Age is an important confounder in studying most health related outcomes [1, s 5], and perhaps the most commonly adjusted variable. In this and next post I will go into (1) what we know about the age effect in relation to total hip replacements (THR) re-operations and mortality, (2) what I found in my study on age and health-related quality of life (HRQoL) using splines, and (3) how I implemented and evaluated different splines using R for this study.
Increased re-operation rates for younger patients due to aseptic loosening is today widely recognized –, [6, s 79], , . On the other hand, the risk of fractures and dislocations is higher among elderly. Cook et al. showed that patients age 80 and above have an odds ratio of 4.4 (95% CI, 2.9–6.4) for fractures compared to patients below 80 . Malkani et al. reported that patients 85 and above were associated with an almost 50% higher relative risk of early dislocation compared to patients between 65 and 69 .
As expected, age is also related to mortality within 90 days. SooHoo et al. reported an odds ratio of 2.6 (95% CI, 2.2 to 3.0) for patients over the age of 75 compared to patients between 65 and 75 . Hunt et al. studied over 400,000 patients and similarly reported an increase in the elderly, although they noted that this increase was primarily among men. The Kaplan-Meier 90-day mortality estimates for patients age 80 and above were 1.9% for men (95% CI, 1,7 to 2•11) vs 1.1% for women (95% CI, 1,0 to 1.2); the corresponding rates for patients between 65 and 69 were 0.3% for men (95% CI, 03 to 0.4) vs 0.2% for women (95% CI, 0.1 to 0.2) .
Surprisingly, prior to our study  there was no consensus regarding the impact of age on HRQoL after THR . Some studies report decreasing improvement in HRQoL after THR with age –, while others indicate little effect if any –. None of these studies used splines, thus potentially missing out on more complex relations.
Our study was based on a nation-wide cohort of almost 30,000 patients operated due to primary osteoarthritis between 2008 and 2010. For estimating HRQoL, we used the generic health outcome questionnaire EQ-5D of the EuroQol group that consists of 2 parts: the EQ-5D index and the EQ VAS estimates.
We found that age had little effect until patient’s late 60:s, after which it had a negative impact on both HRQoL outcomes. Below image illustrates the effect:
The effect can also be illustrated using a contrast-table:
|Table 3: Age estimates with 70 years as reference.|
|Age (years)||Estimate||95% CI||P-value|
|40 vs. 70 years||0.011||0.003 – 0.018||0.004|
|50 vs. 70 years||0.009||0.004 to 0.013||< 0.001|
|60 vs. 70 years||0.007||0.005 to 0.009||< 0.001|
|70 vs. 70 years||Ref.||–||–|
|80 vs. 70 years||-0.019||-0.022 to -0.017||< 0.001|
|90 vs. 70 years||-0.042||-0.048 to -0.037||< 0.001|
|40 vs. 70 years||1.2||-0.1 to 2.4||0.078|
|50 vs. 70 years||1.2||0.4 to 2.0||0.002|
|60 vs. 70 years||1.3||1.0 to 1.6||< 0.001|
|70 vs. 70 years||Ref.||–||–|
|80 vs. 70 years||-4.2||-4.7 to -3.8||< 0.001|
|90 vs. 70 years||-9.3||-10.3 to -8.3||< 0.001|
It is hardly surprising that the room for improvement is less in elderly, although even the majority of older patients improve their HRQoL. It is also important to note that other outcomes not measured by the EQ-5D tool may be of importance to the patient.
From a purely statistical viewpoint, the bend occurs at the perhaps worst possible place – the median age for THR patients. We can therefore expect that the residual confounding effect may be substantial when modeling age using a regular linear term, i.e. a straight line.
Since many use cut points to adjust for confounding in this setting, I want to remind that these introduce a cut-point bias. Also, if we use a fine-grained-split for age, e.g. cutting age in 5-year intervals, we may remove the confounding but will also spend more degrees of freedom, risking a less stable model. Furthermore, if the effect that we are studying happens to be confined to one or two age-groups, we may encounter multicollinearity.
M. Gordon, M. Greene, Paolo Frumento, Ola Rolfson, Göran Garellick, och André Stark, ”Age and health related quality of life after total hip replacement: Decreasing gains in patients above 70 years of age”, Acta Orthop, vol 85, num 3, ss 244–249, jun 2014.
Implementation in R
In the next post (coming soon) I will show hot to implement splines in R and compare different alternatives.
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