How bad could it be? Worst-case bounds on bias in multistate models due to unobserved transitions

Multistate models are often used in social research to analyze how individuals move between states. A typical application is the estimation of the lifetime spent in a certain state, like the lifetime spent in employment, or the lifetime spent in good health. Unfortunately, the estimation of such quantities is prone to several biases. In this paper, we study the bias due to the often implicitly used assumption that there are no unobserved transitions between states. This assumption does often not hold for the panel data typically used to estimate multistate models, as the states occupied by individuals are only known at specific points in time, and further transitions between panel waves are not recorded. We present partially identified estimates of the lifetime spent in a state, or worse-case bounds, which show the maximum possible level of bias due to unobserved transitions. We provide two examples studying the lifetime spent in disability (disabled life expectancy; DLE). The first example applies our methods to results on cohort trends in DLE in the U.S. taken from Crimmins et al. (2009). In the second example, we replicate findings from Mehta and Myrskyla (2017), and apply our methods to data from the U.S. Health and Retirement Study (HRS) in order to estimate the effects of health behaviors on DLE.