Old-age Frailty Patterns and Implications for Long-term Care Programmes

Abstract

This paper examines patterns in old-age frailty within a multistate model that characterises the stochastic process of biological ageing. Using aggregate population-level U.S. mortality data, we study differences in frailty by gender and cohort. Our results show that, on average, women tend to be frailer than men at older ages with the male–female divergence growing considerably past age 80. We also find that average frailty levels have fluctuated over time with a distinct peak-and-trough pattern. These cohort trends in frailty and the subsequent dynamic forecasts of frailty among newer cohorts closely mirror how late-life disability has evolved among older Americans in recent decades, underscoring the important connection between frailty conditions and disability among older adults. The implications of these findings on spending for long-term care programmes within the broader health insurance system are discussed.

Appendix

This Appendix presents the correlations between the fitted model parameters ($\mu_{0}$, $\mu$, $\lambda_{0}$, and $\lambda$) in the stochastic ageing model. The matrix of scatter plots in Figure A1, which displays the bivariate correlations among each pair of parameter estimates, shows a reasonable spread of data points. We note that some correlations are weak; for example, the correlation coefficient for $\lambda_{0}$ and $\mu$ is only 0.03 for females. The correlation coefficient between $\lambda_{0}$ and $\mu_{0}$ is −0.62 for males and −0.64 for females, both which are moderate. The highest bivariate correlation is between $\lambda$ and $\mu_{0}$ for males (coefficient of 0.91), although the corresponding value for females is somewhat lower at 0.32. Consistent with Yashin et al. and Fong et al.²² we observe a negative correlation between parameter estimates $\mu$ and $\lambda$ whereby the correlation coefficients are −0.52 and −0.63 for males and females, respectively. This statistical relationship can be rationalized as follows: in any given frailty state $i$, a higher mortality hazard ($\mu$) implies that individuals are more likely to die which logically results in a lower rate of transition to the next frailty state ($\lambda$).

Figure A1

Correlations between fitted model parameters