Open Access Research article

Piecewise exponential models to assess the influence of job-specific experience on the hazard of acute injury for hourly factory workers

Jessica Kubo1*, Mark R Cullen2, Linda Cantley3, Martin Slade3, Baylah Tessier-Sherman3, Oyebode Taiwo3 and Manisha Desai1

Author Affiliations

1 Quantitative Sciences Unit, Stanford University, Palo Alto, CA, USA

2 Department of Medicine, Stanford University, Stanford, CA, USA

3 Department of Internal Medicine, Yale University, New Haven, CT, USA

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BMC Medical Research Methodology 2013, 13:89  doi:10.1186/1471-2288-13-89

Published: 10 July 2013



An inverse relationship between experience and risk of injury has been observed in many occupations. Due to statistical challenges, however, it has been difficult to characterize the role of experience on the hazard of injury. In particular, because the time observed up to injury is equivalent to the amount of experience accumulated, the baseline hazard of injury becomes the main parameter of interest, excluding Cox proportional hazards models as applicable methods for consideration.


Using a data set of 81,301 hourly production workers of a global aluminum company at 207 US facilities, we compared competing parametric models for the baseline hazard to assess whether experience affected the hazard of injury at hire and after later job changes. Specific models considered included the exponential, Weibull, and two (a hypothesis-driven and a data-driven) two-piece exponential models to formally test the null hypothesis that experience does not impact the hazard of injury.


We highlighted the advantages of our comparative approach and the interpretability of our selected model: a two-piece exponential model that allowed the baseline hazard of injury to change with experience. Our findings suggested a 30% increase in the hazard in the first year after job initiation and/or change.


Piecewise exponential models may be particularly useful in modeling risk of injury as a function of experience and have the additional benefit of interpretability over other similarly flexible models.

Piecewise exponential models; Weibull models; Baseline hazard; Time to event data; Occupational health; Censored data; Frailty models; Survival analysis