Living alone and mortality risk following a hip fracture

It is well established that patients with a hip fracture have increased mortality risk. A recent analysis of Norway registry data by my friend, Haakon Meyer, and his colleagues show that hip fracture patients living alone would suffer a greater risk of death than those living with a partner [1]. However, having read the paper, I have come up with another interpretation: yes, living alone was associated with increased mortality risk, but the impact of hip fracture on mortality was greater than living alone.

To me, the data shown in Figure 1 of the paper are the most revealing ones. I have tabulated the data in the following table so that readers can follow the argument:

The above data clearly show that in absolute risk, people living alone had a greater risk of post-hip fracture mortality than those living with a partner. That is the authors’ conclusion, which is true.

However, the data also suggest that in the general population, people living alone had an increased risk of mortality. In fact, in relative term, the increased mortality risk was not much different between the general population and hip fracture patients. For instance, in men, living alone was associated with a 68% increase in mortality risk in the general population, and 64% among hip fracture patients. In women, the mortality risk among those living alone was 40% higher than those living with a partner in the general population, and this increased risk was even greater than that in hip fracture patients (30%). So, these data suggest that the ‘effects’ of hip fracture and living alone on mortality seem independent.

Life expectancy

I propose to interpret the above data in terms of life expectancy. This is something that I have proposed in a recent paper in eLife [2]. I consider that it is difficult for patients (and even doctors) to understand the concept relative risk or SMR, but they readily appreciate the life expectancy (or its related index of ‘Skeletal Age’ [2]). So, the idea is to map the relative risk into life expectancy. This can be done relatively easy by exploiting the relationship between Gompertz law of mortality and relative risk [3]. I don’t bother you with mathematical details, but go straight into the problem as follows.

Assuming that most Norwegians live with a partner, and their life expectancy (LE) is reflected by the national life table (available from www.ssb.no). This LE is actually calculated from the age-specific mortality rate qx. So, for those living alone, their qx is increased by a magnitude shown in the risk ratio (RR) in the above table, and we can recalculate their LE by multiplying qx by RR. We can repeat the calculation for those without a fracture living alone, those with a fracture living with a partner, and those with a fracture living alone (Table 2). (Of course, this is based on the assumption that RR is constant across age groups).

Let me give an example: a 70-year old Norwegian man without a fracture and living with a partner is expected to live 15.7 years (from the Norwegian life table). However, if he lives alone, then his remaining LE is 12.4 years, a reduction of 3.3 years of life. Now, if he has suffered a hip fracture and he lives with a partner, then his remaining LE is 11.9, a reduction of 3.8 years of life. However, if he has suffered a fracture and lives alone, then his LE is 9.2 years, a reduction of 6.5 years of life.

As can be seen from the table, the impact of hip fracture on life expectancy is greater than the impact of living alone. For a 70-year old woman living with a partner, a hip fracture reduces her life expectancy by 4.4 years, but if she lives alone, the reduction of life expectancy is further increased by about 1.6 years.

Thus, living alone further reduces life expectancy over and above that of a hip fracture. So, I agree with the authors that social support for the elderly patients with a hip fracture who live alone is warranted.

References

[1] Dahl, C., et al. Increased Mortality in Hip Fracture Patients Living Alone: A NOREPOS Study. J Bone Miner Res 2021. 36(3): p. 480–488. Web: https://asbmr.onlinelibrary.wiley.com/doi/10.1002/jbmr.4212

[2] Ho-Le, T.P., et al., Epidemiological transition to mortality and re-fracture following an initial fracture. eLife 2021. 10. Web: https://elifesciences.org/articles/61142.

[3] Tsai SP, et al. Standardized mortality ratio and life expectancy. Am J Epidemiol 1992;135:824–31.

osteoporosis | epidemiology | genetics | biostatistics | data enthusiast

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