In a secondary analysis of the Yale Precipitating Events Project, a Frailty Index was constructed for a baseline and a follow-up cohort, respectively. Each step in the process was described, to allow a precise account of what constitutes a health deficit for this purpose, how to select which health deficits to include in a frailty index, how to operationalize any possible deficit (ordinal, continuous and binary) to a range of 0–1 and which characteristics of the frailty index (nature of the distribution; slope in relation to age; presence of a limit) seem to be broadly replicable. Several reproducible characteristics (e.g. the distribution, the slope and limit of deficit accumulation) of each Frailty Index were provided so that they maybe used, as in previous papers [4–11], to describe the overall frailty state of the group. The baseline Frailty Index showed a rate of accumulation to be 0.020 per year (per 1 year increase in age) with an upper limit to the frailty index of about 0.60 while the follow up showed a rate of 0.026 deficits accumulated per year with a limit around 0.70 (Figure 2).

We used a re-sampling by variable procedure to construct confidence intervals for the slopes of the lines (Figure 3). This procedure gives us information about the frailty construct, showing that a range of deficits can in fact be combined to give a result that is informative in the aggregate. In other words, the slope depends on the overall behaviour of the deficit accumulation, and is not driven by a small number of variables. In this regard, earlier work has shown reasonable consistency of the rate of deficit accumulation across community-dwelling random samples [6]. Here, we noted that the follow up cohort had frailty index characteristics – frailty index values, rate and limit similar to those of previously studied community dwelling random samples. Most notable is the 0.03 accumulation of deficits and the age independent limit to frailty of 0.67. The baseline sample had lower estimates – a lower average Frailty Index and a lower maximal limit. This suggests that the baseline cohort was not as frail as the follow up cohort.

The relationship between the Frailty Index and mortality is of interest on several grounds, but here is presented chiefly because it represents a relevant and non-arbitrary test of predictive validity. This is important because predictive validity is one of two types of so-called criterion validation, the other being validation against a so-called "gold standard" [21]. As there is no gold standard for frailty assessment, predictive validation is an important method of validating any approach to frailty operationalization. Note that our intent in checking the ability of the frailty index to predict mortality is validation of the index, rather than developing a mortality prediction index that included frailty. If the frailty index were meant to be a mortality prediction instrument, there might be a rationale for weighting several items, particularly age [26]. One notable result from the Cox analyses is that including the Frailty Index increased the impact of being male on mortality. This likely reflects the observation from earlier studies that while men accumulate fewer deficits than do women, any given level of deficit accumulation is more lethal for them and at any given age, females seem to be more frail than males [6, 11].

The relationship with mortality is also important in understanding how deficit accumulation might operate. Classically, Gompertz described the rate of mortality being exponentially related to age [27]. Equally unsurprisingly, mortality exponentially increases with the accumulation of deficits [5, 8, 19]. In addition, acceleration of deficit accumulation is characteristic of older people prior to death [8].

Our data must be interpreted with caution. Not all items had established cut-points. In addition, cut-points can be difficult to apply across a sample that covers many ages, as the effects of continuous traits can be age-specific.[28] Our approach derived cut-points based on the "interim frailty index" procedure described above. In addition, the sample is small, so that any individual estimates can be unstable; this is where aggregation of items in a frailty index can be helpful, and where the re-sampling strategy is useful.

Our paper also has some strengths. In replicating many of the characteristics of a frailty index in a new sample, we can give additional assurance of the robustness of the approach. By spelling out in detail how each step in constructing a frailty index can be undertaken, and by submitting to an open access journal, we are aiming to make the method widely available. We have also made more precise a method for establishing cut-points for variables that were not constructed for inclusion in a frailty index, thereby further allowing the method to be used. In this regard, the relationship of any given variable to a mean frailty index score of 0.2 might seem arbitrary. In a study that related the frailty index approach to the phenotypic definition of frailty popularized from the Cardiovascular Health Study [22], 0.2 corresponded to the mean frailty index value for persons defined as "pre-frail" [7, 22]. A more recent paper from another group used the 0.2 cut-point on a so-called "deficit index" to distinguish people who were "robust" form those who were "pre-frail"[29]. Finally, like many health surveys, the PEP study has many more variables than are needed to construct a 40-item frailty index. Several eligible variables were not included only because we had reached our target of a 40-item Frailty Index. There is no scientific reason not to include more – we have constructed an frailty index of 70 items. On the other hand, a recurring concern about the frailty index has been the feasibility of calculating it if a lot of variables are used [30]. Here, as in some earlier studies, [7, 19, 31] we have selected variables at random (boot-strapping) from a list of eligible variables to make up the Frailty Index and have again shown that the results are insensitive to the precise composition of the index.

Change in the health status of elderly people is an obvious concern to clinicians and to population planners. In the next round of analyses, we will be interested to know whether the changes in the frailty states (baseline frailty state versus the follow up state) can be described using a so called "stochastic" transition model [32] which we have evaluated in other community-dwelling elderly samples, although not with ones that include as many performance measures as the PEP study [33]. This intriguing possibility is motivating further inquiries by our group.