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.