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Barrie, ON

Novel statistical and epidemiological methods are being applied to ONPHEC to examine the relationships between environmental exposures and chronic diseases in advanced and innovative ways. The following tools may help researchers implement some of these methods with their own data.


Indirect adjustment for unmeasured confounders

To control for important individual-level covariates (e.g., smoking, alcohol consumption, physical activity, diet), often unavailable in large cohort studies using administrative databases, an indirect adjustment method developed by ONPHEC co-principal investigator, Dr. Richard Burnett, can be applied. 

The indirect adjustment method makes use of an auxiliary dataset that contains the individual-level covariates that are not available for the entire cohort, in addition to the covariates that are available for the entire cohort (e.g., age, sex, area-level SES variables). The measure of effect (i.e., hazard ratio, risk ratio, etc.) between the exposure and outcome of interest estimated from the entire cohort is adjusted for the missing covariates by use of:

  • The estimated associations between the missing covariates and the observed covariates (estimated from the auxiliary dataset)

  • The estimated associations between the missing covariates and the outcome (obtained from the literature)

More on this method can be found in:

Shin HH, Cakmak S, Brion O, Villeneuve P, Turner MC, Goldberg MS, Jerrett M, Chen H, Crouse D, Peters P, Pope CA, Burnett RT. Indirect adjustment for multiple missing variables applicable to environmental epidemiology. Environ Res 2014; 134:482–7. View Article

The ONPHEC team has created a R function, as well as a Shiny web application, to apply the indirect adjustment method.

Indirect Adjustment R Code

Indirect Adjustment Web Application


Fitting non-linear concentration-response functions

The concentration-response relationship between the exposure and outcome of interest may not truly be linear, as classic regression models like the Cox proportional hazards model would suggest. ONPHEC co-principal investigator, Dr. Richard Burnett, has developed a new class of flexible concentration-response functions that can be fit to classic survival models using standard statistical software.

Fitting non-linear concentration-response functions involves fitting a variable coefficient risk function to capture the potential non-linear association between the exposure and outcome. The exposure is transformed by either a linear or log-linear function, and then multiplied by a logistic weighting function. The associated parameter giving the hazard ratio of the concentration-response relationship can be estimated using standard survival analysis software.

More on this method can be found in:

Nasari MM, Szyszkowicz M, Chen H, Crouse D, Turner MC, Jerrett M, Pope CA, Hubbell B, Fann N, Cohen A, Gapstur SM, Diver WR, Stieb D, Forouzanfar MH, Kim SY, Olives C, Krewski D, Burnett RT. A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution. Air Qual Atmos Health 2016; 9(8):961–72. View Article

The ONPHEC team has written a R function and a SAS macro to fit nonlinear concentration-response curves using Cox proportional hazards modeling.

Concentration-Response Function R Code

Concentration-Response Function SAS Code