We have extended an earlier conceptualization of functional age [10] to present a method of estimating personal biological age, and from that, to estimate relative fitness and frailty. In particular, we claim that the proportion of deficits accumulated by an individual at a given chronological age allows an operational definition of relative fitness and frailty. To validate this definition of relative fitness and frailty we compared survival both as function of PBA in the cohort, and by varying levels of fitness and frailty within cognitive diagnostic groups.
Calibration equations (1) and (2) comprise our knowledge about the accumulation of deficits in older adults, and thus can be considered as an example of knowledge discovery in databases (KDD). KDD is a set of techniques being developed through a number of disciplines to take advantage of existing databases as means of discovering new knowledge. [24, 25] KDD, defined as the identification of meaningful and useful patterns in databases, includes both the discovery of previously unseen groupings within existing databases [11, 22] and predictive modelling, as also developed in this inquiry.
We are aware of important limitations in our study. First, in order to initially describe a simple model, we have limited our analysis to a set of 20 deficits. While these proved sufficient in earlier analyses, [21–23] alternate formulations of the impairment index may be more efficient. The more essential the deficits that are taken into account, the more precise the estimation of frailty that is obtained [26]. However, it is not yet clear which are the essential properties of signs, symptoms and functional deficits that need to be selected. This is an ongoing area of investigation, but it appears that the number of deficits, rather than their precise nature, might be the most important determinant [26, 27]. We interpret this to mean that frailty might be interpreted as a loss of redundancy in a complex system.
In addition, we were limited in our databases to individuals aged 65 years and older, and drew from the screened clinical sample, so that we cannot make a claim about the representativeness of the data. The incorporation of data on middle-aged and representative samples should allow more general claims about PBA to be examined. Third, to simplify the calculations we have suggested, as a first approximation, that a state variable can be estimated as the proportion of deficits. This may seem naive, as if has the effect of equalizing all the deficits. Evidently, at an individual level, not all deficits are equally important: heart problems or diabetes likely may cause death sooner than for example, difficulties in getting dressed or skin problems per se. The finding that the proportion of deficits in a given individual can include seemingly arbitrary or even trivial ones requires further investigation. For now, we understand this finding to mean that accumulating several deficits results overall in impaired adaptive ability. This is likely to be the case if the signs are redundant, i.e. if a given deficit represents a set of others, and if the items of the index are related. The latter appears to be the case, as illustrated in Figure 7, which shows that the deficits are not independent. The nodes of the graph correspond to the deficits (numbered in the Materials and methods) and the edges represent statistically significant relationships between the deficits (defined as the difference between the unconditional probability of the occurrence of deficit X and conditional probability of deficit X given deficit Y) [11]. This is not surprising when we consider that synergetic relationships are typical for age-associated deficits. In other words, roughly speaking, everything is dependent on everything else in complex organisms so that changes in one subsystem affects many others. For example, vision impairment may be caused by the numerous reasons. Since vision loss, by itself, is not readily regarded as a life-threatening factor, it may indicate a more serious problem (e.g. diabetes, stroke). The more deficits that are used in deriving the frailty index, the greater the chance that such secondary signs are linked to serious illnesses. As argued elsewhere [1, 26, 28] this is a central aspect of many characterizations of frailty. Moreover, whether this holds for any combination of deficits (and not just age-associated ones) additionally requires further study, although we recognize that such summarization does not allow the influence of individual disease states to be tested. [22, 29]
We considered data together for men and women. The differences in mortality of men and women are well known and we recognise that in the next approximation they have to be treated separately. However, here we were limited by the power of data representing, in average, 100 individuals at each age and division the sample by sex would make statistics worse. We intend to address the issue of gender differences in accumulation of deficits in the other paper when dealing with the representative large sample of data.
Have we offered any special insight beyond the commonsense observation that as people age they are more likely to become ill, or that ill people are more likely to die? We believe that we have. In the first instance, we empirically derived an index to distinguish biological from chronological ageing with a result that seems to offer reasonable precision. For example, equation 2 predicts a maximum life span 126 years, compared with the maximum-recorded life span of about 122 years. This is of interest, but we have to be careful with its interpretation. We are not claiming that 126 years is the absolute limit of the human lifespan. Note that this is an average characteristic of the sample, in which older adults with deficits have been over-represented. Moreover, as has been well argued, there is no evidence for such a limit, and considerable evidence against it [30]. The accumulation of deficits in our equations suggests a process whereby damage is initially compensated by redundancy of systems, but when the redundancy is exhausted (i.e., too many deficits are accumulated) any new insult leads to death [31]. Similarly, equation (1) corresponds to the differential equation relating the proportion of the deficits q to the instantaneous rate of increase in deficits; i.e. dq/dt: dq/dt = kq (k = 0.03). In other words, the average annual accumulation of deficits in successful ageing (in this case for individuals with no cognitive impairment) is 3% per year.
Here we used death as the outcome. However, other adverse outcomes, such as institutionalisation can also be considered and will be the subject of further inquiry. This approach also incorporates an important feature of frailty, which has otherwise received little attention in its operationalization, namely its relationship to age. While ageing is readily accepted as being associated with frailty, as argued elsewhere, [1, 26] the notion of frailty finds its roots in the imprecision of chronological age as an explanatory model in predicting adverse outcomes in individual cases. As presented here, PBA represents the individual case, but its relationship to age is inherent in the definition. As noted (Figure 2), individual values of the impairment index can vary widely at any given CA. As a statistical analogy, PBA for a subject represents their individual value; CA represents the mean. In other words, by taking into account both the proportion of deficits accumulated by an individual at a given age, and the average proportion of deficits estimated from the successful ageing group, we are able to describe respectively, an individual or a characteristic of a population. While this is of interest, and served as the basis of further inquiry [27] we are not making a claim to have definitively calculated the PBA. Rather, we have presented one method of so doing, and note that this approach has properties which encourage us to pursue the analysis further in other databases.
