“Skeletal Age” — a new way for fracture risk communication

I have always struggled to make the community and patients appreciate the risk of mortality after a fracture. Well, I think “Skeletal Age” is a way to convey the impact of fracture on mortality.

Here is a well-known fact: the hazard of mortality after a hip fracture is increased by 2.9-fold (95% CI, 2.5 to 3.3) in women and 3.7-fold (3.3 to 4.1) in men [1]. The issue is how to convey this increased risk to patients and the general community.

What does ‘risk’ mean anyway? In the frequentist sense, risk is the probability that an adverse event will occur in a duration of time. Thus, the numerator of risk is the number of events, and the denominator is the number of at-risk people. However, such a definition is hardly applicable to an individual, because for an individual the denominator is 1, and the individual either will or will not have the event. Strictly, an individual risk is not a probability.

I find the concept of “Effective Age” quite interesting. In engineering, effective age is defined as the age of a structure based on its current condition. Thus, for a perfectly maintained structure, its effective age is the same as its chronological age, but for a poorly maintained structure its effective age is older. Such a concept can also be applied to risk communication in medicine.

I propose that ‘skeletal age’ is the age of our skeleton as a result of a fracture. So, for a healthy individual without a fracture, the skeletal age is the same as the individual’s chronological age. However, because fracture is associated with an increased mortality, an individual with a pre-existing fracture is expected to have older skeletal age. The difference between chronological age and skeletal age can be used for conveying the impact of fracture to patients.

Thus, rather than telling patients that their risk of mortality increases by so and so, it may be more meaningful to tell them their skeletal age — the age they would be if they have a fracture. Telling a 60-year old patient with a hip fracture that his skeleton is that predicted for a 80-year old is likely to be more eye opening than tell him a 3-fold increase in mortality risk. Knowing skeletal age may help them to take preventive measure to mitigate his risk of post-fracture mortality.

The more difficult question is how to determine the skeletal age for an individual. Conceptually, the skeletal age of an individual can be defined as:

skeletal age = life expectancy + years gained/lost

where, “life expectancy” can be derived from the life table for a age-and-sex specific population. For example, a 60-year old Australian is expected to live about 84 yr (if a man) or 87 yr (if a woman). Brenner et al [1] have beautifully shown that the number of number of years lost or gained (denoted by Delta)

is a simple function of the hazard ratio of mortality (HR) associated with a risk factor and the rate of mortality (Qx):

Delta = log(HR) / log(Qx)

where Qx is the probability that an individual who has lived to the age x dies before reaching age x + 1. It is fascinating that the Qx is almost a constant with actual value being round 1.1 [2]. In Australia, I have calculated that Qx is 1.093 for men and 1.10 for women aged 35 years and older. In other words, from age 35, the chance of dying before the next birth day increases by about 10% for each year we age. In practice, this relation means that in normal circumstances the average annual risk of death doubles for each log(2) / log(1.1) = 7 years of extra age. Remarkably, this increased risk is constant across populations [3].

Thus, the hazards of mortality associated with a risk factor can be seen as the difference between chronological age and ‘effective age’ (or ‘skeletal age’ in the present discussion).

Back to the idea of skeletal age for an individual with a hip fracture. A meta-analysis [4] has shown that a hip fracture increases an individual’s risk of death by 2.9-fold (for women) and 3.7-fold (for men). Thus, for a 60-year old man with a hip fracture, his skeletal age is roughly 60 + 15 = 75 years. In other words, the hip fracture has taken 15 years off his life expectancy.

The concept of skeletal age can also be used to quantify the beneficial effect of a treatment. Among women with a hip fracture, zoledronic acid reduces the risk of mortality by 28%, and this effect size is equivalent to a gain of approximately 3 years of life. Thus, for a woman with a hip fracture, her life expectancy is lost by ~11 years. However, if she is on zoledronate treatment, the years of life lost is reduced to ~8 years.

In summary, the concept of fracture risk should be redefined to combine the risk that an individual will sustain a fracture and the risk of mortality once a fracture has occurred. The idea of skeletal age presented here can be used to quantify the impact of fracture on mortality for an individual.

References

[1] Brenner H, Gefeller O, Greenland S. Risk and rate advancement periods as measures of exposure impact on the occurrence of chronic diseases. Epidemiology 1993;4:229–36.

A math treatment of this idea is described in the following article: Kulinskaya E, et al. Calculation of changes in life expectancy based on proportional hazards model of an intervention. Insurance: Mathematics and Economics 2020;93:27–35

[2] Spiegelhalter D. Use of “normal” risk to improve understanding of dangers of covid-19. BMJ 2020;370:m3259.

[3] Vaupel JW. Biodemography of human ageing. Nature 2010;464:536–542.

[4] Haentjens P, et al. Meta-analysis: Excess Mortality After Hip Fracture Among Older Women and Men. Ann Int Med 2010;152:380–390. https://www.acpjournals.org/doi/10.7326/0003-4819-152-6-201003160-00008

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osteoporosis | epidemiology | genetics | biostatistics | data enthusiast

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