TABLE 4.
The Effect of a Potential Unmeasured Binary Confounder in the Preterm Birth-to-Outcome Pathway, Considering Varying Relationships Between the Confounder and Outcome
| Prevalence of Binary Unmeasured Confounder | Bias-Corrected Odds Ratio | Odds Ratio Required to Explain Away the Observed Direct Effecta | ||||
|---|---|---|---|---|---|---|
| Normotensive Term Pregnancies (%) | Preeclampsia Term Pregnancies (%) | The Effect Size of the Unmeasured Confounder in Odds Ratio | ||||
| 2.0 | 4.0 | 6.0 | 10.0 | |||
| Peri- or intraventricular hemorrhage (direct effect OR = 3.2) | ||||||
| 1 | 5 | 3.1 | 2.9 | 2.7 | 2.4 | 124.5 |
| 10 | 3.0 | 2.5 | 2.3 | 1.8 | 33.5 | |
| 20 | 2.7 | 2.1 | 1.7 | 1.3 | 14.2 | |
| 40 | 2.3 | 1.5 | 1.1 | 0.8 | 7.0 | |
| 60 | 2.0 | 1.2 | 0.8 | 0.6 | 4.9 | |
| 80 | 1.8 | 1.0 | 0.7 | 0.4 | 3.9 | |
| 99 | 1.6 | 0.8 | 0.6 | 0.4 | 3.3 | |
| 5 | 5 | 3.2 | 3.2 | 3.2 | 3.2 | —b |
| 10 | 3.1 | 2.8 | 2.7 | 2.5 | — | |
| 20 | 2.8 | 2.3 | 2.0 | 1.7 | 56.9 | |
| 40 | 2.4 | 1.7 | 1.3 | 1.0 | 10.2 | |
| 60 | 2.1 | 1.3 | 1.0 | 0.7 | 6.0 | |
| 80 | 1.9 | 1.1 | 0.8 | 0.6 | 4.5 | |
| 99 | 1.7 | 0.9 | 0.7 | 0.5 | 3.7 | |
| 10 | 5 | 3.4 | 3.6 | 3.9 | 4.2 | — |
| 10 | 3.2 | 3.2 | 3.2 | 3.2 | — | |
| 20 | 2.9 | 2.6 | 2.4 | 2.2 | — | |
| 40 | 2.5 | 1.9 | 1.6 | 1.3 | 29.0 | |
| 60 | 2.2 | 1.5 | 1.2 | 1.0 | 8.9 | |
| 80 | 2.0 | 1.2 | 1.0 | 0.7 | 5.6 | |
| 99 | 1.8 | 1.1 | 0.8 | 0.6 | 4.3 | |
| 20 | 5 | 3.7 | 4.5 | 5.1 | 6.2 | — |
| 10 | 3.5 | 4.0 | 4.3 | 4.7 | — | |
| 20 | 3.2 | 3.2 | 3.2 | 3.2 | — | |
| 40 | 2.7 | 2.3 | 2.1 | 2.0 | — | |
| 60 | 2.4 | 1.8 | 1.6 | 1.4 | — | |
| 80 | 2.1 | 1.5 | 1.3 | 1.1 | 15.0 | |
| 99 | 1.9 | 1.3 | 1.1 | 0.9 | 7.4 | |
| 40 | 5 | 4.3 | 6.1 | 7.7 | 10.2 | — |
| 10 | 4.1 | 5.4 | 6.4 | 7.8 | — | |
| 20 | 3.8 | 4.4 | 4.8 | 5.3 | — | |
| 40 | 3.5 | 3.7 | 3.9 | 4.0 | — | |
| 60 | 3.2 | 3.2 | 3.2 | 3.2 | — | |
| 80 | 3.0 | 2.8 | 2.8 | 2.7 | — | |
| 99 | 2.8 | 2.5 | 2.4 | 2.3 | — | |
| 60 | 5 | 4.9 | 7.8 | 10.3 | 14.2 | — |
| 10 | 4.7 | 6.9 | 8.6 | 10.8 | — | |
| 20 | 4.3 | 5.6 | 6.4 | 7.3 | — | |
| 40 | 4.0 | 4.7 | 5.1 | 5.6 | — | |
| 60 | 3.7 | 4.1 | 4.3 | 4.5 | — | |
| 80 | 3.4 | 3.6 | 3.7 | 3.7 | — | |
| 99 | 3.2 | 3.2 | 3.2 | 3.2 | — | |
| 80 | 5 | 5.5 | 9.5 | 12.8 | 18.2 | 0.1 |
| 10 | 5.3 | 8.4 | 10.7 | 13.9 | 0.1 | |
| 20 | 4.8 | 6.8 | 8.0 | 9.4 | 0.1 | |
| 40 | 4.5 | 5.7 | 6.4 | 7.1 | — | |
| 60 | 4.1 | 5.0 | 5.4 | 5.7 | — | |
| 80 | 3.9 | 4.4 | 4.6 | 4.8 | — | |
| 99 | 3.6 | 3.9 | 4.0 | 4.1 | — | |
| Transient tachypnea of the newborn (direct effect OR = 1.6) | ||||||
| 1 | 5 | 1.5 | 1.4 | 1.3 | 1.2 | 17.6 |
| 10 | 1.4 | 1.2 | 1.1 | 0.9 | 7.8 | |
| 20 | 1.3 | 1.0 | 0.8 | 0.6 | 4.1 | |
| 40 | 1.1 | 0.7 | 0.6 | 0.4 | 2.5 | |
| 60 | 1.0 | 0.6 | 0.4 | 0.3 | 2.0 | |
| 80 | 0.9 | 0.5 | 0.3 | 0.2 | 1.7 | |
| 99 | 0.8 | 0.4 | 0.3 | 0.2 | 1.6 | |
| 5 | 5 | 1.6 | 1.6 | 1.6 | 1.6 | — |
| 10 | 1.5 | 1.4 | 1.3 | 1.2 | 27.5 | |
| 20 | 1.4 | 1.1 | 1.0 | 0.8 | 5.7 | |
| 40 | 1.3 | 1.0 | 0.8 | 0.6 | 2.8 | |
| 60 | 1.2 | 0.8 | 0.7 | 0.5 | 2.1 | |
| 80 | 1.1 | 0.7 | 0.6 | 0.4 | 1.8 | |
| 99 | 1.0 | 0.7 | 0.5 | 0.4 | 1.6 | |
| 10 | 5 | 1.7 | 1.8 | 1.9 | 2.1 | — |
| 10 | 1.6 | 1.6 | 1.6 | 1.6 | — | |
| 20 | 1.4 | 1.3 | 1.2 | 1.1 | 14.3 | |
| 40 | 1.3 | 1.1 | 0.9 | 0.8 | 3.3 | |
| 60 | 1.2 | 0.9 | 0.8 | 0.7 | 2.3 | |
| 80 | 1.2 | 0.8 | 0.7 | 0.5 | 1.9 | |
| 99 | 1.1 | 0.7 | 0.6 | 0.5 | 1.7 | |
| 20 | 5 | 1.8 | 2.2 | 2.5 | 3.0 | — |
| 10 | 1.7 | 1.9 | 2.1 | 2.3 | — | |
| 20 | 1.6 | 1.6 | 1.6 | 1.6 | — | |
| 40 | 1.5 | 1.3 | 1.3 | 1.2 | 7.6 | |
| 60 | 1.4 | 1.1 | 1.1 | 1.0 | 3.0 | |
| 80 | 1.3 | 1.0 | 0.9 | 0.8 | 2.2 | |
| 99 | 1.2 | 0.9 | 0.8 | 0.7 | 1.8 | |
| 40 | 5 | 2.1 | 3.0 | 3.8 | 5.0 | — |
| 10 | 2.0 | 2.7 | 3.1 | 3.8 | — | |
| 20 | 1.8 | 2.2 | 2.4 | 2.6 | — | |
| 40 | 1.7 | 1.8 | 1.9 | 2.0 | — | |
| 60 | 1.6 | 1.6 | 1.6 | 1.6 | — | |
| 80 | 1.5 | 1.4 | 1.4 | 1.3 | — | |
| 99 | 1.4 | 1.2 | 1.2 | 1.1 | — | |
| 60 | 5 | 4.9 | 7.8 | 10.3 | 14.2 | 0.4 |
| 10 | 4.7 | 6.9 | 8.6 | 10.8 | 0.3 | |
| 20 | 4.3 | 5.6 | 6.4 | 7.3 | 0.2 | |
| 40 | 4.0 | 4.7 | 5.1 | 5.6 | — | |
| 60 | 3.7 | 4.1 | 4.3 | 4.5 | — | |
| 80 | 3.4 | 3.6 | 3.7 | 3.7 | — | |
| 99 | 3.2 | 3.2 | 3.2 | 3.2 | — | |
| 80 | 5 | 5.5 | 9.5 | 12.8 | 18.2 | 0.5 |
| 10 | 5.3 | 8.4 | 10.7 | 13.9 | 0.5 | |
| 20 | 4.8 | 6.8 | 8.0 | 9.4 | 0.5 | |
| 40 | 4.5 | 5.7 | 6.4 | 7.1 | 0.3 | |
| 60 | 4.1 | 5.0 | 5.4 | 5.7 | 0.1 | |
| 80 | 3.9 | 4.4 | 4.6 | 4.8 | — | |
| 99 | 3.6 | 3.9 | 4.0 | 4.1 | — | |
a
The effect size required to explain away the direct effect of the outcome is calculated from the equation γ=(π1m+B-Bπ0m-1)/(π1m-Bπ0m), where B is the amount of bias necessary to render the association null (B = 3.21 and B = 1.57 for peri- or intraventricular hemorrhage and transient tachypnea of the newborn, respectively) and π1m and π0m are the prevalence of the unmeasured confounder in preeclamptic and normotensive term pregnancies, respectively.
b
The calculation results in odds <0 which are implausible.