Fitting relationships between exposure and standardized mortality ratios

Our plain-English summary of Fitting relationships between exposure and standardized mortality ratios, by J. Hanley, D. Liddell (Journal of Occupational Medicine., 1985).

The study

• Authors: J. Hanley, D. Liddell
• Journal: Journal of Occupational Medicine.
• Published: 1985;27(8):555-60
• Cited by: 11 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

Abstract

Practical methods are described for formal fitting of simple (linear) relationships between exposures in several subgroups and standardized mortality (or morbidity) ratios (SMRs) for these groups, whether derived from a cohort study by the person-years method or otherwise. The observed events are assumed to have Poisson variation about the fitted relationships. Procedures are outlined for obtaining parameter estimates by iterative weighted least squares regression, which is not only equivalent to, but also the simplest form of maximum likelihood estimation. A test of fit is available in a chi 2 statistic for deviations of observed data from "fitted" values. A further test allows one to examine whether the SMR at zero exposure is different from unity. The concept of relative slopes is discussed, and methods are given for obtaining estimates and confidence intervals. Generalizations to more than one exposure, and to quadratic and other relationships, are explained. Steps for computing the basic fits are detailed, and instructions for adapting packaged computer programs given. Illustrations are provided from data of lung cancer SMRs in relation to exposure to asbestos and to smoking.

In plain English

This was a statistics methods paper, not a new study of workers. The authors described practical ways to fit straight-line relationships between subgroups' exposure levels and their standardized mortality ratios (SMRs: observed divided by expected deaths). They illustrated the methods with data published by other researchers: lung cancer deaths among males in an American asbestos textile plant, and lung cancer in relation to asbestos exposure and smoking. For the textile plant, with dust exposure accumulated up to 10 years before death, the fitted SMR at zero exposure was 0.528880, rising by 0.026979 per million particles per cubic foot times years (mpcf·y). The authors reported strong evidence that a line forced to equal 1 at zero exposure fitted less well. The relative slope (the slope divided by the zero-exposure SMR) was 0.05101 per mpcf·y, with confidence limits of 0.0176 and 0.15078. In the smoking example, heavier smoking appeared to go with a shallower relative slope, but the confidence limits overlapped. The authors cautioned that these heavily grouped data were not definitive. They concluded formal fitting methods should be used more commonly.

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, illustrated by reanalysis of previously published lung cancer SMR data
• Who was studied: No new population was studied. The illustrative data came from other studies. The first set covered males in an American asbestos textile plant, with lung cancer deaths counted 20 years after first employment (source: McDonald et al, 1983). The second set covered lung cancer, asbestos exposure and smoking (source: McDonald et al, 1980, on chrysotile mining). The authors condensed this second set from 50 subgroups into nine.
• Exposure: Accumulated dust exposure in million particles per cubic foot multiplied by years (mpcf·y). For the textile plant data, exposure was accumulated up to 10 years before death. The cited source study for these data was of a factory using chrysotile, amosite and crocidolite. The second example used accumulated asbestos exposure from a cited study of chrysotile mining, together with three levels of cigarette smoking (low, moderate, high).
• Main results:
  • Textile plant data, line of the form SMR = a + b·x: the estimated SMR at zero exposure (a) was 0.528880. The estimated slope (b) was an increase of 0.026979 in SMR per mpcf·y of dust exposure accumulated up to 10 years before death. The goodness-of-fit statistic was 0.9336 on 3 degrees of freedom.
  • Textile plant data, line forced to SMR = 1 at zero exposure: the slope was 0.016530 per mpcf·y and the goodness-of-fit statistic was 7.3255 on 4 degrees of freedom. The difference from the unforced line was 6.3919 on 1 degree of freedom. The authors called this strong evidence that the forced line was less satisfactory.
  • Textile plant data: the relative slope r (b divided by a) was 0.05101 per mpcf·y. The authors described r as the excess risk per unit increase in exposure.
  • Textile plant data: the confidence limits for the relative slope were 0.0176 (lower) and 0.15078 (upper) per mpcf·y. The text does not state the confidence level for this interval.
  • Asbestos and smoking example: the fitted relative slopes suggested that the heavier the smoking, the shallower the relative slope for asbestos.
  • Asbestos and smoking example: when the line was fitted separately for each smoking category, the 90% confidence limits on the relative slopes overlapped. A common relative slope close to 0.0017 would be compatible throughout.
• The authors' conclusion: The authors concluded that formal methods of fitting exposure-SMR relationships should be used more commonly. They also argued that the relative slope is a more appropriate measure of the gradient of the exposure-risk relationship.
• Limitations the authors state:
  • The asbestos and smoking data were heavily grouped for teaching purposes, which left small numbers of deaths in some subgroups.
  • The authors stated that the asbestos and smoking findings could not be taken as definitive and must also be examined for biological plausibility.
  • Theoretical objections have been raised to analyses that use ratios of SMRs. The authors added that the practical importance of these objections has not been demonstrated.

Topics

Medical terms in this study, explained in our Lexicon: standardized mortality ratio (SMR), Cohort Study, confidence interval, Lung Cancer.

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