Model Specification

The following series of models were specified to determine if an association exists between plasma concentrations of POPs and the OR of having T2D. Given that there are some conflicting reports and recommendations around the preference of measuring abdominal obesity by waist circumference or by waist-to-hip ratio 235,236_{, I}

conducted a sensitivity analysis replacing waist circumference with waist-to-hip ratio in the logistic regression models. Two models were specified without a POP parameter to determine the base models into which a POP measure was added. Models with a POP measure were tested with both measures of individual POP compounds and summed measures of groups of POP compounds.

3.8.1. Models Without a Pollutant Parameter

The parameters described above for obesity, physical activity and age were included in the basic model for predicting the OR of having T2D. The measure selected as the physical activity parameter for the model was the daily energy expenditure during leisure activities. Years of age at the time of the physical examination was the measure selected for the parameter of age.

The obesity parameters selected were body mass index (BMI), waist

circumference (WC) and waist to hip ratio (WHR). WC and WHR are closely associated measures of abdominal obesity. Including both in the same model is anticipated to introduce a problem of collinearity into the model. Separate models were tested with WC (model 1) and with WHR (model 2) as a sensitivity analysis. The testing of two models with different measures of abdominal obesity demonstrates the robustness of the results across two different measures.

(1)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸)

(2)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊𝐸𝐸) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊𝐸𝐸 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸)

Where ln(p/(1-p)) is the natural logarithmic OR of having T2D; WC is waist

circumference; WHR is the waist to hip ratio; BMI is body mass index; ENERGYX is daily energy expenditure during leisure activities; and AGE is years of age at the time of the physical examination. The model fit and diagnostics for each model were assessed as described in the following chapter.

An interaction term between BMI and the abdominal obesity parameter (WC or WHR) was included in each of the above models. Health Canada has reported that increased waist circumference was associated with no increase in risk for many health conditions when BMI is above 35.239 _{It was expected that an interaction term could be}

binary BMI term was suitable in specifying the interaction term. The cut-points tested were based on previous studies examining increased health risk associated with BMI and abdominal obesity.240 _{However, a cut point with a statistically significant coefficient}

could not be identified. Therefore, the interaction term is the product of BMI and the abdominal obesity parameter.

3.8.2. Models Including a Pollutant Parameter

To test if POP plasma concentrations were associated with the OR of having T2D, the specifications of basic models 1 and 2 were altered to include a measure of plasma concentration for a POP compound. For example, model 1 is nested within model 3 which includes one of the POP compounds listed in Table 1 in section 3.5. Similarly, model 2 is nested within model 4. As described above, there were nineteen specific POP compounds selected for analysis with the following models 3 and 4: (3)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6(𝑃𝑃𝑃𝑃𝑃𝑃)

(4)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊𝐸𝐸) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊𝐸𝐸 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸)

+ 𝛽𝛽6(𝑃𝑃𝑃𝑃𝑃𝑃)

Where POP is the log transformed lipid-adjusted plasma concentration measure for one of the nineteen selected compounds listed in Table 1. The other parameters are

described above for models 1 and 2. In total nineteen variants of model 3 were tested. Each variant has a different individual POP compound. Similarly, nineteen variants of model 4 were also tested. Each of the variants for model 4 also specified a different POP compound from Table 1. The plasma concentration measures for each POP compound were log transformed to improve model fit and diagnostics as described in the section on model diagnostics in the following chapter.

The measures of summed molar weight of each POP grouping as listed in Table 2 were tested in models 5 and 6. Since the summed measures were of non-lipid-

adjusted molar weights, it is necessary to include in these models a parameter for total lipids in plasma. The inclusion of total lipids into the models was necessary to adjust the model for total lipids in plasma.

(5) ln � 𝑝𝑝 1 − 𝑝𝑝� = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6(𝑃𝑃𝑃𝑃𝑃𝑃) + 𝛽𝛽7(𝐿𝐿𝐵𝐵𝑃𝑃𝐵𝐵𝐿𝐿𝐿𝐿) (6) ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊𝐸𝐸) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊𝐸𝐸 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6(𝑃𝑃𝑃𝑃𝑃𝑃) + 𝛽𝛽7(𝐿𝐿𝐵𝐵𝑃𝑃𝐵𝐵𝐿𝐿𝐿𝐿)

Where LIPIDS was the measure of total lipids (g/L) in plasma. The calculation for estimating total lipids is discussed above in section 3.6. The other parameters are described above for models 1 and 2.

The above models estimate the coefficient for each of the POP measures listed in Tables 1 and 2. These coefficients will vary considerable between different POP measures. The variation in coefficients among different POP measures is related in part to the range of values for each POP measure. The coefficients can be standardized to estimate the change in the log OR of having T2D given an interquartile change in the POP measure. The POP measures were standardized by first calculating the

interquartile range between the 25th _{and 75}th _{percentiles of each POP measure. Next}

each POP was then divided by its own interquartile range. The interquartile scaled POP measures were then tested in models 7 to 10. Models 7 to 10 were similar to models 3 to 6 except for the use of the interquartile scaled POP measures (POPiq). As with

models 3 and 4, there were nineteen variants for each of models 7 and 8 for each of the individual interquartile scaled POP measures.

(7)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6�𝑃𝑃𝑃𝑃𝑃𝑃𝐵𝐵𝐼𝐼�

(8)

ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊𝐸𝐸) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊𝐸𝐸 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸)

+ 𝛽𝛽6�𝑃𝑃𝑃𝑃𝑃𝑃𝐵𝐵𝐼𝐼�

Models 9 and 10 had five variants similar to models 5 and 6. Each variant of models 9 and 10 had one of the interquartile scaled summed POP groupings.

(9) ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6�𝑃𝑃𝑃𝑃𝑃𝑃𝐵𝐵𝐼𝐼� + 𝛽𝛽7(𝐿𝐿𝐵𝐵𝑃𝑃𝐵𝐵𝐿𝐿𝐿𝐿) (10) ln �_{1 − 𝑝𝑝}𝑝𝑝 � = 𝛽𝛽0+ 𝛽𝛽1(𝑊𝑊𝑊𝑊𝐸𝐸) + 𝛽𝛽2(𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽3(𝑊𝑊𝑊𝑊𝐸𝐸 ∗ 𝐵𝐵𝐵𝐵𝐵𝐵) + 𝛽𝛽4(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) + 𝛽𝛽5(𝐴𝐴𝐸𝐸𝐸𝐸) + 𝛽𝛽6�𝑃𝑃𝑃𝑃𝑃𝑃𝐵𝐵𝐼𝐼� + 𝛽𝛽7(𝐿𝐿𝐵𝐵𝑃𝑃𝐵𝐵𝐿𝐿𝐿𝐿)