Table 6-1. The application of the case-only approach for the preventive (negative) interaction effect between blood chromium levels and glycohemoglobin levels on albuminuria (micro and macro) | |
logit P(D = 1) = β0 + β2’E OR for 1 unit difference of environmental exposure = exp.(β2’) |  |
OR for a 1 μg/L difference of blood chromium level: 2.20 (95% CI 1.48–3.32) | Effect estimate |
When a 1 μg/L of blood chromium level (μg/L) differs, the fold-difference in the odds of albuminuria is 2.20 (95% CI 1.48–3.32) times. | Explanation |
logit P(D = 1) = β0 + β1’S OR for 1 unit difference of susceptibility factor = exp.(β1’) |  |
OR for 1% difference of glycohemoglobin level: 1.57 (95% CI 1.44–1.73) | Effect estimate |
When a 1% of blood glycohemoglobin level differs, the fold-difference in the odds of albuminuria is 1.57 (95% CI 1.44–1.73) times. | Explanation |
logit P(D = 1) = β0 + β1S + β2E + β3SE ICRc/nc = exp.(β3) | Eq. (8) Eq. (9) |
ICRc/nc: 0.72 (95% CI 0.35–1.60) | Effect estimate |
When a 1 μg/L of both blood chromium level and 1% of blood glycohemoglobin level coincide, the multiplicative ICR is 0.72 (95% CI 0.35–1.60), with statistical insignificance. | Explanation |
logit P(S = 1) = η0 + η1E S-E ORc/nc = exp.(η1) | Eq. (6) Eq. (7) |
S-E ORc/nc: 0.76 (95% CI 0.47–1.06) | Effect estimate |
In the the population with cases and non-cases, blood chromium levels and blood glycohemoglobin levels are independent. Therefore, the case-only ICR can be a good substitute for the ICR acquired from the population with cases and non-cases. | Explanation |
logit P(S = 1) = γ0 + γ1E ICRCO = exp.(γ1) | Eq. (4) Eq. (5) |
ICRCO: 0.59 (95% CI 0.28–0.95) | Effect estimate |
When only the cases are analyzed (case-only approach), the case-only ICR is 0.59 (95% CI 0.28–0.95), with a statistical significance (a negative interaction effect). | Explanation |
Table 6-2. The application of the case-only approach for the aggravating (positive) interaction effect between blood cobalt levels and old ages on albuminuria (micro and macro) | |
logit P(D = 1) = β0 + β2’E OR for 1 unit difference of environmental exposure = exp.(β2’) |  |
OR for 1 μg/L difference of blood cobalt level: 1.09 (95% CI 0.98–1.20) | Effect estimate |
When a 1 μg/L of blood cobalt level (μg/L) differs, the fold-difference in the odds of albuminuria is 1.09 (95% CI 1.31–1.57) times. | Explanation |
logit P(D = 1) = β0 + β1’S OR for 1 unit difference of susceptibility factor = exp.(β1’) |  |
OR for a 1-year difference of age: 1.05 (95% CI 1.04–1.05) | Effect estimate |
When 1-year in age differs, the fold-difference in the odds of albuminuria is 1.05 (95% CI 1.04–1.05) times. | Explanation |
logit P(D = 1) = β0 + β1S + β2E + β3SE ICRc/nc = exp.(β3) | Eq. (8) Eq. (9) |
ICRc/nc: 1.13 (95% CI 0.99–1.37) | Effect estimate |
When a 1 μg/L difference of both blood cobalt level and 1-year difference of age coincide, the multiplicative ICR is 1.13 (95% CI 0.99–1.37), with statistical insignificance. | Explanation |
logit P(S = 1) = η0 + η1E S-E ORc/nc = exp.(η1) | Eq. (6) Eq. (7) |
S-E ORc/nc: 1.06 (95% CI 1.03–1.10) | Effect estimate |
In the a population with cases and non-cases, blood cobalt level and age in years show a slight association (not completely independent). Therefore, the case-only ICR must be multiplied by the S-E ORc/nc to be ICRc/nc according to Eq. (3). | Explanation |
logit P(S = 1) = γ0 + γ1E ICRCO = exp.(γ1) | Eq. (4) Eq. (5) |
ICRCO: 1.14 (95% CI 1.03–1.37) | Effect estimate |
When only the cases were analyzed (case-only approach), the case-only ICR was 1.14 (1.03–1.37), with a statistical significance (a positive interaction effect). | Explanation |
\({\mathrm{ICR}}_{\mathrm{c}/\mathrm{nc}}=\frac{{\mathrm{RR}}_{\mathrm{s}\mathrm{e}}}{{\mathrm{RR}}_{\mathrm{s}}{\mathrm{RR}}_{\mathrm{e}}}=\left(\frac{\mathrm{ag}}{\mathrm{c}\mathrm{e}}\right)\left(\frac{\left(\mathrm{c}+\mathrm{D}\right)\left(\mathrm{e}+\mathrm{F}\right)}{\left(\mathrm{a}+\mathrm{B}\right)\left(\mathrm{g}+\mathrm{H}\right)}\right)=\left({\mathrm{ICR}}_{\mathrm{CO}}\right)\left(\mathrm{S}-\mathrm{E}\ {\mathrm{OR}}_{\mathrm{c}/\mathrm{nc}}\right)\) | Eq. (2) |
ICRCO: 1.14 (1.03–1.37) × S-E ORc/nc: 1.06 (95% CI 1.03–1.10) |  |
ICRc/nc: 1.21 (95% CI 1.06–1.51) | Effect estimate |
The ICRCO multiplied by the S-E ORc/nc produced the ICRc/nc of 1.21 (95% CI 1.06–1.51). | Explanation |