Estimation of finite population duration distributions from longitudinal survey panels with intermittent followup
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Estimation of finite population duration distributions from longitudinal survey panels with intermittent followup Dagmar M. Hajducek · J. F. Lawless
Received: 27 January 2012 / Accepted: 20 December 2012 / Published online: 5 January 2013 © Springer Science+Business Media New York 2013
Abstract We consider survival or duration times associated with spells (sojourns in some state) or events experienced by individuals in a population over a specified time period. Duration distributions can be estimated from data recorded during followup of panel members in longitudinal surveys, but adjustments for the sample design, population structure and losses to followup are typically required. We provided weighted Kaplan–Meier estimates that allow for these features and, in particular, adjust for dependent loss to followup through the use of inverse probability of censoring weights. Keywords Dropout · Inverse probability weights · Loss to followup · Spell durations · Survival distributions · Weighted Kaplan–Meier estimates 1 Introduction Models in which individuals may spend time in various states are used in economics, medicine, sociology and other areas. For example, in this paper we consider employment histories in which a person may be unemployed, employed, or not in the labor force at any given time. We will use the term spell to denote a period in which an individual is in some specific state; this terminology is common in economics and the social sciences (e.g. see Kovacevic and Roberts 2007; Pyy-Martikainen and Rendtel 2009).
D. M. Hajducek (B) Department of Psychology, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada e-mail: [email protected] J. F. Lawless Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada e-mail: [email protected]
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Fig. 1 Weighted KM estimates for jobless spells starting in 1999 and 2000, from 1999 residents in a Ontario, 359 and 270 spells; b Quebec, 311 and 211 spells
Survival or duration distributions associated with spells experienced by individuals in a population are of considerable interest as descriptive quantities. For example, Fig. 1 shows weighted Kaplan–Meier (KM) survival function estimates, obtained using methodology developed in this paper, for the durations of jobless spells starting in Ontario and Quebec, respectively, in 1999 and 2000, for persons residing in Ontario and Quebec in 1999. These are based on data from Statistics Canada’s Survey of Labour and Income Dynamics (SLID) and they estimate finite population duration distributions, defined as follows. Let N spells with durations Y1 , Y2 , . . . , Y N be experienced by individuals in a specified population P, over a specified period of time. Then S P (y) =
N 1 I Yj ≥ y N
(1)
j=1
gives the population duration distribution. Note that a given individual may have more than one spell (or no spells), but the interest here is on the population aggregate number of spells and their durations and not on the dy
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