A simple approach for fitting linear relative rate models in SAS

Our plain-English summary of A simple approach for fitting linear relative rate models in SAS, by D.B. Richardson (American Journal of Epidemiology, 2008).

The study

• Author: D.B. Richardson
• Journal: American Journal of Epidemiology
• Published: 2008;168(11):1333-8
• Cited by: 20 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

Abstract

The linear relative rate model has been employed in epidemiologic analyses of a variety of environmental and occupational exposures. In contrast to an exponential rate model, the linear relative rate model implies that the excess relative rate of disease changes in an additive fashion with exposure. The linear relative rate model may be fitted using EPICURE (HiroSoft International Corporation, Seattle, Washington), a specialized statistical software package widely used for such analyses. In this paper, the author presents a simple approach to fitting the linear relative rate model to epidemiologic data using PROC NLMIXED in the SAS statistical software package (SAS Institute Inc., Cary, North Carolina). This approach is illustrated via analyses of data from a study of mortality in a cohort of South Carolina asbestos textile workers (1940-2001).

In plain English

This is a statistical methods paper, not a new study of the health effects of asbestos. The author showed how a type of statistical model called a linear relative rate model, usually fitted with specialized software called EPICURE, could be fitted with a few lines of code in the SAS software package. To illustrate the method, the author reanalyzed data from an earlier study by Hein and colleagues. That study covered lung cancer deaths among workers employed in asbestos textile production at a South Carolina plant between 1940 and 1965, with deaths tracked through 2001. Exposure was cumulative asbestos exposure in fiber-years per mL, counted with a 10-year lag. The paper's figure describes this exposure as chrysotile asbestos. SAS and EPICURE gave nearly identical results. In both programs the estimated excess relative rate of lung cancer death was 0.01974 per fiber-year/mL, with a 95% confidence interval of 0.01119 to 0.03216. Allowing the exposure effect to differ between men and women gave no evidence of a better model fit. The author concluded that such models can be easily fitted in SAS. The author also noted a limit of the linear model: if its linear term falls below zero, it implies an impossible negative disease rate.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Statistical methods paper demonstrating software, with an illustrative reanalysis of existing cohort mortality data
• Who was studied: All workers employed in asbestos textile production at a South Carolina plant between January 1, 1940, and December 31, 1965, with vital status followed through December 31, 2001. The data came from a prior analysis by Hein et al. This paper does not give the number of workers or deaths.
• Exposure: Cumulative asbestos exposure in fiber-years per mL, computed from length of employment in each job and the estimated exposure rate for that job, lagged by 10 years. The figure legend describes it as chrysotile asbestos.
• Main results:
  • Parameter estimates and standard errors from SAS PROC NLMIXED were nearly identical to those from the AMFIT module of EPICURE.
  • The asbestos exposure coefficient (excess relative rate of lung cancer mortality per fiber-year/mL) was 0.01974 in both programs. Its standard error was 0.0052 in SAS and 0.0051 in EPICURE.
  • The likelihood-based 95% confidence interval for the asbestos coefficient was 0.01119 to 0.03216, the same in SAS and EPICURE.
  • Adding a term to allow the exposure effect to differ by sex gave no evidence of improved model fit (likelihood ratio test chi-square 0.857, 1 degree of freedom, identical in both programs).
• The authors' conclusion: The author concluded that analyses using a linear relative rate model can be easily carried out in SAS PROC NLMIXED.
• Limitations the authors state:
  • The linear relative rate model's linear term cannot be negative, because a negative value would imply a negative disease rate. Exponential models do not have this problem.
  • By default, SAS PROC NLMIXED starts all parameters at 1, and model convergence may need better starting values or rescaling of the intercept.

Topics

The National Library of Medicine indexes this study under subjects our site covers: Asbestos textiles, Asbestosis.

Medical terms in this study, explained in our Lexicon: Occupational Exposure.

Related studies

• Lung cancer mortality in North Carolina and South Carolina chrysotile asbestos textile workers — L. Elliott, D. Loomis, et al. (2012)
• Increased lung cancer mortality among chrysotile asbestos textile workers is more strongly associated with exposure to long thin fibres — D. Loomis, J.M. Dement, et al. (2012)
• Estimates of historical exposures by phase contrast and transmission electron microscopy for pooled exposure--response analyses of North Carolina and South Carolina, USA asbestos textile cohorts — J.M. Dement, D. Loomis, et al. (2011)
• DREM 2.0: Improved reconstruction of dynamic regulatory networks from time-series expression data — M.H. Schulz, W.E. Devanny, et al. (2012)
• Software for Apportionment of Asbestos-Related Mesotheliomas — R.M. Ross (2016)
• Estimating the effect of cumulative occupational asbestos exposure on time to lung cancer mortality: using structural nested failure-time models to account for healthy-worker survivor bias — A.I. Naimi, S.R. Cole, et al. (2014)

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