depressed | No_Happy | 1.00 | 0.99 | 1 |
| Diabetes | Lost_weight | 1.00 | 0.99 | 1 |
| Effort | Depressed | 1.00 | 0.85 | 1 |
| Effort | Health | 0.93 | 0.85 | 1 |
| Effort | Lone | 1.00 | 0.94 | 1 |
| Grip | Arthritis | 0.99 | 0.99 | 1 |
| Grip | Memory | 0.99 | 0.97 | 1 |
| Groom | Toilet | 0.87 | 0.91 | 1 |
| H_change | Bed | 0.86 | 1.00 | 1 |
| H_change | Memory | 1.00 | 1.00 | 1 |
| Health | Diabetes | 1.00 | 0.96 | 1 |
| Health | H_change | 1.00 | 0.99 | 1 |
| Health | No_Happy | 0.97 | 0.91 | 1 |
| Heart_attack | CHF | 1.00 | 1.00 | 1 |
| High_BP | Diabetes | 1.00 | 0.99 | 1 |
| High_BP | Heart_attack | 1.00 | 1.00 | 1 |
| In_out_chair | Arthritis | 1.00 | 1.00 | 1 |
| In_out_chair | Health | 0.81 | 0.90 | 1 |
| In_out_chair | Memory | 0.99 | 1.00 | 1 |
| Lift | Grip | 1.00 | 0.98 | 1 |
| Lift | High_BP | 0.84 | 0.99 | 1 |
| Meals | Eat | 0.95 | 0.98 | 1 |
| Meds | Finance | 1.00 | 0.94 | 1 |
| No_Happy | No_Energy | 1.00 | 1.00 | 1 |
| Shop | Dead | 0.85 | 1.00 | 1 |
| Shop | Finance | 1.00 | 0.97 | 1 |
| Shop | Meals | 1.00 | 0.84 | 1 |
| Shop | Meds | 0.89 | 0.89 | 1 |
| Stairs | Grip | 0.81 | 0.98 | 1 |
| Tired | Depressed | 1.00 | 0.84 | 1 |
| Tired | H_change | 0.80 | 0.95 | 1 |
| Tired | Lone | 1.00 | 0.94 | 1 |
| Tired | No_Energy | 1.00 | 1.00 | 1 |
| Walk_out | Toilet | 0.94 | 0.98 | 1 |
| Walk_out | Walk | 0.99 | 0.95 | 1 |
| Bed | Heart_attack | 0.68 | 1.00 | 0 |
| Depressed | H_change | 0.81 | 0.62 | 0 |
| Depressed | High_BP | 0.76 | 0.99 | 0 |
| Depressed | Lost_weight | 0.52 | 1.00 | 0 |
| Dress | Groom | 0.79 | 0.89 | 0 |
| Dress | Shop | 0.99 | 0.55 | 0 |
| Dress | Walk_out | 0.79 | 0.65 | 0 |
| Effort | Grip | 0.69 | 0.97 | 0 |
| Effort | H_change | 0.51 | 0.97 | 0 |
| Effort | Lift | 0.75 | 0.47 | 0 |
| Effort | Stairs | 0.99 | 0.50 | 0 |
| Effort | Tired | 1.00 | 0.51 | 0 |
| Exercise | No_Energy | 0.99 | 0.77 | 0 |
| Grip | Exercise | 0.62 | 1.00 | 0 |
| Grip | No_Energy | 0.62 | 0.90 | 0 |
| Groom | Eat | 0.64 | 0.98 | 0 |
| Groom | Walk | 0.84 | 0.54 | 0 |
| H_change | Anorexia | 0.57 | 1.00 | 0 |
| H_change | Arthritis | 0.57 | 1.00 | 0 |
| H_change | Grip | 0.80 | 0.78 | 0 |
| H_change | Lost_weight | 0.77 | 1.00 | 0 |
| Health | CLD | 0.54 | 0.98 | 0 |
| Health | High_BP | 0.67 | 1.00 | 0 |
| Heart_attack | Stroke | 0.57 | 0.64 | 0 |
| High_BP | Stroke | 0.63 | 1.00 | 0 |
| In_out_chair | CLD | 0.54 | 0.95 | 0 |
| In_out_chair | Dress | 1.00 | 0.67 | 0 |
| In_out_chair | Effort | 0.96 | 0.52 | 0 |
| In_out_chair | H_change | 0.79 | 0.99 | 0 |
| In_out_chair | Lift | 1.00 | 0.60 | 0 |
| In_out_chair | Stairs | 1.00 | 0.53 | 0 |
| In_out_chair | Tired | 1.00 | 0.54 | 0 |
| Lift | Bed | 0.75 | 0.99 | 0 |
| Lift | Depressed | 0.61 | 0.62 | 0 |
| Lift | Dress | 0.99 | 0.64 | 0 |
| Lift | Health | 0.54 | 0.84 | 0 |
| Lift | Shop | 1.00 | 0.70 | 0 |
| Lift | Walk_out | 1.00 | 0.69 | 0 |
| Lone | No_Happy | 1.00 | 0.51 | 0 |
| Lost_weight | Dead | 0.69 | 1.00 | 0 |
| Meals | Groom | 0.85 | 0.58 | 0 |
| Meds | Meals | 0.95 | 0.19 | 0 |
| Shop | Exercise | 0.66 | 0.94 | 0 |
| Shop | Groom | 0.54 | 0.86 | 0 |
| Stairs | Dress | 1.00 | 0.67 | 0 |
| Stairs | Groom | 0.56 | 0.92 | 0 |
| Stairs | High_BP | 0.78 | 0.99 | 0 |
| Stairs | Shop | 0.96 | 0.69 | 0 |
| Stairs | Walk_out | 1.00 | 0.70 | 0 |
| Tired | Grip | 0.75 | 0.96 | 0 |
| Toilet | Eat | 0.59 | 0.98 | 0 |
| Toilet | Walk | 0.81 | 0.17 | 0 |
| Walk_out | Anorexia | 0.52 | 1.00 | 0 |
| Walk_out | Exercise | 0.70 | 0.93 | 0 |
| Walk_out | Health | 0.98 | 0.75 | 0 |
| Walk_out | Shop | 1.00 | 0.65 | 0 |
The arcs with the greatest strength, greater than or equal to 0.8, for both the presence and direction of arcs, correspond to the first 37 (last column with a value of one). The colors in the first two columns represent the classification of nodes: red: Dead; yellow: AS (Affective Status); light blue: Symptoms; gray: SRH (Self-rated health); green: ADL-IADL (activities of daily living and instrumental activities of daily living); orange: Physical Health; pink: Comorbidities CLD; navy blue: Cognition. Nodes with the presence and direction of arcs strength of 0.8 and more are colored in light green in the third and fourth columns. Nodes only with the presence of arcs strength of 0.8 or more are colored in light orange in the third column. Nodes only with the direction of arcs strength of 0.8 or more are colored in light blue in the fourth column.
References
- Clegg, A.; Young, J.; Iliffe, S.; Rikkert, M.O.; Rockwood, K. Frailty in elderly people. Lancet 2013, 381, 752–762. [Google Scholar] [CrossRef]
- Baztán, J.J.; De La Puente, M.; Socorro, A. Frailty, functional decline and mortality in hospitalized older adults. Geriatr. Gerontol. Int. 2017, 17, 664–666. [Google Scholar] [CrossRef] [PubMed]
- Rockwood, K.; Hogan, D.; Macknight, C. Conceptualisation and Measurement of Frailty in Elderly People. Drugs Aging 2000, 17, 295–302. [Google Scholar] [CrossRef]
- Searle, S.D.; Mitnitski, A.; Gahbauer, E.A.; Gill, T.M.; Rockwood, K. A standard procedure for creating a frailty index. BMC Geriatr. 2008, 8, 24. [Google Scholar] [CrossRef] [PubMed]
- Rockwood, K.; Mitnitski, A. Frailty in Relation to the Accumulation of Deficits. J. Gerontol. Ser. A 2007, 62, 722–727. [Google Scholar] [CrossRef]
- Rockwood, K.; Andrew, M.; Mitnitski, A. A Comparison of Two Approaches to Measuring Frailty in Elderly People. J. Gerontol. Ser. A 2007, 62, 738–743. [Google Scholar] [CrossRef] [PubMed]
- Rockwood, K.; Song, X.; MacKnight, C.; Bergman, H.; Hogan, D.B.; McDowell, I.; Mitnitski, A. A global clinical measure of fitness and frailty in elderly people. CMAJ 2005, 173, 489–495. [Google Scholar] [CrossRef] [PubMed]
- Lachmann, R.; Stelmach-Mardas, M.; Bergmann, M.M.; Bernigau, W.; Weber, D.; Pischon, T.; Boeing, H. The accumulation of deficits approach to describe frailty. PLoS ONE 2019, 14, e0223449. [Google Scholar] [CrossRef]
- Theou, O.; Rockwood, M.R.; Mitnitski, A.; Rockwood, K. Disability and co-morbidity in relation to frailty: How much do they overlap? Arch. Gerontol. Geriatr. 2012, 55, e1–e8. [Google Scholar] [CrossRef]
- Mitnitski, A.B.; Rutenberg, A.D.; Farrell, S.; Rockwood, K. Aging, frailty and complex networks. Biogerontology 2017, 18, 433–446. [Google Scholar] [CrossRef]
- Farrell, S.G.; Mitnitski, A.B.; Rockwood, K.; Rutenberg, A.D. Network model of human aging: Frailty limits and information measures. Phys. Rev. E 2016, 94, 052409. [Google Scholar] [CrossRef]
- Farrell, S.G.; Mitnitski, A.B.; Theou, O.; Rockwood, K.; Rutenberg, A.D. Probing the network structure of health deficits in human aging. Phys. Rev. E 2018, 98, 032302. [Google Scholar] [CrossRef]
- Rutenberg, A.D.; Mitnitski, A.B.; Farrell, S.G.; Rockwood, K. Unifying aging and frailty through complex dynamical networks. Exp. Gerontol. 2018, 107, 126–129. [Google Scholar] [CrossRef] [PubMed]
- Taneja, S.; Mitnitski, A.B.; Rockwood, K.; Rutenberg, A.D. Dynamical network model for age-related health deficits and mortality. Phys. Rev. E 2016, 93, 022309. [Google Scholar] [CrossRef]
- García-Peña, C.; Ramírez-Aldana, R.; Parra-Rodriguez, L.; Gomez-Verjan, J.C.; Pérez-Zepeda, M.U.; Gutiérrez-Robledo, L.M. Network analysis of frailty and aging: Empirical data from the Mexican Health and Aging Study. Exp. Gerontol. 2019, 128, 110747. [Google Scholar] [CrossRef]
- Wong, R.; Michaels-Obregon, A.; Palloni, A. Cohort Profile: The Mexican Health and Aging Study (MHAS). Int. J. Epidemiol. 2017, 46, e2. [Google Scholar] [CrossRef]
- Lauritzen, S.L. Graphical Models; Oxford Statistical Science Series; The Clarendon Press: Oxford, UK, 1996. [Google Scholar]
- Bondy, J.A.; Murty, U.S.R. Graph Theory with Applications; The Macmillan Press Ltd.: New York, NY, USA, 1976. [Google Scholar]
- Højsgaard, S.; Edwards, D.; Lauritzen, S. Graphical Models with R; Springer: Boston, MA, USA, 2012; ISBN 978-1-4614-2298-3. [Google Scholar]
- Nagarajan, R.; Scutari, M.; Lèbre, S. Bayesian Networks in R: With Applications in Systems Biology; Springer: New York, NY, USA, 2013; ISBN 978-1-4614-6445-7. [Google Scholar]
- Cowell, R.G.; Dawid, P.; Lauritzen, S.L.; Spiegelhalter, D.J. Probabilistic Networks and Expert Systems; Springer: New York, NY, USA, 1999; ISBN 0-387-98767-3. [Google Scholar]
- Pearl, J. Fusion, propagation, and structuring in belief networks. Artif. Intell. 1986, 29, 241–288. [Google Scholar] [CrossRef]
- Scutari, M. Learning Bayesian Networks with the Bnlearn R Package. J. Stat. Softw. 2010, 35, 1–22. [Google Scholar] [CrossRef]
- Robin, X.; Turck, N.; Hainard, A.; Tiberti, N.; Lisacek, F.; Sanchez, J.-C.; Müller, M. pROC: An open-source package for R and S+ to analyze and compare ROC curves. BMC Bioinform. 2011, 12, 77. [Google Scholar] [CrossRef]
- Idler, E.L.; Benyamini, Y. Self-Rated Health and Mortality: A Review of Twenty-Seven Community Studies. J. Health Soc. Behav. 1997, 38, 21–37. [Google Scholar] [CrossRef]
- Idler, E.L.; Russell, L.B.; Davis, D. Survival, Functional Limitations, and Self-rated Health in the NHANES I Epidemiologic Follow-up Study, 1992. Am. J. Epidemiol. 2000, 152, 874–883. [Google Scholar] [CrossRef] [PubMed]
- MacKenbach, J.P.; Simon, J.G.; Looman, C.W.; Joung, I.M. Self-assessed health and mortality: Could psychosocial factors explain the association? Int. J. Epidemiol. 2002, 31, 1162–1168. [Google Scholar] [CrossRef]
- Vuorisalmi, M.; Lintonen, T.; Jylhä, M. Global self-rated health data from a longitudinal study predicted mortality better than comparative self-rated health in old age. J. Clin. Epidemiol. 2005, 58, 680–687. [Google Scholar] [CrossRef] [PubMed]
- Gobbens, R.J. Associations of ADL and IADL disability with physical and mental dimensions of quality of life in people aged 75 years and older. PeerJ 2018, 6, e5425. [Google Scholar] [CrossRef] [PubMed]
- Sien, N.Y.; Jung, H. Assessment of the Six Activities of Daily Living in Adults. Singap. Fam Physician 2012, 38, 26–36. [Google Scholar]
- Mahoney, F.I.; Barthel, D.W. Functional evaluation: The Barthel Index. Md. State Med. J. 1965, 14, 61–65. [Google Scholar]
- Shah, S.; Vanclay, F.; Cooper, B. Improving the sensitivity of the Barthel Index for stroke rehabilitation. J. Clin. Epidemiol. 1989, 42, 703–709. [Google Scholar] [CrossRef] [PubMed]
- Granger, C.V.; Hamilton, B.B.; Keith, R.A.; Zielezny, M.; Sherwin, F.S. Advances in functional assessment for medical rehabilitation. Top. Geriatr. Rehabil. 1986, 1, 59–74. [Google Scholar] [CrossRef]
- Jylhä, M. What is self-rated health and why does it predict mortality? Towards a unified conceptual model. Soc. Sci. Med. 2009, 69, 307–316. [Google Scholar] [CrossRef]
- Mossey, J.M.; Shapiro, E. Self-rated health: A predictor of mortality among the elderly. Am. J. Public Health 1982, 72, 800–808. [Google Scholar] [CrossRef]
- Böhme, S.; Renneberg, B. Predicting Self-Rated Health in Diabetes and Chronic Heart Failure—A Multiple Mediation Model. Front. Public Health 2015, 3, 266. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Peña, M.E.Y.; Barrera, V.H.; Cordero, X.F.; Gil de Miguel, A.; Pérez, M.R.; Andres, A.L.-D.; Jiménez-García, R. Self-perception of health status, mental health and quality of life among adults with diabetes residing in a metropolitan area. Diabetes Metab. 2010, 36, 305–311. [Google Scholar] [CrossRef]
- Ho, S.Y.; Mak, K.K.; Thomas, G.N.; Schooling, M.; Fielding, R.; Janus, E.D.; Lam, T.H. The relation of chronic cardiovascular diseases and diabetes mellitus to perceived health, and the moderating effects of sex and age. Soc. Sci. Med. 2007, 65, 1386–1396. [Google Scholar] [CrossRef]
- Jamrozik, K. Age-specific relevance of usual blood pressure to vascular mortality: A meta-analysis of individual data for one million adults in 61 prospective studies. Lancet 2002, 360, 1903–1913. [Google Scholar] [CrossRef]
- Bowling, C.B.; Davis, B.R.; Luciano, A.; Simpson, L.M.; Sloane, R.; Pieper, C.F.; Einhorn, P.T.; Oparil, S.; Muntner, P. Sustained blood pressure control and coronary heart disease, stroke, heart failure, and mortality: An observational analysis of allhat. J. Clin. Hypertens. 2019, 21, 451–459. [Google Scholar] [CrossRef]
- World Health Organization. A Global Brief on Hypertension: Silent Killer, Global Public Health Crisis: World Health Day 2013; World Health Organization: Geneva, Switzerland, 2013. [Google Scholar]
- Institute for Health Metrics and Evaluation—IHME GBD Compare Data Visualization. 2019. Available online: http://vizhub.healthdata.org/gbd-compare/ (accessed on 15 October 2020).
- Almeida, O.P.; Tamai, S. Congestive heart failure and cognitive functioning amongst older adults. Arq. Neuro-Psiquiatr. 2001, 59, 324–329. [Google Scholar] [CrossRef] [PubMed]
- Chen, R.; Ovbiagele, B.; Feng, W. Diabetes and Stroke: Epidemiology, Pathophysiology, Pharmaceuticals and Outcomes. Am. J. Med Sci. 2016, 351, 380–386. [Google Scholar] [CrossRef] [PubMed]
- Kaul, K.; Tarr, J.M.; Ahmad, S.I.; Kohner, E.M.; Chibber, R. Introduction to Diabetes Mellitus. Diabetes 2013, 771, 1–11. [Google Scholar] [CrossRef]
- Emdin, C.A.; Anderson, S.G.; Woodward, M.; Rahimi, K. Usual Blood Pressure and Risk of New-Onset Diabetes. J. Am. Coll. Cardiol. 2015, 66, 1552–1562. [Google Scholar] [CrossRef] [PubMed]
- Sun, D.; Zhou, T.; Heianza, Y.; Li, X.; Fan, M.; Fonseca, V.A.; Qi, L. Type 2 Diabetes and Hypertension. Circ. Res. 2019, 124, 930–937. [Google Scholar] [CrossRef] [PubMed]
- Yang, X.; Chen, J.; Pan, A.; Wu, J.H.; Zhao, F.; Xie, Y.; Wang, Y.; Ye, Y.; Pan, X.-F.; Yang, C.-X. Association between Higher Blood Pressure and Risk of Diabetes Mellitus in Middle-Aged and Elderly Chinese Adults. Diabetes Metab. J. 2020, 44, 436–445. [Google Scholar] [CrossRef] [PubMed]
- Moreno, B.; De Faria, A.P.; Ritter, A.M.V.; Yugar, L.B.T.; Ferreira-Melo, S.E.; Amorim, R.; Modolo, R.; Fattori, A.; Yugar-Toledo, J.C.; Coca, A.; et al. Glycated hemoglobin correlates with arterial stiffness and endothelial dysfunction in patients with resistant hypertension and uncontrolled diabetes mellitus. J. Clin. Hypertens. 2018, 20, 910–917. [Google Scholar] [CrossRef]
- Ferrannini, E.; Cushman, W.C. Diabetes and hypertension: The bad companions. Lancet 2012, 380, 601–610. [Google Scholar] [CrossRef]
- Conen, D.; Ridker, P.M.; Mora, S.; Buring, J.E.; Glynn, R.J. Blood pressure and risk of developing type 2 diabetes mellitus: The Women’s Health Study. Eur. Heart J. 2007, 28, 2937–2943. [Google Scholar] [CrossRef] [PubMed]
- Hayashi, T.; Tsumura, K.; Suematsu, C.; Endo, G.; Fujii, S.; Okada, K. High normal blood pressure, hypertension, and the risk of type 2 diabetes in Japanese men. The Osaka Health Survey. Diabetes Care 1999, 22, 1683–1687. [Google Scholar] [CrossRef] [PubMed]
- Alibhai, S.M.; Greenwood, C.; Payette, H. An approach to the management of unintentional weight loss in elderly people. Can. Med. Assoc. J. 2005, 172, 773–780. [Google Scholar] [CrossRef] [PubMed]
- Stajkovic, S.; Aitken, E.M.; Holroyd-Leduc, J. Unintentional weight loss in older adults. Can. Med. Assoc. J. 2011, 183, 443–449. [Google Scholar] [CrossRef] [PubMed]
- Payette, H.; Coulombe, C.; Boutier, V.; Gray-Donald, K. Weight Loss and Mortality Among Free-Living Frail Elders: A Prospective Study. J. Gerontol. Ser. A 1999, 54, M440–M445. [Google Scholar] [CrossRef] [PubMed]
- Tully, C.L.; Snowdon, D.A. Weight Change and Physical Function in Older Women: Findings from the Nun Study. J. Am. Geriatr. Soc. 1995, 43, 1394–1397. [Google Scholar] [CrossRef]
- Reise, S.P.; Henson, J.M. A Discussion of Modern Versus Traditional Psychometrics As Applied to Personality Assessment Scales. J. Pers. Assess. 2003, 81, 93–103. [Google Scholar] [CrossRef] [PubMed]
- McGrory, S.; Shenkin, S.; Austin, E.; Starr, J.M. Lawton IADL scale in dementia: Can item response theory make it more informative? Age Ageing 2014, 43, 491–495. [Google Scholar] [CrossRef] [PubMed]
- Kempen, G.; Myers, A.; Powell, L. Hierarchical structure in ADL and IADL: Analytical assumptions and applications for clinicians and researchers. J. Clin. Epidemiol. 1995, 48, 1299–1305. [Google Scholar] [CrossRef]
- Fieo, R.; Watson, R.; Deary, I.J.; Starr, J.M. A Revised Activities of Daily Living/Instrumental Activities of Daily Living Instrument Increases Interpretive Power: Theoretical Application for Functional Tasks Exercise. Gerontology 2010, 56, 483–490. [Google Scholar] [CrossRef]
- Suurmeijer, T.P.; Doeglas, D.M.; Moum, T.; Briançon, S.; Krol, B.; Sanderman, R.; Guillemin, F.; Bjelle, A.; Heuvel, W.J.V.D. The Groningen Activity Restriction Scale for measuring disability: Its utility in international comparisons. Am. J. Public Health 1994, 84, 1270–1273. [Google Scholar] [CrossRef]
- Kojima, G.; Iliffe, S.; Walters, K. Frailty index as a predictor of mortality: A systematic review and meta-analysis. Age Ageing 2018, 47, 193–200. [Google Scholar] [CrossRef]
- Veld, L.P.M.O.H.; Beurskens, A.J.H.M.; de Vet, H.C.W.; van Kuijk, S.M.J.; Hajema, K.; Kempen, G.I.J.M.; van Rossum, E. The ability of four frailty screening instruments to predict mortality, hospitalization and dependency in (instrumental) activities of daily living. Eur. J. Ageing 2019, 16, 387–394. [Google Scholar] [CrossRef] [PubMed]
- Stow, D.; Matthews, F.; Barclay, S.; Iliffe, S.; Clegg, A.; De Biase, S.; Robinson, L.; Hanratty, B. Evaluating frailty scores to predict mortality in older adults using data from population based electronic health records: Case control study. Age Ageing 2018, 47, 564–569. [Google Scholar] [CrossRef]
- Mexican Health and Aging Study. Available online: http://www.mhasweb.org/ (accessed on 6 July 2022).
Figure 1.
Averaged Bayesian network associated with frailty components and the dead node considering a bootstrap sample of 100, using a hc algorithm with BIC score for each sample. Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: No_Happy, Lone, No energy, Depressed, Tired, and Effort); light blue: symptoms (Anorexia, Bed, and Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and instrumental activities of daily living: In_out_chair, Stairs, Shop, Dress, Walk, Eat, Groom, Meals, Meds, Finance, and Toilet); orange: physical health (Grip, Exercise, Lift, and Walk_out); pink: comorbidities (CLD, Stroke, Cancer, CHF, Arthritis, Heart_Attack, Diabetes, and High_BP); navy blue: cognition (Memory). A color scale distributes edge colors according to strength of the relationship between the variables: yellow–green–purple (from 0.5 to 1.0, respectively).
Figure 1.
Averaged Bayesian network associated with frailty components and the dead node considering a bootstrap sample of 100, using a hc algorithm with BIC score for each sample. Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: No_Happy, Lone, No energy, Depressed, Tired, and Effort); light blue: symptoms (Anorexia, Bed, and Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and instrumental activities of daily living: In_out_chair, Stairs, Shop, Dress, Walk, Eat, Groom, Meals, Meds, Finance, and Toilet); orange: physical health (Grip, Exercise, Lift, and Walk_out); pink: comorbidities (CLD, Stroke, Cancer, CHF, Arthritis, Heart_Attack, Diabetes, and High_BP); navy blue: cognition (Memory). A color scale distributes edge colors according to strength of the relationship between the variables: yellow–green–purple (from 0.5 to 1.0, respectively).
Figure 2.
Directed graph induced by the set of ancestors of the Dead node (nodes from which there are directed paths to Dead). Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: Depressed, Tired, and Effort); light blue: symptoms (Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and Instrumental activities of daily living: In_out_chair, Stairs, Shop, and Dress); orange: physical health (Lift and Walk_out); pink: comorbidities (Diabetes and High_BP).
Figure 2.
Directed graph induced by the set of ancestors of the Dead node (nodes from which there are directed paths to Dead). Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: Depressed, Tired, and Effort); light blue: symptoms (Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and Instrumental activities of daily living: In_out_chair, Stairs, Shop, and Dress); orange: physical health (Lift and Walk_out); pink: comorbidities (Diabetes and High_BP).
Figure 3.
Network associated with the averaged Bayesian network for the frailty components and dead node induced by those arcs with a strength (both presence and direction) of 0.8 and more. Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: No Happy, Lone, No energy, Depressed, Tired, and Effort); light blue: symptoms (Anorexia, Bed, and Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and instrumental activities of daily living: In_out_chair, Stairs, Shop, Walk, Eat, Groom, Meals, Meds, Finance, and Toilet); orange: physical health (Grip, Lift, and Walk_out); pink: comorbidities (CHF, Arthritis, Heart_Attack, Diabetes, and High_BP); navy blue: cognition (Memory). (A–C) correspond to the three connected components associated with the network. Three clusters are independent of each other; since strength is 0.8 or more, arcs are in the same colour.
Figure 3.
Network associated with the averaged Bayesian network for the frailty components and dead node induced by those arcs with a strength (both presence and direction) of 0.8 and more. Nodes are colored according to the following classification: black: Dead; yellow: AS (Affective Status: No Happy, Lone, No energy, Depressed, Tired, and Effort); light blue: symptoms (Anorexia, Bed, and Lost_weight); gray: SRH (Self-rated health: Health and H_change); green: ADL-IADL (activities of daily living and instrumental activities of daily living: In_out_chair, Stairs, Shop, Walk, Eat, Groom, Meals, Meds, Finance, and Toilet); orange: physical health (Grip, Lift, and Walk_out); pink: comorbidities (CHF, Arthritis, Heart_Attack, Diabetes, and High_BP); navy blue: cognition (Memory). (A–C) correspond to the three connected components associated with the network. Three clusters are independent of each other; since strength is 0.8 or more, arcs are in the same colour.
Figure 4.
(a) ROC curve model for evidence consisting of the values of all variables except Dead; (b) ROC curve model for evidence consisting of the values of variables Walk_out and Health.
Figure 4.
(a) ROC curve model for evidence consisting of the values of all variables except Dead; (b) ROC curve model for evidence consisting of the values of variables Walk_out and Health.
Table 1.
Prevalence of the 35 deficits included in the Frailty Index and death in the total sample.
| Deficit Description (Name) | n = 10,983 Frequency (%) |
|---|---|
| Help dressing (Dress) | 983 (8.95) |
| Help getting in/out of a chair (In_out_chair) | 3264 (29.72) |
| Help walking around the room (Help_Walk) | 160 (1.46) |
| Help eating (Eat) | 101 (0.92) |
| Help grooming (Groom) | 150 (1.37) |
| Help using toilet (Toilet) | 128 (1.17) |
| Help up/down one flight of stairs (Stairs) | 2594 (23.62) |
| Help lifting 10 pounds (Lift) | 2557 (23.28) |
| Help shopping groceries (Shop) | 865 (7.88) |
| Help with preparing a hot meal (Meals) | 630 (5.74) |
| Help taking medication (Meds) | 162 (1.48) |
| Help with finances (Finance) | 169 (1.54) |
| Lost five kilos or more of weight in the last two years (Lost_weight) | 2375 (21.62) |
| Poor/regular self-rated health (Health) | 1315 (11.97) |
| Compared to 2 years ago much worse or worse self-rated health (H_change) | 3149 (28.67) |
| Spent one day or more in bed due to sickness or injury (Bed) | 1941 (17.67) |
| Within the past week: Felt tired (Tired) | 6402 (58.29) |
| Difficulty walking a block (Walk_out) | 1353 (12.32) |
| Feel everything is an effort (Effort) | 3810 (34.69) |
| Feel depressed (Depressed) | 3705 (33.73) |
| Not feeling happy (No_Happy) | 2187 (19.91) |
| Feel lonely (Lone) | 3196 (29.10) |
| Feel without energy (No_Energy) | 5639 (51.34) |
| Hypertension/high blood pressure (High_BP) | 4727 (43.04) |
| Heart attack (Heart_attack) | 378 (3.44) |
| Heart failure (CHF) | 207 (1.88) |
| Stroke (Stroke) | 203 (1.85) |
| Cancer (in the last 10 years) (Cancer) | 227 (2.07) |
| Diabetes (Diabetes) | 2394 (21.80) |
| Arthritis or rheumatism (Arthritis) | 1490 (13.57) |
| Respiratory illness (CLD) | 639 (5.82) |
| Worse memory quality compared to two years ago (Memory) | 2342 (21.32) |
| Weak dominant hand strength (Grip) | 2566 (23.36) |
| Loss of appetite in the last 2 years (Anorexia) | 515 (4.69) |
| Not doing exercise or hard physical work at least3 times a week (Exercise) | 6647 (60.52) |
| Died between 2012 and 2015 (Dead) | 574 (5.23) |
The procedure to obtain and categorize the FI variables is shown in Table A1.
Table 2.
Indegree, outdegree, and sum of both measures for the averaged Bayesian network associated with frailty components and dead.
Table 2.
Indegree, outdegree, and sum of both measures for the averaged Bayesian network associated with frailty components and dead.
| Deficit | Indegree + Outdegree | Outdegree | Indegree |
|---|---|---|---|
| H_change | 11 | 6 | 5 |
| In_out_chair | 10 | 10 | 0 |
| Lift | 10 | 8 | 2 |
| Shop | 10 | 6 | 4 |
| Health | 9 | 5 | 4 |
| Walk_out | 9 | 6 | 3 |
| Effort | 9 | 8 | 1 |
| Depressed | 9 | 6 | 3 |
| Grip | 9 | 4 | 5 |
| Stairs | 8 | 6 | 2 |
| Groom | 7 | 3 | 4 |
| Tired | 7 | 5 | 2 |
| High_BP | 7 | 3 | 4 |
| Dress | 6 | 3 | 3 |
| Toilet | 4 | 2 | 2 |
| Meals | 4 | 2 | 2 |
| Lost_weight | 4 | 1 | 3 |
| No_Happy | 4 | 1 | 3 |
| Lone | 4 | 1 | 3 |
| No_Energy | 4 | 0 | 4 |
| Heart_attack | 4 | 2 | 2 |
| Exercise | 4 | 1 | 3 |
| Walk | 3 | 0 | 3 |
| Eat | 3 | 0 | 3 |
| Meds | 3 | 2 | 1 |
| Bed | 3 | 1 | 2 |
| Diabetes | 3 | 1 | 2 |
| Arthritis | 3 | 0 | 3 |
| Memory | 3 | 0 | 3 |
| Anorexia | 3 | 0 | 3 |
| Finance | 2 | 0 | 2 |
| Stroke | 2 | 0 | 2 |
| CLD | 2 | 0 | 2 |
| Dead | 2 | 0 | 2 |
| CHF | 1 | 0 | 1 |
| Cancer | 0 | 0 | 0 |
Variables are ordered from the greatest to the lowest indegree and outdegree (11 for Health_change and 0 for Cancer, respectively).
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Ramírez-Aldana, R.; Gomez-Verjan, J.C.; García-Peña, C.; Gutiérrez-Robledo, L.M.; Parra-Rodríguez, L. Understanding Frailty: Probabilistic Causality between Components and Their Relationship with Death through a Bayesian Network and Evidence Propagation. Electronics 2022, 11, 3001. https://doi.org/10.3390/electronics11193001
AMA Style
Ramírez-Aldana R, Gomez-Verjan JC, García-Peña C, Gutiérrez-Robledo LM, Parra-Rodríguez L. Understanding Frailty: Probabilistic Causality between Components and Their Relationship with Death through a Bayesian Network and Evidence Propagation. Electronics. 2022; 11(19):3001. https://doi.org/10.3390/electronics11193001
Chicago/Turabian StyleRamírez-Aldana, Ricardo, Juan Carlos Gomez-Verjan, Carmen García-Peña, Luis Miguel Gutiérrez-Robledo, and Lorena Parra-Rodríguez. 2022. "Understanding Frailty: Probabilistic Causality between Components and Their Relationship with Death through a Bayesian Network and Evidence Propagation" Electronics 11, no. 19: 3001. https://doi.org/10.3390/electronics11193001
APA StyleRamírez-Aldana, R., Gomez-Verjan, J. C., García-Peña, C., Gutiérrez-Robledo, L. M., & Parra-Rodríguez, L. (2022). Understanding Frailty: Probabilistic Causality between Components and Their Relationship with Death through a Bayesian Network and Evidence Propagation. Electronics, 11(19), 3001. https://doi.org/10.3390/electronics11193001
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