Fitting Relationships Between Exposure and Standardized Mortality Ratios

Evaluation of the Exposure—Response Relationship of Lung Cancer Mortality and Occupational Exposure to Hexavalent Chromium Based on Published Epidemiological Data

“…To evaluate nonlinearity in the exposure-response data, we assumed that the number of lung cancer deaths follows a Poisson distribution. Subsequently, a linear nonthreshold multiplicative model was fit to categorical standardized mortality ratio (SMR) results using iteratively reweighted least-squares estimation with the procedure PROC NLIN in the SAS statistical software package (SAS Institute, Cary, NC; Hanley and Liddell, 1985;Hertz-Picciotto and Smith, 1993):…”

A Graphical Method to Evaluate Exposure-Response Relationships in Epidemiologic Studies Using Standardized Mortality or Morbidity Ratios

“…For the calculation of the linear slope, we assume that the number of events follows a Poisson distribution. A linear nonthreshold multiplicative model is fit to the SMR results from the categorical analysis (three categories; see above) using iteratively re-weighted least-squares estimation [Hanley and Liddell 1985; Hertz-Picciotto and Smith 1993]:…”

“…For the calculation of the linear slope, we assume that the number of events follows a Poisson distribution. A linear nonthreshold multiplicative model is fit to the SMR results from the categorical analysis (three categories; see above) using iteratively re-weighted least-squares estimation [Hanley and Liddell 1985;Hertz-Picciotto and Smith 1993]: where E[] indicates the expectation of a random variable (in this case from a Poisson distribution), obs i is the observed number of events at exposure level i, α represents any difference between the study cohort and the external referent population with respect to baseline rate, EXP i is the expected number of events at exposure level i, β is the slope based on maximum likelihood estimation, and x is the exposure level. In addition, a goodness of fit statistic is calculated which follows a chi-square distribution with (k -N) degrees of freedom, where k is the number of exposure categories and N is the number of parameters estimated.…”

Current intelligence bulletin 69: NIOSH practices in occupational risk assessment.

“…As another example, if SMRs are reported at different levels of exposure, then weighted least-squares regression or maximum likelihood estimation methods can be used. Examples of these techniques have been described in several reports [Breslow and Day 1987;Crump and Allen 1985;Hanley and Liddell 1985;Rothman et al 2008;Smith 1988;Smith et al 1994;Steenland and Savitz 1997].…”

“…A NIOSH example of a limited data approach is not available; however, examples are available in the literature [Chovil et al 1981;Crump and Allen 1985;Hanley and Liddell 1985;Smith 1988;Steenland and Savitz 1997]. For example, Steenland and Savitz [1997] used a simple linear model to examine the dose-response between airborne nickel levels and lung cancer mortality.…”