Appendix Table 2.
HRs for Consumption of ≥4 Cups per Day Compared With Nondrinkers, Corrected for Different Levels of Confounding by an Unmeasured Dichotomous Confounder Using Sensitivity Analysis*
| P1 | P0 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0.0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
| Γ = 1.2 | ||||||||||
| 0.0 | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – | – |
| 0.1 | 0.80 (0.74–0.87) | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – |
| 0.3 | 0.84 (0.77–0.90) | 0.82 (0.76–0.88) | 0.80 (0.74–0.87) | 0.79 (0.73–0.85) | – | – | – | – | – | – |
| 0.5 | 0.87 (0.80–0.94) | 0.85 (0.79–0.92) | 0.84 (0.77–0.90) | 0.82 (0.76–0.88) | 0.80 (0.74–0.87) | 0.79 (0.73–0.85) | – | – | – | – |
| 0.7 | 0.90 (0.83–0.97) | 0.88 (0.82–0.95) | 0.87 (0.80–0.93) | 0.85 (0.78–0.91) | 0.83 (0.77–0.90) | 0.82 (0.74–0.86) | 0.80 (0.74–0.86) | 0.79 (0.73–0.85) | – | – |
| 0.9 | 0.93 (0.88–1.02) | 0.91 (0.84–0.98) | 0.90 (0.83–0.96) | 0.88 (0.81–0.95) | 0.86 (0.80–0.93) | 0.85 (0.78–0.91) | 0.83 (0.77–0.90) | 0.82 (0.76–0.88) | 0.80 (0.74–0.86) | 0.79 (0.73–0.85) |
| Γ = 1.3 | ||||||||||
| 0.0 | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – | – |
| 0.1 | 0.81 (0.75–0.88) | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – |
| 0.3 | 0.86 (0.80–0.93) | 0.84 (0.77–0.90) | 0.81 (0.75–0.87) | 0.79 (0.73–0.85) | – | – | – | – | – | – |
| 0.5 | 0.91 (0.84–0.98) | 0.88 (0.82–0.95) | 0.86 (0.79–0.92) | 0.83 (0.77–0.90) | 0.81 (0.75–0.87) | 0.79 (0.73–0.85) | – | – | – | – |
| 0.7 | 0.96 (0.88–1.03) | 0.93 (0.86–1.00) | 0.90 (0.83–0.97) | 0.88 (0.81–0.94) | 0.85 (0.79–0.92) | 0.83 (0.77–0.89) | 0.81 (0.75–0.87) | 0.79 (0.73–0.85) | – | – |
| 0.9 | 1.00 (0.93–1.08) | 0.97 (0.90–1.05) | 0.95 (0.87–1.02) | 0.92 (0.85–0.99) | 0.90 (0.83–0.96) | 0.87 (0.81–0.94) | 0.85 (0.79–0.91) | 0.83 (0.77–0.89) | 0.81 (0.75–0.87) | 0.79 (0.73–0.85) |
| Γ = 1.5 | ||||||||||
| 0.0 | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – | – |
| 0.1 | 0.83 (0.77–0.89) | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – |
| 0.3 | 0.91 (0.84–0.98) | 0.86 (0.80–0.93) | 0.82 (0.76–0.89) | 0.79 (0.73–0.85) | – | – | – | – | – | – |
| 0.5 | 0.99 (0.91–1.06) | 0.94 (0.78–1.01) | 0.90 (0.82–0.96) | 0.86 (0.79–0.92) | 0.82 (0.76–0.88) | 0.79 (0.73–0.85) | – | – | – | – |
| 0.7 | 1.07 (0.98–1.15) | 1.02 (0.94–1.09) | 0.97 (0.90–1.04) | 0.93 (0.86–1.00) | 0.89 (0.82–0.96) | 0.85 (0.79–0.92) | 0.82 (0.76–0.88) | 0.79 (0.73–0.85) | – | – |
| 0.9 | 1.14 (1.06–1.23) | 1.09 (1.01–1.17) | 1.04 (0.96–1.12) | 1.00 (0.92–1.07) | 0.95 (0.88–1.03) | 0.92 (0.85–0.99) | 0.88 (0.81–0.95) | 0.85 (0.78–0.91) | 0.82 (0.76–0.88) | 0.79 (0.73–0.85) |
| Γ = 2.0 | ||||||||||
| 0.0 | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – | – |
| 0.1 | 0.87 (0.80–0.94) | 0.79 (0.73–0.85) | – | – | – | – | – | – | – | – |
| 0.3 | 1.03 (0.95–1.10) | 0.93 (0.86–1.00) | 0.86 (0.79–0.92) | 0.79 (0.73–0.85) | – | – | – | – | – | – |
| 0.5 | 1.18 (1.10–1.28) | 1.08 (1.00–1.16) | 0.99 (0.91–1.06) | 0.91 (0.84–0.98) | 0.85 (0.78–0.91) | 0.79 (0.73–0.85) | – | – | – | – |
| 0.7 | 1.34 (1.24–1.44) | 1.22 (1.13–1.31) | 1.12 (1.03–1.20) | 1.03 (0.95–1.11) | 0.96 (0.89–1.03) | 0.90 (0.83–0.96) | 0.84 (0.78–0.90) | 0.79 (0.73–0.85) | – | – |
| 0.9 | 1.50 (1.39–1.62) | 1.36 (1.26–1.47) | 1.25 (1.16–1.34) | 1.15 (1.07–1.24) | 1.07 (0.99–1.15) | 1.01 (0.92–1.08) | 0.94 (0.87–1.01) | 0.88 (0.82–0.95) | 0.83 (0.77–0.90) | 0.79 (0.73–0.85) |
HR = hazard ratio.
Values are HR (95% CI). T is the HR for mortality, and U is an unmeasured dichotomous confounder for non– coffee drinkers and for drinkers of ≥4 cups per day. P1 is the proportion exposed to U in the group exposed to ≥4 cups of caffeinated coffee, and P0 is the proportion exposed to U in the group not exposed to coffee. We assume that U is positively associated with coffee consumption, so that P1 ≥ P0. The corrected HR (HRcorrected) is computed as HRobs/([ΓP1 + {1 − P1}]/[ΓP0 + {1 − P0}]), where HRobs is the observed HR (0.79 in this case). Cells with no formatting represent settings where the corrected HR is <1 and is significant, boldface cells represent settings where the CI includes 1, and boldface and italic cells represent settings where the corrected HR is >1 and is significant.