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Sharpening Bounds on Principal Effects with Covariates
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    Estimation of treatment effects in randomized studies is often hampered by possible selection bias induced by conditioning on or adjusting for a variable measured post-randomization. One approach to obviate such selection bias is to consider inference about treatment effects within principal strata, that is, principal effects. A challenge with this approach is that without strong assumptions principal effects are not identifiable from the observable data. In settings where such assumptions are dubious, identifiable large sample bounds may be the preferred target of inference. In practice these bounds may be wide and not particularly informative. In this work we consider whether bounds on principal effects can be improved by adjusting for a categorical baseline covariate. Adjusted bounds are considered which are shown to never be wider than the unadjusted bounds. Necessary and sufficient conditions are given for which the adjusted bounds will be sharper (i.e., narrower) than the unadjusted bounds. The methods are illustrated using data from a recent, large study of interventions to prevent mother-to-child transmission of HIV through breastfeeding. Using a baseline covariate indicating low birth weight, the estimated adjusted bounds for the principal effect of interest are 63% narrower than the estimated unadjusted bounds.

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    P30 AI050410/AI/NIAID NIH HHS/United States
    R01 AI085073/AI/NIAID NIH HHS/United States
    R01-AI085073/AI/NIAID NIH HHS/United States
    R37 AI054165/AI/NIAID NIH HHS/United States
    U48-DP001944/DP/NCCDPHP CDC HHS/United States
    U54 GM104942/GM/NIGMS NIH HHS/United States
    U54-GM104942/GM/NIGMS NIH HHS/United States
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