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Random effects regression models for trends in standardised mortality ratios
  1. David B Richardson1,
  2. Stephen R Cole1,
  3. Haitao Chu2
  1. 1Department of Epidemiology, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
  2. 2Division of Biostatistics, University of Minnesota School of Public Health, Minneapolis, Minnesota, USA
  1. Correspondence to Dr David B Richardson, Department of Epidemiology, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; david_richardson{at}


Objectives Standardised mortality ratios (SMRs) play an important role in the epidemiological literature, particularly in evaluations of occupational hazards. While some authors have argued that comparisons of SMRs should be avoided, many investigators find such analyses appealing particularly when data are sparse. For example, calendar period-specific SMRs often are examined to identify emerging problems or to assess whether a hazard that impacted death rates in the past has abated. However, because the distribution of people with respect to age usually changes as calendar time advances, comparisons of SMRs across calendar periods can produce misleading results.

Methods We propose a random effects model to reduce the potential bias arising from comparisons of SMRs. This approach is illustrated using data from a study of workers employed at the Department of Energy's Oak Ridge National Laboratory.

Results When there is homogeneity across strata of covariates in the ratio of death rates in the target population to that in the reference population, the proposed model yields results equivalent to those obtained by a classical analysis of SMRs. However, as evidence against such homogeneity increases, the model yields a random effects version of SMRs for which patterns will conform better to those obtained from an internal analysis of rate ratios.

Conclusions The proposed random effects model can reduce potential bias arising in the comparisons of SMRs.

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