PHLT 8520 Week 9 Sensitivity Argument Example

How Strong Would the Hidden Confounder Have to Be? A Sensitivity Argument Testing an Illustrative Risk Ratio of 1.8 for Night Work and Preterm Birth Against Financial Strain From a Second Job

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Walden University

PHLT 8520: Advanced Epidemiological Methods

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Month Day, Year

How Strong Would the Hidden Confounder Have to Be? A Sensitivity Argument Testing an Illustrative Risk Ratio of 1.8 for Night Work and Preterm Birth Against Financial Strain From a Second Job

The Estimate Under Pressure

For this exercise the restricted first-birth cohort is given an illustrative result. Among 3,410 first pregnancies, 168 of 1,560 women with at least one night on their timekeeping record in the window delivered preterm (10.8%), compared with 111 of 1,850 who worked only days or evenings (6.0%). With the four Week 3 covariates in the model, the risk ratio is 1.80, with a 95% confidence interval from 1.42 to 2.28. These numbers are invented for the exercise.

The adjustment set closes the paths drawn in Week 3, but one confounder was named there and never measured: financial strain severe enough that a woman holds a second job. A second job could push her toward night rosters at the health system, where nights pay a differential, and could raise preterm risk through fatigue, stress and reduced prenatal visits. Rather than say only that this confounder "may explain" the result, this paper asks how strong it would have to be.

The E-Value

VanderWeele and Ding (2017) define the E-value as the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need with both the exposure and the outcome, conditional on measured covariates, to move the observed risk ratio to 1. For a risk ratio above 1, it equals the risk ratio plus the square root of the risk ratio multiplied by one less than itself.

For the point estimate, 1.80 plus the square root of 1.80 times 0.80 gives 1.80 plus 1.20, or 3.00. To erase the association, financial strain would need to make night work three times as likely and preterm birth three times as likely, both after adjustment for job grade, salary band, age and chronic disease. To move the lower confidence limit to 1, it would need associations of about 2.2 with each.

Table 1

E-Values for the Illustrative Estimate

Note. Calculated from the illustrative composite estimate.

Is a Strength of Three Believable?

With Night Work

Within the same job titles and salary bands, would women under financial strain be three times as likely to work nights? Night differentials make nights attractive to anyone who needs income, and a woman with a second daytime job might take nights at the hospital to fit both. A risk ratio between 1.5 and 2.5 seems plausible; 3 seems high once salary band is held constant, since strain and pay are closely linked. The cohort holds one partial check. Employees must disclose outside employment under the system's conflict-of-interest policy, and in the composite file 7% of women in the first-birth cohort filed a disclosure. Among them, night work was about 1.9 times as common as among women without one, a figure that sits inside the plausible range and is likely an undercount, since many second jobs go undisclosed.

With Preterm Birth

Would strain triple the risk of preterm birth among women who share job grade, salary, age and baseline health? Socioeconomic gradients in preterm birth are real, but adjusted associations of individual financial measures with preterm birth are usually well below 2. Goldenberg et al. (2008) list low socioeconomic status among many risk factors whose effects are modest individually. A risk ratio of 1.3 to 1.6 seems the most that could survive the existing adjustment.

Combining the Two

The E-value assumes equal strength on both sides. Ding and VanderWeele (2016) give a bounding factor for unequal strengths: the product of the two risk ratios divided by their sum minus one. With 2.5 for night work and 1.6 for preterm birth, the bound is 4.0 divided by 3.1, or 1.29. A confounder that strong could reduce the risk ratio from 1.80 to roughly 1.4, but not to 1. Even with generous assumptions, financial strain alone does not plausibly account for the whole association.

Table 2

Maximum Bias From Financial Strain Under Different Assumptions

Note. Bounding factor equals the product of the two risk ratios divided by their sum minus one; the last column divides 1.80 by the bound.

What the Argument Does Not Settle

An E-value measures robustness to one kind of bias. It does not address the others this course has examined. Week 7 found that early ultrasound dating was less common in the night group, an error that could push the estimate away from the null. Selection, examined in Week 5, probably pushes the other way. A risk ratio of 1.8 is also far larger than the modest or null estimates from larger studies, including a pooled range of about 1.04 to 1.18 for shift work and preterm delivery (Palmer et al., 2013) and no excess in Danish payroll data (Specht et al., 2019). That gap is itself a reason for caution: when a result departs sharply from a body of better-measured evidence, the first suspect is the study, not the biology.

The sensitivity argument therefore narrows the problem instead of resolving it. It shows that a single unmeasured socioeconomic confounder is unlikely to explain the whole association. It leaves measurement error in gestational dating as the leading alternative explanation, which the Week 10 validation work must address. Lash et al. (2014) recommend combining such analyses when several biases are plausible, and the final methods paper will report the confounding and dating analyses together, so readers see how the estimate behaves when both are considered.

Summary

An illustrative risk ratio of 1.8 has an E-value of 3.0, and of about 2.2 for its lower limit. Plausible strengths for financial strain, judged within the existing adjustment, would explain only part of the association. The result is robust to that confounder but not yet credible, since it sits far above better-measured evidence and may be inflated by differential dating.

References

Ding, P., & VanderWeele, T. J. (2016). Sensitivity analysis without assumptions. Epidemiology, 27(3), 368-377. https://doi.org/10.1097/EDE.0000000000000457

Goldenberg, R. L., Culhane, J. F., Iams, J. D., & Romero, R. (2008). Epidemiology and causes of preterm birth. The Lancet, 371(9606), 75-84. https://doi.org/10.1016/S0140-6736(08)60074-4

Lash, T. L., Fox, M. P., MacLehose, R. F., Maldonado, G., McCandless, L. C., & Greenland, S. (2014). Good practices for quantitative bias analysis. International Journal of Epidemiology, 43(6), 1969-1985. https://doi.org/10.1093/ije/dyu149

Palmer, K. T., Bonzini, M., Harris, E. C., Linaker, C., & Bonde, J. P. (2013). Work activities and risk of prematurity, low birth weight and pre-eclampsia: An updated review with meta-analysis. Occupational and Environmental Medicine, 70(4), 213-222. https://doi.org/10.1136/oemed-2012-101032

Specht, I. O., Hammer, P. E. C., Flachs, E. M., Begtrup, L. M., Larsen, A. D., Hougaard, K. S., Hansen, J., Hansen, Å. M., Kolstad, H. A., Rugulies, R., Garde, A. H., & Bonde, J. P. (2019). Night work during pregnancy and preterm birth: A large register-based cohort study. PLOS ONE, 14(4), Article e0215748. https://doi.org/10.1371/journal.pone.0215748

VanderWeele, T. J., & Ding, P. (2017). Sensitivity analysis in observational research: Introducing the E-value. Annals of Internal Medicine, 167(4), 268-274. https://doi.org/10.7326/M16-2607