To address potential residual time-dependent confounding over the 16-year follow-up period, we repeated the analysis using a marginal structural Cox proportional hazards model, a method designed to adjust for time-dependent confounding associated with time- varying exposures.^1,2 It first involved fitting two pooled logistic regression models to estimate the conditional probability of being exposed to CCBs at six-month intervals during follow-up; one for the numerator and the other for the denominator of the stabilized inverse-probability-of-treatment weights (IPTWs). The numerator treatment model included baseline covariates (same as the ones listed on the text) and follow-up time. The second denominator treatment model included covariates (same as the ones listed in the text) measured at each time interval, and follow-up time. In both treatment models, the follow-up time variable was modelled using a restricted cubic spline with five knots to reduce bias due to model misspecification from linearity assumptions.³ A stabilized IPTW for each patient was computed using the predicted probabilities from the two treatment models. These stabilized IPTWs were then used to estimate the HR of breast cancer associated with the use of CCBs with 95% CIs calculated using robust variance estimators.²

References

(1) Robins JM, Hernan MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11(5):550-560.

(2) Hernan MA, Brumback B, Robins JM. Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology.

2000;11(5):561-570.

(3) Cole SR, Hernan MA. Constructing inverse probability weights for marginal structural models. Am J Epidemiol. 2008;168(6):656-664.

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eAppendix 2. Sensitivity analysis using the Array approach to assess residual confounding by an unknown or unmeasured confounder

5.05.5 4.04.5 3.03.5 2.02.5 1.01.5 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

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Abbreviations: PC0, confounder prevalence among other antihypertensive drug users; PC1, confounder prevalence among calcium channel blocker drug users; RR, relative risk.

Graphical representation using the Array approach described by Schneeweiss.²⁶ The graph was constructed based on an observed hazard ratio of 0.97, and assuming a confounder prevalence of 0.2 among users of other antihypertensive drugs.

The adjustment of an unknown or unmeasured confounder would move the observed HR away from 0.97 only if it is strongly associated with the outcome (RR > 1.50) and imbalanced between the exposure groups. As unmeasured potential confounders such as age at first birth (relative risk [RR]: 1.27), parity (RR: 1.33), and age at menarche (RR: 1.39) are not strongly associated with breast cancer

incidence,³⁶ further adjustment for these variables is unlikely to materially change the observed HR under most plausible assumptions.

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