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Understanding variation in disease risk: the elusive concept of frailty.

Aalen OO, Valberg M, Grotmol T, Tretli S - Int J Epidemiol (2014)

Bottom Line: Heterogeneity often manifests itself as clustering of cases in families more than would be expected by chance.We emphasize that apparently moderate familial relative risks can only be explained by strong underlying variation in disease risk between families and individuals.Finally, we highlight the potential impact of frailty variation in the interpretation of standard epidemiological measures such as hazard and incidence rates.

View Article: PubMed Central - PubMed

Affiliation: Oslo Centre for Biostatistics and Epidemiology, Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway and Cancer Registry of Norway, Institute of Population-Based Cancer Research, Oslo, Norway o.o.aalen@medisin.uio.no.

No MeSH data available.


Assume that the hazard rates in two risk groups are  and  respectively. When frailty variables are introduced, the observed relative risk declines over time as shown in the figure. Three frailty distributions are used; one leads to a crossover of the hazard ratio. This case corresponds to a frailty distribution with a positive probability of zero frailty (i.e. a non-susceptible group). See Aalen et al.2, Chapter 6, for technical details.
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dyu192-F6: Assume that the hazard rates in two risk groups are and respectively. When frailty variables are introduced, the observed relative risk declines over time as shown in the figure. Three frailty distributions are used; one leads to a crossover of the hazard ratio. This case corresponds to a frailty distribution with a positive probability of zero frailty (i.e. a non-susceptible group). See Aalen et al.2, Chapter 6, for technical details.

Mentions: Consider two groups of individuals with hazard rates and, such that the hazard ratio is 2. In each of these groups there would necessarily be some unobserved heterogeneity between individuals. By introducing equally distributed frailty variables in the two groups, a decreasing hazard ratio over time may be obtained. Depending on the choice of frailty distribution, the hazard ratio may even cross over and become lower than 1, such that the high-risk group appears to become the low-risk group (Figure 6). The decrease (and possible cross-over) of the hazard ratio over time is a frailty effect. Individuals in the high-risk group will on average experience events earlier than those in the low-risk group. This causes the proportion of highly susceptible individuals in the high-risk group to decrease faster than in the low-risk group, leaving an increasing proportion of less susceptible individuals. Thus, the hazard ratio will decrease. If, for instance, the population contains a non-susceptible subgroup, then the susceptible individuals in the high-risk group would be exhausted earlier than in the low-risk group, causing the relative risk to cross over and become lower than 1, even if the hazard ratio stays constant on the individual level. This means that when frailty is not observed and cannot be accounted for, a wrong conclusion could be drawn regarding the true relationship between two groups. This is in fact a time-dependent version of Simpson’s paradox, which means that the observed relationship (concerning risk of disease, for example) between two groups is reversed at an aggregate level compared with what would be observed at a more detailed level if covariates could be conditioned on.Figure 6.


Understanding variation in disease risk: the elusive concept of frailty.

Aalen OO, Valberg M, Grotmol T, Tretli S - Int J Epidemiol (2014)

Assume that the hazard rates in two risk groups are  and  respectively. When frailty variables are introduced, the observed relative risk declines over time as shown in the figure. Three frailty distributions are used; one leads to a crossover of the hazard ratio. This case corresponds to a frailty distribution with a positive probability of zero frailty (i.e. a non-susceptible group). See Aalen et al.2, Chapter 6, for technical details.
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Related In: Results  -  Collection

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dyu192-F6: Assume that the hazard rates in two risk groups are and respectively. When frailty variables are introduced, the observed relative risk declines over time as shown in the figure. Three frailty distributions are used; one leads to a crossover of the hazard ratio. This case corresponds to a frailty distribution with a positive probability of zero frailty (i.e. a non-susceptible group). See Aalen et al.2, Chapter 6, for technical details.
Mentions: Consider two groups of individuals with hazard rates and, such that the hazard ratio is 2. In each of these groups there would necessarily be some unobserved heterogeneity between individuals. By introducing equally distributed frailty variables in the two groups, a decreasing hazard ratio over time may be obtained. Depending on the choice of frailty distribution, the hazard ratio may even cross over and become lower than 1, such that the high-risk group appears to become the low-risk group (Figure 6). The decrease (and possible cross-over) of the hazard ratio over time is a frailty effect. Individuals in the high-risk group will on average experience events earlier than those in the low-risk group. This causes the proportion of highly susceptible individuals in the high-risk group to decrease faster than in the low-risk group, leaving an increasing proportion of less susceptible individuals. Thus, the hazard ratio will decrease. If, for instance, the population contains a non-susceptible subgroup, then the susceptible individuals in the high-risk group would be exhausted earlier than in the low-risk group, causing the relative risk to cross over and become lower than 1, even if the hazard ratio stays constant on the individual level. This means that when frailty is not observed and cannot be accounted for, a wrong conclusion could be drawn regarding the true relationship between two groups. This is in fact a time-dependent version of Simpson’s paradox, which means that the observed relationship (concerning risk of disease, for example) between two groups is reversed at an aggregate level compared with what would be observed at a more detailed level if covariates could be conditioned on.Figure 6.

Bottom Line: Heterogeneity often manifests itself as clustering of cases in families more than would be expected by chance.We emphasize that apparently moderate familial relative risks can only be explained by strong underlying variation in disease risk between families and individuals.Finally, we highlight the potential impact of frailty variation in the interpretation of standard epidemiological measures such as hazard and incidence rates.

View Article: PubMed Central - PubMed

Affiliation: Oslo Centre for Biostatistics and Epidemiology, Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway and Cancer Registry of Norway, Institute of Population-Based Cancer Research, Oslo, Norway o.o.aalen@medisin.uio.no.

No MeSH data available.