TY  - JOUR
A1  - Vaupel, James W.
A1  - Missov, Trifon
T1  - Unobserved population heterogeneity: A review of formal relationships
Y1  - 2014/09/17
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 659
EP  - 686
DO  - 10.4054/DemRes.2014.31.22
VL  - 31
IS  - 22
UR  - https://www.demographic-research.org/volumes/vol31/22/
L1  - https://www.demographic-research.org/volumes/vol31/22/31-22.pdf
L2  - https://www.demographic-research.org/volumes/vol31/22/31-22.pdf
N2  - Background: Survival models accounting for unobserved heterogeneity (frailty models) play an important
role in mortality research, yet there is no article that concisely summarizes useful relationships. 

Objective: We present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways. For some relationships we present proofs that, albeit formal, tend to be simple and intuitive. 

Methods: We organize the article in a progression, starting with general relationships and then turning to models with stronger and stronger assumptions. 

Results: We start with the general case, in which we do not assume any structure of the underlying
baseline hazard, the frailty distribution, or their link to one another. Then we sequentially assume, first, a relative-risk model; second, a gamma distribution for frailty; and, finally, a Gompertz and Gompertz-Makeham specification for baseline mortality. 

Comments: The article might serve as a handy overall reference to frailty models, especially for mortality
research. 

ER  -