Demographic Consequences of Barker Frailty

Abstract

In this paper we develop a formal model to represent effects of early life conditions with delayed health impacts on old age mortality. The model captures several mechanisms through which early conditions influence adult health and mortality. The model is an extension of the standard frailty model in demographic analysis but has distinct and unique implications. We show that populations with Barker frailty experience adult mortality patterns equivalent to a class of time-varying and/or age dependent frailty. We demonstrate formally and via simulations that populations with Barker frailty could experience unchanging or increasing adult mortality even when background mortality has been declining for long periods of time. We also show that the rate of increase of adult mortality rates in populations with Barker frailty will change over time and will always be lower that the rate of increase of adult mortality in the background mortality pattern. We argue that Barker frailty should be pervasive in low-to-middle income populations, e.g. those that experienced a mortality decline fueled largely by post-1950 medical innovations that reduced the load and lethality of infectious and parasitic diseases.

Appendix: Main Definitions

$$\displaystyle\begin{array}{rcl} \Lambda _{sB}(y)& =& \mathop{\int }\nolimits _{0}^{Y _{2} }\mu _{s}(x)dx + R\mathop{\int }\nolimits _{Y _{1}}^{y}\mu (x)dx {}\\ \bar{\Lambda }(y,t)& =& \Lambda _{sB}(y)k(t)E_{yt}(\delta ) {}\\ E_{yt}^{exp}(\delta )& =& \frac{1} {\lambda +k(t)\Lambda _{sB}(y)} {}\\ E_{yt}^{exp}(\delta (t))& =& \frac{1} {\lambda (t) + k(t)\Lambda _{sB}(y)} {}\\ \left [CV _{yt}(\delta )\right ]Gamma(r,\lambda )& =& \frac{\sqrt{r}} {r} {}\\ \left [CV _{yt}(\delta )\right ]^{2}Gamma(r,\lambda )& =& \frac{1} {r} {}\\ \end{array}$$

Table A.1 Summary of formal relations for the rate of change of average mortality rates at age y > Y₁