#### Publication Date

2017-11-02

#### Availability

Open access

#### Embargo Period

2017-11-02

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PHD)

#### Department

Biology (Arts and Sciences)

#### Date of Defense

2017-08-02

#### First Committee Member

Carol C. Horvitz

#### Second Committee Member

Don DeAngelis

#### Third Committee Member

Isaac Skromne

#### Fourth Committee Member

Robert Stephen Cantrell

#### Fifth Committee Member

Shripad Tuljapurkar

#### Abstract

Mortality modeling has come a long way since the demographer Benjamin Gompertz (1779-1865). We address populations where mortality is structured by the joint effects of age and state and individuals can change state at each age. Dynamic states are the most complex and interesting states to consider and we focus on three categories of states: being married or unmarried, being below or above a particular income threshold, or being in one of four income states. We examine how the transience of our particular states at each age drives the cohort dynamics such as the demographic structure and lifespan inequalities within the cohort. In each chapter we used two U.S. nationally representative data-sets (the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth) to statistically estimate the probabilities of survival and transitions between states at each age with regression analysis. These probabilities were incorporated into discrete age and discrete state matrices. We examine age-specific state struc- ture, the average remaining life expectancy, its variance, cohort simulations, dynamic heterogeneity and individual trajectories. In chapter 2 we find that the survival advantage of being married changed with age. At young ages, it was negligible. At mid to late ages it was considerable, and at late old ages, it was disadvantageous. The probability of staying and becoming married decreases with age. Married people live longer than unmarried people, the benefit is enhanced for males at mid-ages. At early ages more women entered marriage than men, while at late ages more women exited marriage than men. In contrast to our dynamic model, the results of a model in which state became fixed at some particular age leads to conflicting results among interviews. In chapter 3 we consider three threshold income levels. We find, consistent with earlier literature, that for most ages the above threshold income state has the highest one-period survival probability at each age for mid-ages to about age 80. The advantage is greatest between those above and below the 1× poverty threshold (1 × the annual official poverty line) when compared to those above and below 2× or 3× poverty. Yet more state switching occurs across the threshold as the income threshold is increased. The largest discrepancy in average remaining life expectancy and its variance occurs at mid-ages. And fewer individuals are in the lower income state between ages 40-60. Our results suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of the higher income states, more disparities). This chapter extends the literature on individual poverty dynamics and stage-by-age matrix models. In chapter 4 we again used state-by-age modeling to capture individual entry and exit in dynamic states, and the four income states considered here are: <1×, 1-2×, 2-3×, >3× the poverty threshold. These income states are very relevant since current income inequality research examines the spread of income in various populations but few studies consider how dynamic heterogeneity and probabilities of transitioning in and out of income states at each age influence mortality disparities in cohorts. We find that for most ages the higher income states have the highest probability of surviving from one year to the next until about age 86 when the order of the income states does not equate to the order of survival advantage. In general, each income state has the highest annual probability of staying in the same state at each age, with the next highest transition being to move to higher income states. The greatest advantage in average remaining life expectancy between consecutive states is for those in <1× poverty moving to 1-2× poverty at ages 32-49. The largest discrepancy in average remaining life expectancy and its variance between all states and the <1× poverty state occurs at mid-ages (40-60). And the fewest individuals are in the lower income states between ages 40-60. Our findings are consistent with results based on other data sets, but we also investigate the dynamic heterogeneity in income state at each age. They reveal that annual stasis probabilities in income state at each age influences the cohort state structure, the dynamic heterogeneity of the cohort, and inequalities or income related mortality disparities at each age. The dynamic models and analysis used here provide a link between distinct characteristics of individuals in a cohort, such as various state variables and senescence, with the dynamics of age-structured cohorts. This dissertation extends the literature on modeling individuals in a cohort that are undergoing dynamic heterogeneity and stage-by-age matrix models. And it serves as a bridge between stage by age matrix models and other multistate methods.

#### Keywords

age by stage model; dynamic heterogeneity; marital status; poverty; mortality modeling

#### Recommended Citation

Bernstein, Shayna, "Age by Stage Modeling of Dynamic Heterogeneity" (2017). *Open Access Dissertations*. 1974.

https://scholarlyrepository.miami.edu/oa_dissertations/1974