An empirical comparative study on biological age estimation algorithms

Mechanisms of Ageing and Development 131 (2010) 69–78

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An empirical comparative study on biological age estimation algorithms with an application of Work Ability Index (WAI) Il Haeng Cho a,*, Kyung S. Park a, Chang Joo Lim b a b

Human Centered Systems Design Laboratory, Department of Industrial & Systems Engineering, KAIST, 305-701, Republic of Korea Department of Game and Multimedia Engineering, Korea Polytechnic University, 429-793, Republic of Korea

A R T I C L E I N F O

A B S T R A C T

Article history: Received 22 March 2009 Received in revised form 15 November 2009 Accepted 4 December 2009 Available online 11 December 2009

In this study, we described the characteristics of five different biological age (BA) estimation algorithms, including (i) multiple linear regression, (ii) principal component analysis, and somewhat unique methods developed by (iii) Hochschild, (iv) Klemera and Doubal, and (v) a variant of Klemera and Doubal’s method. The objective of this study is to find the most appropriate method of BA estimation by examining the association between Work Ability Index (WAI) and the differences of each algorithm’s estimates from chronological age (CA). The WAI was found to be a measure that reflects an individual’s current health status rather than the deterioration caused by a serious dependency with the age. Experiments were conducted on 200 Korean male participants using a BA estimation system developed principally under the concept of non-invasive, simple to operate and human function-based. Using the empirical data, BA estimation as well as various analyses including correlation analysis and discriminant function analysis was performed. As a result, it had been confirmed by the empirical data that Klemera and Doubal’s method with uncorrelated variables from principal component analysis produces relatively reliable and acceptable BA estimates. ß 2009 Elsevier Ireland Ltd. All rights reserved.

Keywords: Biological Age Work Ability Index Uncorrelated biomarker Multiple linear regression Principal component analysis

1. Introduction There have been various attempts on assessing biological age (BA) by a range of computational algorithms. However, few studies are reported on direct comparison of these algorithms, revealing which algorithm is most reliable and acceptable as to be implemented on a BA estimation system. BA is an abstract concept. Although the concept of BA can be found in many scientific papers throughout last half a century, a concrete and precise definition that can be generally accepted is difficult to find. Klemera and Doubal (2006) explained it as a quantity expressing the ‘‘true global state’’ of ageing organism, or ‘‘true life expectancy’’ of the individual better than corresponding chronological age (CA). As it is obvious, CA does not correlate perfectly with BA. Two people may be of the same age, but differ in their mental and physical capacities. BA describes a person’s general condition at a particular time of the CA. It is determined by the individual’s physical, psychological, and social characteristics, rather than chronology. Thus, the BA of a person could be defined as the CA at which ‘most normal’ people are in the physical state of that person.

* Corresponding author at: 3rd floor, 121-12, Samsungdong, Kangnamgu, Seoul, 135-509, Korea. Tel.: +82 10 9855 0777; fax: +82 42 350 3110. E-mail address: [email protected] (I.H. Cho). 0047-6374/$ – see front matter ß 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.mad.2009.12.001

The common assess to BA estimation is through measurements of various age-dependent variables, so-called biomarkers, and aggregating these measures into a value in units of years with some computational algorithms. The algorithms include multiple linear regression (MLR) methods, principal component analysis (PCA), and somewhat unique and novel methods as Hochschild (1989a,b, 1994) and Klemera and Doubal had proposed. Using the data obtained from experiments, this paper examines these methods as well as some variations of them, and ultimately, proposes the most suitable method for valid BA estimation. The details of each method are discussed in the following sections. Validation of BA has always been a controversial issue, as the term itself is an abstract concept, and the absence of the true value in the reality makes it difficult to evaluate the validity of the estimated BA. (This is not to deny the existence of the conceptual value of BA.) Ingram (1988) and McClearn (1997) offered inspiration how to deal with the validation issue. They asserted that the validation of BA is ascertained by examining the validity of biomarkers from which the BA is estimated. Ingram pointed out that two types of validity should be established in the development of biomarkers of ageing; they are construct validity and predictive validity. Construct validity refers to how well a candidate biomarker reflects the construct, and predictive validity refers to the usefulness of a biomarker in longitudinal studies (Ingram, 1988). The focus of this paper is not on the selection of biomarkers (which is still very important), but rather on the validity of the final

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estimated value of BA with various computational algorithms. Therefore, instead of examining whether individual biomarkers are actually measuring ageing process, the present authors propose the use of Work Ability Index (WAI) as an alternative measure taken in the real world to be examined for the correspondence with the attributes of BA estimates (BAE). The objective of this study is to find the most appropriate method of BA estimation by examining the association between WAI and the differences of each algorithm’s BAE from CA. 2. Materials and methods

anthropometric/morphologic, sensorimotor and cognitive variables. One physiological variable, the pulmonary function, however were included as it showed strongest correlation with CA, and as it is feasible to make a simple measuring device of such with the assistance of the latest technology advance. To utilize the supporting results from past researches, we selected biomarkers that are somewhat similar to the ones of Hochschild (1989a,b, 1994), as they seemed to meet the criteria mentioned above. However, some modifications and additions, especially for cognitive tests, were made (see Table 1). Cognitive tests were carefully selected to measure human performances of the specific cognitive functional outcome. For a simple representation, the selected biomarkers were classified as the three; physical functions (variables starting with ‘p’), cognitive functions (with ‘c’) and reaction times (with ‘r’). Total of 12 tests were administered and 16 variables were measured.

2.1. Selection of biomarkers

2.2. Experiments

Anstey et al. (1996) published an outstanding review of extensive studies related to measurement of BA and empirical findings of the correlation of more than 170 biomarkers with the ageing rates. According to the authors, the biomarkers are classified into seven categories—anthropometric/morphologic, sensorimotor, cognitive, psychosocial, physiological/biomedical, behavioral and dentition. From author to author of BA-related research, the reasons given for the choice of biomarkers vary. Some of the rationales are that the biomarkers; showed significant change with age; were not too highly correlated with another biomarker; were quantitative and cover essential areas of human functional capacity; were convenient to measure and calculate; were used in previous studies, and thus, provide relevant information (Hollingsworth et al., 1965; Ries, 1974; Webster and Logie, 1976; Borkan and Norris, 1980; Chodzko-Zajko and Ringel, 1987; Nakamura et al., 1988). From the findings of Anstey et al., biomarkers that have strong associations (r > 0.4) with CA are grip strength, simple reaction time, visual accommodation, visual acuity, auditory acuity, digit symbol, systolic blood pressure, diastolic blood pressure, vital capacity, and forced expiratory volume. Particularly, measures of pulmonary and auditory function showed the strongest correlation with CA, whereas psychosocial variables show the least association. The specific aim for the development of a BA estimation system in our study was to develop a system that is (1) non-invasive, (2) simple to operate and (3) based on human functions. We developed a system that is simple in its means of measurement, i.e. ‘noninvasive’. Non-invasive means a medical procedure which does not penetrate mechanically, nor break the skin or a body cavity, i.e. it does not require an incision into the body. Some medically oriented BA estimation systems require either extracting blood from the subjects, or employing burdening medical equipments that could trouble some of the subjects. This implies exclusion of biomedical, or dentistry measures, along with the psychosocial variables that showed least association. ‘Simple to operate’ involves development in such a way that the system does not lay burden on participants both with time and usage, and moreover be designed to be operative by the subject alone. This is important, especially for performance oriented tests, because it can eliminate inclusion of variance influenced by the motivation provided by the instructor. ‘Human function-based’ implies implemented criteria for the selection of biomarkers, which characterizes the system itself. As we had eliminated biomedical, dentistry, and psychosocial variables, the biomarker variables for our system were left with mainly

Biomarkers are strongly sex-dependent, as well as race-dependent as they are to reflect the ageing rate of population to be studied. Voitenko and Toka (1983) and Uttley and Crawford (1994) reported differences in correlations of biomarkers between men and women, and thus suggested that BAE should be calculated independently for men and women. If different ethnic groups are studied (which is not the case in this study,) then the analyses should be carried out separately as well. Although ageing is a process that occurs over the entire life span, we are concerned with biological changes that occur after sexual maturation. Ruiz-Torres et al. (1990) developed a theoretical vitality function as a reference curve, based on experimental results of examining concentration of substances from blood samples of 226 healthy individuals. According to their study, the maximum vitality is reached approximately at the age of 30 years and shows steady decline thereafter (see Fig. 1). With the support of the findings and other BA-related studies, it is reasonable to impose restrictions on the estimation of BA for those aged more than 30 years. Originally, the experiment was planned to cover till the age of 85, but many of participants over the age of 70 failed to successfully complete the cognitive tests, and thus, were excluded. Due to limited local resource, only Korean male participants are studied so far. However, to ensure enough number of subjects for significant statistical analyses, 200 participants, uniformly distributed in the range of 30–70 years of age (n = 25 for each interval of 5 years of age), contributed in our experiment. There were no missing data as the experiment proceeded only on the completion of each test. However, seven of the participants were detected as outliers from residual analysis of the MLR method, and thus were excluded. Table 3 shows the age distribution of 193 participants whose data are used in the analyses hereinafter. Making the most of the mobility feature of the developed biomarker testing system, the experiment was conducted in various locations in Korea, including universities, affiliated offices, fitness clubs, hospitals and Jjimjilbang’s (Korean-style sauna or fomentation room). The subjects from the last location, the sauna, were very obliging as they were not pressed for time and had a good interest of their own health. Moreover, such a place offered a population of various age enabling a successful gathering of uniform distribution of the subject’s age for the experiment. Even though the system was developed to be operative by the subject alone, all experiments were conducted in company with an instructor to avoid any error and missing data. Participants were first asked to complete WAI questionnaire with the assistance of an instructor. No burden was placed on the subjects as all the experiments were conducted anonymously, and furthermore, consents were

Table 1 Selected biomarkers. Biomarkers Physical functions Hearing capacity Pulmonary functions Handgrip strength Vibrotactile sensitivity Visual accommodation Cognitive functions Numeric memory Associated memory Topological memory Concentration

Reaction times Acoustic reaction time Visual reaction time Muscular reaction time

Variable names

Brief description (units)

pHAP pFVC pFEV pHGL pHGR pVIB pACM

Highest audible pitch (kHz) Forced vital capacity (0.1 L) Forced expiratory volume in 1 s (0.1 L) Left handgrip strength (10 N) Right handgrip strength (10N ) Response to a vibratory stimulus on a palm (dB) Focal range test using a Landolt ring (0.1 diopter)

cNUM cASS cAwn cTOP cTwn cCON

Visual digit-span memory test (# of digits) Memory test linking names with faces (10 s) Number of mistakes made for cASS (# of errors) Memory test: which picture is at what place (10 s) Number of mistakes made for cTOP (# of errors) Speed test: pointing icons from 1 to 15 sequentially, mixed in random positions (s)

rART rVRT rMRT

Time to respond to an acoustic stimulus (10 ms) Time to respond to a visual stimulus (10 ms) Time to move from a position A to B on a screen (10 ms)

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factor analysis, which only considers the common or shared variance in defining the structure of the variables, it can be used to elucidate the underlying structure by examining the pattern of the factor loadings (Hair et al., 2006). Hofecker et al. (1980), Nakamura et al. (1988), Nakamura and Miyao, 2007), Nakaumra (1991), and MacDonald et al. (2004) are some of the authors who published studies that applied PCA or factor analysis in BA estimation. Nakamura et al.’s approach was somewhat unique as they only used the 1st principal component score as an equation for assessing biological score of age-related changes in physiological functions. In addition to that, they transformed the biological score to T-score using the mean and standard deviation of the CA of the population under study to present the BA in units of years. They showed that the PCA model provides practically useful and theoretically valid BA estimation in contrast with the MLR model. In this study, however, we will use all the components, or factors, as new uncorrelated variables.

Fig. 1. Vitality function versus chronological age of three spanish subpopulations. ‘‘Reprinted from Archives of Gerontology and Geriatrics, January–February; 10(1), Ruiz-Torres A., Agudo A, Vicent D and Beier W, Measuring human aging using a twocompartmental mathematical model and the vitality concept, pp. 72, 1990, with permission from Elsevier.’’. obtained for the use of their data. This is especially important for the WAI which requires highly subjective answers. After being briefed about each test of biomarkers, they were given a trial, and then, the actual test took place. An additional questionnaire, inquiring about the ‘mortality risk factors’ for the implementation of Hochschild’s method (HocM), were asked; however, regrettably only 122 participants were asked for this questionnaire. To complete a set of the experiments for a person, it required approximately 50 min to 1 h. 2.3. BA Estimation algorithms 2.3.1. Multiple linear regression (MLR) The MLR method is the most common and basic approach in BA-related studies (e.g. Hollingsworth et al., 1965; Takeda et al., 1982; Voitenko and Toka, 1983; Dubina et al., 1984; Kroll and Saxtrup, 2000; Bae et al., 2008). In these papers, the BA of a certain individual (BAi) is estimated on the basis of several (m) measured parameters (= biomarker variables) using MLR. It is the sum of which components are a product of the test score x ji ði ¼ 1; . . . ; n; j ¼ 1; . . . ; mÞ of biomarkers in the i-th individual and the coefficient bj. BAi ¼ b0 þ

m X b j x ji

x j ¼ d j þ e j CA

ð j ¼ 1; . . . ; mÞ

(3)

Note that CA is now an independent variable, and biomarker scores xj are the dependent variables. The final step of HocM involves transforming the SBA to BAE in units of years. This is done by applying similar idea of defining Stanford-Binet’s IQ index, which needs an arbitrarily chosen (but reasonably chosen in this case with BA estimation), mean and standard deviation. The author tried to make the distribution of BAE similar to that of age at death of population under study with some compensation for the skewness of the distribution.

(1)

j¼1

The coefficients bj are calculated from the correlations between CA and each of the parameters using least sum of squares. Therefore, BA is estimated as linearly best fitted value of CA, which brings up the controversial issue of the paradox of biomarkers. In the MLR approach, the presumption of Eq. (1) is that BAi is equal to the Predicted_CAi, revealing that CA is used as the dependent variable as shown in Eq. (2). BAi ¼ Predicted CAi ¼ b0 þ

2.3.3. Hochschild’s method (HocM) Hochschild (1989a,b, 1994) developed a nonstandard and lengthy, but yet very specific and apparently reasonable approach which evaluated biomarkers according to their impact on life expectancy or mortality. He proposed the validation criteria as the correlation of biomarker scores with (a) mortality rate, (b) interventions that influence mortality rate and (c) the quality of later life. To quantify these measures into an aggregated value, which he named ‘Composite Validation Variables (CVV)’, he conducted an additional questionnaire inquiring about mortality risk factors such as smoking, type of diet, exercise level, education level and residential district. The Pearson correlation value between CVV and STAj (Standardized Test Age: an intermediate value obtained in HocM for each biomarker variable, j) were substituted as the weighting coefficients of each biomarker when the biomarker scores were to be combined into a single value, Standardized Biological Age (SBA), by a series of calculations like standardizations and weighted summation procedures as described in detail in his papers. The most unique element of HocM compared to the conventional multiple linear regression methods is that it uses regressions for individual biomarkers, so-called, reverse regression technique. As a result, the multiple linear regression of CA on biomarker scores in Eq. (2) is replaced with m simple linear equations of biomarker scores on CA as Eq. (3).

m X b j x ji

(2)

2.3.4. Klemera and Doubal’s method (KDM) An attention-grabbing work is published by Klemera and Doubal (2006). As the title of their paper, ‘a new approach to the concept and computation of biological age’ had been developed by mathematically modeling the BA estimation procedure. Using the mathematical relations among BA, CA and biomarkers, the authors defined BA formally and constructed hypothesis to demonstrate the validation of their work by computer-generated simulations. The merits of the work are in its attempt to find the optimum way of computation for hypothetical BA estimation, and in its applicability for nonlinearity of certain biomarkers. They defined BA and the biomarker score X as the following equations:

j¼1

This is assuming that CA is to be predicted from the measured values of xji of biomarkers. However, CA does not depend on measured values of BMs, but on the calendar. Therefore, it is logically contradictory to make CA the dependent variable and to use a regression equation designed to predict it. This explains the paradox of biomarkers. Many of the past studies sought to find a set of biomarkers that has high magnitude of correlation with CA, and believed the higher the correlation, the greater the reliability of biological age estimation. However, as Ingram (1988) noted, a perfect correlation between a biomarker and CA yields the biomarker as perfectly useless as an alternative to CA as a predictor of anything. In addition to that, the MLR method also encounters criticism for the distortion of the BAE at regression edges, so-called, regression to sample mean; younger individuals than the sample mean are estimated too old and older individuals are estimated too young. Multicollinearity is another concern as it causes unstable and erratic estimation of coefficients, when the independent variables are highly intercorrelated. Correlations of the variables must be studied, as the biomarkers employed in a study often show relatively high correlations among the pairs of them. 2.3.2. Principal component analysis (PCA) PCA is used when the objective is to summarize most of the original information (variance) in a minimum number of factors for prediction purposes. The strength of PCA is that it extracts new variables in a reduced number which are uncorrelated to each other by an orthogonal rotation. As PCA shares similar procedure as common

BA ¼ CA þ RBA ð0; s2BA Þ X ¼ F X ðBAÞ þ

RX ð0; s2X Þ

RBA ð0; s2BA Þ,

(4) (5)

RX ð0; s2X Þ

where are random variables with zero mean and variance s2BA , s2X , respectively, and FX(BA) is the governing function of a biomarker by BA. Combining Eqs. (4) and (5) and assuming that FX is linear function with slope k and intercept q, the following equation is obtained. 2

X ¼ kCA þ q þ Rð0; k s2BA þ s2X Þ

(6)

From Eq. (6), it can be noticed that their method shares similar concept of the reverse regression technique of HocM. Using the mathematically formulated definitions, the authors derived the optimum estimate of BA by minimizing the distance of point determined by values of biomarkers from one-dimensional line (or curve) determined by the regression functions in the space of all biomarkers (refer to their paper for elaborated descriptions). They provided two alternatives for the optimum estimate of BA, one without (Eq. (7)), and one with applying CA as another biomarker, but in a different way as the other biomarkers (Eq. (8)). Pm BAE ¼

2 j¼1 ðx j  q j Þðk j =sX j Þ Pm 2 ðk =s Þ j Xj j¼1

(7)

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I.H. Cho et al. / Mechanisms of Ageing and Development 131 (2010) 69–78

Table 2 Items of the Work Ability Index (WAI).

1 2 3 4 5 6 7

Items

Score range

Current work ability compared with the lifetime best Work ability in relation to the demands of the job Number of current diseases diagnosed by a physician Estimated work impairment due to diseases Sick leave during the past year (12 months) Own prognosis of work ability 2 years from now Mental resources

0–10 2–10 1–7 1–6 1–5 1–7 1–4

‘‘Reprinted from Occupational Medicine, 57(2), Ilmarinen, J, The Work Ability Index (WAI), pp. 160, 2007, with permission of Oxford University Press.’’

Pm BAEC ¼

physical and cognitive function tests are statistically significant at or beyond the 0.1% level. Visual and muscular reaction time (rVRT and rMRT) tests showed relatively less significant level, whereas acoustic reaction time (rART) test was not significant suggesting that the test was not relevant to show age-related changes. Thus, the variable rART is excluded from the analyses hereinafter. By examining the correlation of the biomarker variables with CA, it was assured that tests for hearing capacity (pHAP, r = 0.739), pulmonary function (pFVC, r = 0.616), associated memory (cASS, r = 0.605), topological memory (cTOP, r = 0.642) and concentration (cCON, r = 0.643) show specific age-related changes.

3.2. Results of each algorithm

 q j Þðk j =s2X j Þ þ ðCA=s2BA Þ Pm 2 ðk j =sÞ þ ð1=s2BA Þ

j¼1 ðx j

(8)

2.4. Work Ability Index (WAI) as a validating measure of BA The WAI, developed in the early 80s by researchers of the Finnish Institute of Occupational Health (FIOH), is an instrument used in clinical occupational health and research to assess work ability. It consists of a questionnaire that inquires about the individual’s health status and both physical and mental resources in conjunction with the work demands (Tuomi et al., 1998; Ilmarinen, 2007). Table 2 details the items of the WAI. Numerous research activities (Kloimu¨ller et al., 2000; Tuomi et al., 2001; de Zwart et al., 2002; Radkiewich and Widerszal-Bazyl, 2005; Lin et al., 2006) had been carried out for the validity and reliability of WAI, and the questionnaire had been translated into 25 different languages for the international use in various industries for occupational health surveillance. Besides its major aim to promote the work ability of the employees, the WAI also reveals the participant’s health status numerically by offering an aggregate result in quantity ranging from 7 to 49. Although the final outcome of WAI is the qualitative classification among 4 different classes – poor, moderate, good and excellent – of the individual’s health status according to the score, we intended to use the quantitative measure directly for more sensitive correlation analysis.

3. Results 3.1. Descriptive statistics of the data Table 3 shows the mean and standard deviations of the biomarker variables derived from the experiment. From one-way ANOVA, the results of the significance tests on differences of means among 5-year age groups were obtained. They indicated that all

3.2.1. Multiple linear regression (MLR) The MLR analysis was performed having CA as a dependent variable and 15 biomarker variables as independent variables. In addition to that, careful examinations for outliers and influential points were performed, taking the advantage of various diagnostic tools provided for MLR, such as COVRATIO, DFFITS, Cook’s D, and residual plot diagnostics (Belsley et al., 2004). Seven observations were deleted from the list (thus, n = 193) as they either had higher values of studentized deleted residual than 3, or were detected as outliers rather than influential points from examining the diagnostic statistics mentioned above and partial residual plots. Another powerful diagnostics of MLR is to detect multicollinearity, which is a serious concern in many of the biomarkers employed in BA estimation related studies. Our study is no exception as some of the variables showed high inter-correlations: pFVC and pFEV (r = 0.848), pHGL and pHGR (r = 0.899), cASS and cTOP (r = 0.728), cTOP and cTwn (r = 0.773). With the full MLR model of 15 biomarkers, the adjusted R-square was 0.774 (F = 44.951, p < 0.001) and the standard error of the estimate was 5.51 years. Although the explanatory power of the model is satisfactory, as we had concerned, variance inflation factor (VIF) of the some variables were greater than 5, implicating that the associated regression coefficients are poorly estimated because of the multicollinearity (Montgomery et al., 2006). Subsequently, we decided to remove four variables – pFEV, pHGL, cASS, cTwn – among the inter-correlated variables above and keep the ones with

Table 3 Means and standard deviations of the biomarker variables by 5-year age group, and correlations with CA. Age group

pHAP pFVC pFEV pHGL pHGR pVIB pACM cNUM cASS cAwn cTOP cTwn cCON rART rVRT rMUS a b c d e

30–34

35–39

40–44

45–49

50–54

55–59

60–64

65–69

Total

n = 24

n = 24

n = 25

n = 25

n = 25

n = 23

n = 23

n = 24

n = 193a

F-Ratio

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

Mean

S.D.

14.37 45.54 36.62 40.58 40.23 38.04 53.58 9.62 3.81 2.75 3.15 4.16 11.74 19.07 25.05 10.09

1.43 4.86 3.79 6.67 5.59 2.21 5.86 1.13 1.98 2.06 1.20 3.90 2.27 5.54 4.44 3.48

14.16 43.62 36.12 36.70 37.11 36.95 50.62 8.29 4.67 4.29 3.53 4.91 13.88 21.42 25.47 8.68

1.71 6.83 6.66 5.85 4.99 2.11 7.25 1.87 1.86 3.71 1.05 3.14 2.48 6.77 4.29 2.65

12.28 40.80 33.08 34.59 35.68 37.28 52.04 7.64 6.54 6.40 5.27 8.24 14.04 21.73 26.29 10.31

2.35 5.05 5.17 6.42 5.86 2.09 6.29 1.44 1.94 5.33 2.119 6.39 2.94 5.66 4.38 4.49

11.32 42.36 34.52 37.07 37.78 38.44 50.88 7.64 5.17 5.08 4.11 6.92 14.96 22.05 27.19 9.37

2.78 5.78 5.83 6.48 5.56 2.48 4.96 1.35 1.82 4.37 1.36 4.75 3.31 5.76 4.32 3.72

9.48 38.20 31.24 33.82 34.62 37.24 47.96 7.64 6.27 6.80 4.51 9.08 14.80 21.18 27.02 10.12

2.51 4.38 3.86 5.39 4.93 2.02 7.10 1.44 3.21 4.81 2.03 5.02 2.51 5.97 6.36 4.34

8.13 36.47 29.30 29.93 30.91 36.21 45.30 7.34 9.26 9.87 8.49 12.39 16.32 21.91 26.37 12.02

2.61 6.08 6.22 3.73 3.39 1.75 9.56 2.03 5.67 7.20 5.04 10.27 4.14 6.65 5.74 5.26

8.21 31.95 26.04 30.03 31.19 35.82 40.21 6.30 10.53 9.21 9.30 13.08 18.30 23.42 26.60 13.08

2.27 5.08 5.90 6.50 5.00 2.18 10.60 2.14 4.12 5.15 3.45 7.78 3.50 6.88 4.80 4.63

7.08 33.70 27.33 31.33 32.04 36.16 39.33 6.04 11.40 10.04 10.12 15.79 21.50 22.48 31.85 11.54

2.60 4.70 5.31 4.44 4.48 2.27 11.34 1.23 3.69 5.26 3.35 7.46 3.04 5.86 7.89 5.39

10.66 39.15 31.84 34.32 35.00 37.04 47.58 7.57 7.16 6.76 6.01 9.26 15.66 21.65 26.98 10.62

3.48 6.94 6.48 6.67 5.87 2.28 9.42 1.89 4.16 5.44 3.74 7.38 4.13 6.14 5.66 4.45

Age distribution of 193 Korean male participants after excluding outliers. Significant tests on differences of means among 5-year age groups by one-way ANOVA. Significant at the 0.001 level (2-tailed). Significant at the 0.01 level (2-tailed). Significant at the 0.05 level (2-tailed).

34.91c 18.99c 12.74c 10.03c 10.65c 4.40c 10.52c 11.44c 17.83c 7.23c 24.66c 9.77c 23.16c 0.98 3.59d 2.66e

b

Corr. with CA

0.74c 0.62c 0.54c 0.46c 0.47c 0.27c 0.50c 0.52c 0.61c 0.43c 0.64c 0.50c 0.64c 0.16e 0.26c 0.23d

I.H. Cho et al. / Mechanisms of Ageing and Development 131 (2010) 69–78

higher correlation with CA. We then obtained a model seemingly more stable having all VIF of the variables less than three. The modified model has the adjusted R-square of 0.758 (F = 55.561, p < 0.001) and the standard error of the estimate of 5.71 years. As a result, the BAE as a function of the 11 biomarker variables were expressed by the following equation: BAE ¼ 56:397  1:575ðpHAPÞ  0:365ðpFVCÞ  0:018ðpHGRÞ þ 0:329ðpVIBÞ  0:011ðpACMÞ  0:104ðcNUMÞ þ 0:130ðcAwnÞ þ 0:459ðcTOPÞ þ 0:742ðcCONÞ  0:043ðrVRTÞ þ 0:005ðrMUSÞ:

(9)

Note that the coefficients of pVIB and rVRT have the opposite signs to the signs of their correlation coefficients with CA, which provide evidence of the erroneous estimation of coefficients in the MLR approach. 3.2.2. Principal component analysis (PCA) Another fine approach to eliminate multicollinearity is through PCA with an orthogonal factor rotation. In this study, VARIMAX rotation is used, which seeks to simplify the columns of the factor matrix. As stated earlier, 15 biomarker variables (excluding rART) are used in the initial PCA. However, the variables, pVIB and rMUS showed low communalities, which represent the amount of variance accounted for by the factor solution for each variable. This result agrees with that of the correlation analysis where the two variables showed low correlation with CA in Table 3. Thus, the two variables are additionally excluded from the model for further PCA. The eigen values greater than 1 are used for the threshold value of factor extraction, resulting extraction of three components. The three components accounted for 28.6%, 23.9% and 14.4% of the total variance, respectively. Given the sample size of approximately 200, guidelines for identifying significant factor loadings suggest the loadings should be greater than 0.40 to be significant at the 0.05 level and a power level of 80% (Hair et al., 2006). The factor loadings in this study, as can be seen in the dotted boxes of Table 4, satisfactorily meet the requirement as most of the values are greater than 0.70. Although the variable, pHAP, showed a crossloading on both components 2nd and 3rd, we decided to retain the variable as it was proved to be the one with the highest correlation with CA. The rotated component matrix in Table 4, which is sorted by factor loadings on each component, exhibits a rather surprising

result. Notice that all cognitive functions (cASS, cTOP, cAwn, cTwn, cNUM, cCON) are assigned to the 1st component, and most of the physical functions (pHGL, pHGR, pFEV, pFVC) are to the 2nd. The 3rd component seems to be accounting for functions related to one’s eyes and ears (rVRT, pACM, pHAP). It illustrates the strength of such an analysis to identify the latent dimensions or constructs represented in the original variables. It is also good evidence that the biomarkers were well defined and the measurements were taken in orderly fashion to reflect the characteristics of the functions in interest. With new variables (= factor scores), which are derived from linear combinations of the standardized values of the original variables and the factor score coefficients on each component, MLR was performed having CA as the dependent variable. Note that these variables produced by PCA, represent each component and are perfectly uncorrelated to each other, which is a fruitful outcome especially for such biomarker variables that are likely to be inter-correlated. The following equation estimates the BA using the variables from PCA: BAE ¼ 49:734 þ 6:164ðFactor Scores for Cognitive FunctionsÞ  5:178ðFactor Scores for Physical FunctionsÞ  4:421ðFactor Scores for Eye & Ear FunctionsÞ:

3.2.3. Hochschild’s method (HocM) The general procedure illustrated by Hochschild was followed. However, a few distinctions are made on the method of constructing the CVV. First, the questionnaire for mortality risk factors was set up similarly, but with some variations, to that of Hochschild’s, as it consisted of 23 items that had been studied often in the past for age-related changes. Following the same method for probing the empirical data of the items whether they are actually measuring the age-related changes or not, correlation analyses were performed between the items and SBA calculated by his method. From our study, 11 items turned out to be associated with SBA. Subsequently, some of these items were combined and recalculated as summated scales, resulting in the final eight mortality risk factors (Table 5) to be used for the calculation of CVV. Second, besides the original approach in determining the weights for mortality risk factors, we employed MLR in calculating

The variables are sorted by factor loadings on each component for a clear representation. Two variables are excluded for having low communalities. The component matrix is derived from PCA when pVIB and rMUS are excluded.

b c

(10)

The model has the adjusted R-square of 0.621 (F = 105.807, p < 0.001) and the standard error of the estimate of 7.14 years.

Table 4 Communalities of the variables and VARIMAX rotated component matrix.

a

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Table 5 Weight parameters needed for the Hochschild’s method (HocM). Mortality risk factors

Weights obtained from subjective judgment

Weights obtained from MLR with WAIa

Number of cigarettes smoked per day Summated score for eating habits Emphasis on red meat in diet Vitamins supplements Summated score for exercise level Education level Contentment scale of life BMI (body mass index)

4 2 3 1 2 4 2 3

1.334 0.373 0.071 0.072 0.283 0.318 0.794 0.707

Pearson correlations between CVV and STAjb

c

jrj p W%

pHAP

pFVC

pHGR

pVIB

pACM

cNUM

cAwn

cTOP

cCON

rVRT

rMUS

0.028 0.379 3.1

0.129 0.079 14.1

0.021 0.409 2.3

0.039 0.334 4.3

0.188 0.019d 20.6

0.050 0.292 5.5

0.001 0.496 0.1

0.127 0.081 13.9

0.115 0.103 12.6

0.110 0.114 12.0

0.105 0.125 11.5

a The coefficients of MLR of WAI on mortality risk factors are used as the weights. If not otherwise stated, the results of HocM reported in this paper are derived from the weights obtained with the use of WAI. b Standardized test agej: a manipulated value for each biomarker variable j in the HocM. c jrj: the absolute value of the correlation is used as the weight. p: p-value for the1-tailed significant test. W%: the percent of total weight assigned to each biomarker variable. d Only one variable was significant at the 0.05 level (1-tailed).

the weights, since we had additional information on hand, the WAI. Hochschild reported that the weights of the mortality risk factors were pre-determined to avoid bias in calculations. Although the weights were, as he noted, based on evidence of association of factors with subsequent mortality, they were determined subjectively by the analyst. Thus, to eliminate the involvement of subjective judgment, MLR was performed having the WAI score as the dependent variable to find the weights, which are needed to aggregate the risk factors into the CVV. As the CVV represents the current status of the individual’s mortality risk, it is reasonable to use the WAI score, which also represents the individual’s current health status. Consequently, this CVV is used to assign weights for each biomarker variable. Eleven biomarker variables that were found to be significant to show age-related changes from MLR were used for the HocM. However, most of the Pearson correlations between CVV and STAj, unfortunately, failed to be significant at the 0.05 level, which resulted in considerably different contribution level of each biomarker variable compared to the previous analyses. This is probably due to both the difficulty in finding appropriate risk factors that actually represent individual’s mortality risk, and the limited number of samples (n = 122 out of total 193) of whom the mortality risk factor questionnaires were obtained. Although it raises some suspicions about the stability of the BAE with our data by HocM, it is essential to study the characteristics of the renowned method in BA-related studies. Last, another distinction is made on the determination of the parameter c in Eq. (11) that is used for the transformation of SBA to BAE in units of years. BAE ¼ ðc  CAÞ  SBA þ CA

(11)

Initially, we followed the same manner as HocM to find the value of c that makes the distribution of BAE similar to that of age at death of the population under study (i.e. Korean male with mean = 75.1 and s.d. = 16.0). But, in this way, the obtained value c, even with some compensation for the skewness of the distribution, induced the standard deviation of BAE to be too large. The parameter c, basically, determines the degree of the variance inflation of the BAE distribution. As Hochschild provided us with the possibility of custom tailoring the distribution, and as the general acceptance of standard deviation of BA lies in between 5 to 10 years, we set the value c = 0.1, so that the deviation is

approximately 5 years. Nevertheless, this value does not have any influence on the correlation with the WAI score. 3.2.4. Klemera and Doubal’s method (KDM) Similarly with HocM, five variables with no-correlation with CA or severe inter-correlations were excluded, and the rest 11 biomarker variables were used to calculate the BAE. In addition to that, the absolutely uncorrelated variables produced from PCA were also assessed with KDM. These estimates were named KD1 and KD2, respectively. The outstanding mathematical model developed by Klemera and Doubal, however, requires some complicated calculations. From the computer simulation described in their paper, it is shown that the BAE with Eq. (8), in which CA is accounted as another biomarker, is superior to the BAE with Eq. (7). However, the Eq. (8) requires values for sX j and s2BA . The quantities sX j are the standard deviations of X j  ðk j BA þ q j Þ. Since BA cannot be measured, we used the residual mean square (RMS) corresponding to the regressions of each biomarker Xj on CA instead of the unavailable RMS of Xj on BA. The consequence is that the resulting variance of the BA estimator is not minimal as additional variance k2j s2BA is added to s2X . Nonetheless, it may still be small and, after all, the j results look as reasonable as those obtained with other methods. To find a substitute value for s2BA , the BAE with Eq. (7) need to be computed preliminarily. The s2BA is not derived directly from the calculated data of BAE, but from a series of calculations involving introduction of new variable definitions like rchar, so-called characteristic correlation coefficient, which represents an aggregate property of biomarker variables’ association with CA. It was found that rchar of KD1 and KD2 are 0.556 and 0.464, respectively, which presented reasonable values for the precision of BAE from their simulation results, given the sample size of 193. They made presumptions that there exist ‘true values’ of BA (BAT) that are not necessarily same as the ‘estimates’ of BA (BAE). Thus, note that s2BA here is not S2 ðBAE  CAÞ, but S2 ðBAT  CAÞ. Using the relationship, S2 ðBAT  CAÞ ¼ S2 ðBAE  CAÞ  S2 ðBAE  BAT Þ

(12)

s2BA ð  S2 ðBAT  CAÞÞ was obtained. The details of derivation of Eq. (12) can be found from Klemera and Doubal (2006). In brief, when Eq. (7), where CA is not used in the expression, is applied,

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differences BAE  BAT and BAT  CA are independent random variables. As noted by Klemera and Doubal, the standard deviation sBA should not be a constant but a function linearly increasing with CA, to be more realistic. This concept is also shared by HocM as can be observed from Eq. (11). So, having the obtained value of sBA as the average standard deviation ðsBA Þ for the average age under study, a linear function was fitted to correspond sBA at CAmin to ðsBA  2:5Þ, and sBA at CAmax to ðsBA þ 2:5Þ. The value 2.5 was chosen on the similar ground as the determination of the parameter c with HocM. At last, the linearly increasing sBAs were substituted in Eq. (8) to derive BAE of KD1 and KD2.

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3.3. Comparison with WAI for validation The relationships between CA and BAE of each algorithm were examined using scatter plots in Fig. 2 along with fitted linear regression lines and 95% individual prediction intervals. Clearly, intercepts of the fitted line of MLR and PCA deviate far from the origin, indicating potential erroneous estimates at both edges of the prediction interval. On the other hand, with KD1 and KD2, the gradual increment of standard deviations of the estimates can be observed as had been discussed earlier. However, the undesirable upper right protrusion is common through all the algorithms; for this reason, we believe, it is rather caused by the attributes of

Fig. 2. Scatter plots of CA versus each algorithm’s BA estimates among 193 male participants grouped by WAI classes.

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I.H. Cho et al. / Mechanisms of Ageing and Development 131 (2010) 69–78

elderly individuals who participated in this study than by any defects of the algorithms. Fig. 2 also depicts the relationship among the groups of WAI classes and BAE. Notice most of the colored squares (WAI: poor) are positioned above the mean regression line, and most of the colored triangles (WAI: excellent) are below. It briefly ascertain adequacy of the general measurement of biomarkers in this experiment and of the candidate estimation algorithms to some degree, and most importantly, it justifies the use of WAI for the comparison of various BA estimation algorithms. In our experiment with 193 individuals, the mean and standard deviation of the WAI score were 37.37 and 5.81, respectively. It is an interesting empirical result as the mean value 37 is just the score that divides the classification of WAI into halves (refer to the legend in Fig. 3). The distribution of WAI score shown in Fig. 3 does not present any serious tendency with age, although there is a slight decline of the score and an increase in variance as CA increases. One-way ANOVA on the differences of WAI means among 5-year age groups was found to be not significant at 0.05 level (F = 1.911, p = 0.070), indicating that it is difficult to say, statistically, there are age-related changes with WAI scores. However, as the p-value is just little above the significant level, we cannot totally disregard the influence of age on WAI score. An optimistic interpretation would be that WAI is a measure that reflects more on one’s current health status than the deterioration caused by a serious dependency with the age; and thus, it becomes a good subject for comparison of various BA estimation algorithms, where the interest is in how well each algorithm detects the current health status of an individual given the CA of the person. According to Ingram (1988), strong support of the construct validity is to demonstrate that the biomarker could differentiate between groups with established differences in the rate of ageing and/or life span. Discriminant function analysis would serve the purpose well. Hence, the analysis is applied to see how much each algorithm’s estimates are correctly classifying the WAI classes. As the WAI classification is done with uneven scales of the WAI score, and as the adjacent scores at the boundaries of the classes (e.g. 27 and 28, or 43 and 44) lead different classification, we combined the classes ‘Poor’ and ‘Moderate’ as ‘Unhealthy’, and ‘Good’ and ‘Excellent’ as ‘Healthy’ for a simple but clear representation of the discrimination ability. Prior probabilities needed for the analysis were computed from the two group sizes (p = 0.378 and 0.622, respectively). Having only one independent variable, i.e. the differences of algorithm’s estimates from CA, discriminant function analyses were conducted for each algorithm.

Table 6 Comparison results of BA estimation algorithms with WAI. MLR Pearson correlations with WAI scoresa Standard deviation of BAE (sðBAE CAÞ )

PCA

0.479 5.545

Discriminant function analysisd Overall (%) 68.4 Unhealthy–unhealthy (%) 47.9 Healthy–healthy (%) 80.8

HocM

0.456 b

7.087

69.4 52.1 80.0

b

KD1

0.609 c

5.208

74.6 53.4 87.5

KD2

0.637

0.633

3.942

3.247

79.3 54.8 94.2

79.8 57.5 93.3

a

All significant at the 0.001 level (2-tailed). The standard deviations of MLR and PCA are slightly different from the standard error of the estimates presented in the text, as the former is s.d. of BAE  CA whereas the latter is square root of the residual mean square with the degree of freedom n  p. (n is the sample size, and p is the number of coefficients in MLR.) c The standard deviation of HocM was deliberately set to approximately 5 years (see text), whereas the others are all computed value from the empirical data. d Percent of successful classification (e.g. healthy-healthy means the percent of correct classification of healthy individual into the ‘Healthy’ category.). b

Fig. 4. Graphical representation of the comparison results in Table 6.

The results are shown in Table 6 and Fig. 4 for a graphical representation, along with our final result, the Pearson correlation between the WAI scores and the differences of each algorithm’s estimates from CA. The higher the correlation, the stronger the estimates reflect the health status of the individuals. Furthermore, for the HocM, when the weights were determined from the subjective judgment, the Pearson correlation with the WAI score was 0.573, whereas the HocM with the use of WAI was 0.609. Although applying the WAI in the determination of weights violates the independency for fair comparison, the KD1 (0.637) and KD2 (0.633) were found to be more correlated with WAI, even in that favor for the HocM. For further inspection, standard deviations of the estimates are also included in the table. Note that the standard deviation here is sðBAE CAÞ , the differences between the BA ‘estimates’ and CA, as the ‘true value’ of BA is not applicable for all the algorithms. 4. Discussion

Fig. 3. Workability Index (WAI) of 193 male participants and its classification.

The Klemera and Doubal’s methods, KD1 and KD2, turned out to be most correlated with WAI, indicating that the estimates of the methods adequately correspond to the health status of the individuals. The two methods both presented satisfactory values for all the criteria used in this study, including (i) Pearson correlation with WAI scores, (ii) the standard deviation ðsðBAE CAÞ Þ and (iii) discrimination ability between healthy and unhealthy individuals. Although KD1 showed a little higher correlation with WAI than KD2, the present authors would like to propose using

I.H. Cho et al. / Mechanisms of Ageing and Development 131 (2010) 69–78

KD2 (i.e. KDM with uncorrelated PCA variables), since KD1 might suffer from violation of the assumptions that all biomarker variables should be uncorrelated. The validity of the optimal estimate equation of KDM (Eq. (8)) fundamentally depends on meeting such an assumption. In spite of the exclusion of heavily inter-correlated variables, it cannot be expected that all mutual correlations had been disappeared with the variables for KD1. Note that all acceptable biomarkers must be correlated with CA, hence they are correlated to each other, too. It is the additional correlation caused by other reasons than CA dependency that is to be suppressed. In its pure form, it is the correlation of values of biomarkers measured on people of the same CA. The application of PCA is, probably, the best answer to enabling the estimation of BA with perfectly uncorrelated variables. However, a caution must be taken into account when applying PCA that very small number of variables (or factors) would lead to large standard error of BAE  BAT as demonstrated by computer simulation conducted by Klemera and Doubal. Our study also had relatively small number of variables of PCA, but it was compensated to some extent by having a tolerable value of characteristic correlation coefficient (rchar). This paper illustrates merits and demerits of five different biological age (BA) estimation algorithms with detailed processes of statistical analysis. The common access method of BA, namely MLR serves its advantage with extensive diagnostic tools available for the method. For instance, examining the residual plots and diagnostic statistics, like COVRATIO, DFFITS and Cook’s Distance measure, enable to detect any potential outliers, and the feature of diagnostic tools for multicollinearity can be a great assistance in constructing a valid set of biomarker variables for BA estimation. When an investigation is undertaken for an appropriate BA estimation algorithm, one should initiate with MLR making the most use of the diagnostic tools for the stabilization of the empirical data. If the existence of multicollinearity is suspected, provided that the measurements and overall experimental plan were appropriate, variable conversion or exclusion should be carefully considered. One breakthrough technique from the multicollinearity is the application of PCA. Not only it generates uncorrelated variables, but it also provides information about the underlying structure of the variables. Anstey et al. (1996) pointed out that researchers in BA-related studies should not settle down with finding validated biomarkers that successfully represent age-related changes or feel rest assured of accomplishing an acceptable estimation of BA, but should also look into possibility of predicting specific functional outcome or human performance, such as competence at work, driving difficulties or falls. Such remarks inspired us to make the best of the latent dimension or the underlying structure of the variables identified from PCA. The clear identification of cognitive and physical functions from the mixture of original biomarker variables in the dataset provided us a ground to make the additional application of the current BA estimation system; that is, to provide separate results for both cognitive and physical capabilities in parallel with the BAE. Once the uncorrelated variables are attained, the Klemera and Doubal’s method can be applied to produce reliable and acceptable BAE, as had been confirmed with the empirical data from this study. The Hochschild’s method, on the other hand, also appeared to be relatively reasonable method to predict BA. However, by introducing the CVV, which is the aggregated value of mortality risk factors for each individual, a careful investigation is required to determine which risk factors are to be questioned. Moreover, to adopt the method for a newly developed system, a large number of subjects are needed to be questioned and be measured with the particular system. It is thus quite difficult to implement Hochschild’s method into other systems. Nonetheless, applying the

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