Statistics and Its Interface

Volume 4 (2011)

Number 4

Comparing strategies to estimate the association of obesity with mortality via a Markov model

Pages: 451 – 461



Bingshu E. Chen (Department of Community Health and Epidemiology, Queens University, Kingston, Ontario, Canada)

Katherine M. Flegal (National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, Maryland, U.S.A.)

Mitchell H. Gail (Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland, U.S.A.)

Barry I. Graubard (Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland, U.S.A.)


We used a first order discrete Markov model to investigate strategies to obtain unbiased estimates of the relative mortality hazard for comparing obese with non-obese participants. This hazard ratio is confounded by the fact that obese participants can be either sick or well, as can non-obese participants, and participants can migrate over time from their initial classification on obesity and health status. The parameters of the model were estimated from national survey data and used to illustrate different analytic approaches. The purpose was to compare analytic approaches and not to provide an analysis of a particular data set. Under this model, short term health-stratum-specific estimates are unbiased for estimating the health-stratumspecific instantaneous mortality hazard ratios from obesity, and updating information on body mass index and disease status during long term follow-up reduces bias. For followup over 10 or 20 years, exclusion of participants with preexisting disease, excluding the first five years of follow-up, and methods of analysis that ignore health status yield biased estimates of the instantaneous mortality hazard ratios. However, over 10 or 20 year time periods, long-term average mortality hazard ratios or cumulative mortality relative risks are a better reflection of the total impact of obesity, including its tendency to accelerate transitions to sickness under this model, than are instantaneous mortality hazard ratios. Over these longer time periods, average relative hazard estimates or cumulative mortality relative risks based on initially well participants, on initially sick participants, and on the combined initial population each provide valuable descriptions of associations of obesity with mortality.


causation, Markov chain, mortality, obesity, reverse causation

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