Table 2.
Hypothetical results from rate regressions in which a covariate is or is not a confounder or a source of multicollinearity
| Model | Model variables | Exposure coefficient estimate | Rate ratio estimate | SE for coeff. | 95% CL | Coefficient bias estimate * | Indicates bias? | Indicates strongly collinear? | Root MSE estimate * | Collapsibility χ 2 and P -value 33 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | X,W 1 …W J , U 1 …U H | 0.693 | 2.00 | 0.24 | 1.25,3.20 | Referent | 0.24 | |||
| Some mutually exclusive alternative possibilities under model 2 (minimal model in which all unforced variables U 1 …U H are dropped) | ||||||||||
| 2a | X,W 1 …W J | 0.693 | 2.00 | 0.24 | 1.25, 3.20 | 0 | No | No | 0.24 | 0, P = 1 |
| 2b | X,W 1 …W J | 1.099 | 3.00 | 0.20 | 2.03, 4.44 | 0.405 | Yes | No | 0.45 | 9.34, P = 0.002 |
| 2c | X,W 1 …W J | 0.693 | 2.00 | 0.14 | 1.52, 2.63 | 0 | No | Yes | 0.14 | 0, P = 1 |
| 2d | X,W 1 …W J | 1.099 | 3.00 | 0.14 | 2.28, 3.95 | 0.405 | Yes | Yes | 0.43 | 4.03, P = 0.04 |
*Taking model 1 as the referent (‘gold standard’).