Nonparametric Bounds and Sensitivity Analysis of Treatment Effects

Richardson, Amy; Hudgens, Michael G.; Gilbert, Peter B.; Fine, Jason P.

doi:10.1214/14-sts499

Cited by 53 publications

(47 citation statements)

References 100 publications

(144 reference statements)

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“…By Theorem (i), we obtain the bounds for

ACE false(T \to Y false)

as [−0.331, 0.165]. Using the bootstrap method, we obtain the first quartile of the lower bounds and third quartile of the upper bounds to construct an uncertainty region (confidence interval for bounds; see more in A. Richardson, Hudgens, Gilbert, & Fine, ) as [−0.349, 0.173]. Both the bounds and the uncertainty region include 0, that is, the surrogate paradox cannot be excluded without further assumptions.…”

Section: Discussionmentioning

confidence: 99%

Novel criteria to exclude the surrogate paradox and their optimalities

Yin

Liu

Geng

et al. 2019

Scandinavian J Statistics

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When the primary outcome is hard to collect, a surrogate endpoint is typically used as a substitute. However, even when a treatment has a positive average causal effect (ACE) on a surrogate endpoint, which also has a positive ACE on the primary outcome, it is still possible that the treatment has a negative ACE on the primary outcome. Such a phenomenon is called the surrogate paradox and greatly challenges the use of surrogates. In this paper, we provide criteria to exclude the surrogate paradox. Our criteria are optimal in the sense that they are sufficient and “almost necessary” to exclude the paradox: If the conditions are satisfied, the surrogate paradox is guaranteed to be absent, whereas if the conditions fail, there exists a data‐generating process with surrogate paradox that can generate the same observed data. That is, our criteria capture all the observed information to exclude the surrogate paradox.

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“…By Theorem (i), we obtain the bounds for

ACE false(T \to Y false)

Section: Discussionmentioning

confidence: 99%

Novel criteria to exclude the surrogate paradox and their optimalities

Yin

Liu

Geng

et al. 2019

Scandinavian J Statistics

View full text Add to dashboard Cite

show abstract

“…By Proposition 1, the bound of HR(T → Y ) is [0.033, 0.105] and the bound does not change with c 1 . Using bootstrap, we obtain the 95% uncertainty region (confidence interval for bounds, see more in Richardson et al (2014)) of HR(T → Y ) as [0.011, 0.119]. That is, under 95% confidence level, for any c 1 > 0.119, if the proportion of individuals that have glycated hemoglobin level increased to > 6% in one year follow up due to intensive treatment is less than c 1 , then, no more than c 1 proportion of individuals will get progression of diabetic retinopathy due to the intensive treatment.…”

Section: Discussionmentioning

confidence: 99%

On the individual surrogate paradox

Yin

Liu

et al. 2019

Biostatistics

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When the primary outcome is difficult to collect, surrogate endpoint is typically used as a substitute. It is possible that for every individual, treatment has a positive effect on surrogate, and surrogate has a positive effect on primary outcome, but for some individuals, treatment has a negative effect on primary outcome. For example, a treatment may be substantially effective in preventing the stroke for everyone, and lowering the risk of stroke is universally beneficial for a longer survival time, however, the treatment may still causes death for some individuals. We define such paradoxical phenomenon as individual surrogate paradox. The individual surrogate paradox is proposed to capture the treatment effect heterogeneity, which is unable to be described by either the surrogate paradox based on average causal effect (ACE) (Chen et al., 2007) or that based on distributional causal effect (DCE) (Ju and Geng, 2010). We investigate existing surrogate criteria in terms of whether the individual surrogate paradox could manifest. We find that only the strong binary surrogate can avoid such paradox without additional assumptions. Utilizing the sharp bounds, we propose novel criteria to exclude the individual surrogate paradox. Our methods are illustrated in an application to determine the effect of the intensive glycemia on the risk of development or progression of diabetic retinopathy.

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“…For example, see figure 2 of Richardson, Hudgens, Gilbert, and Fine (2014). They informally discuss how to use these bands to check robustness of the claim that the true parameter is nonzero, but they do not formally discuss breakdown points or inference on them.…”

Section: Nonparametric Neighborhoodsmentioning

confidence: 99%

Inference on breakdown frontiers

Masten¹,

Poirier²

2017

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A breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes deviations from random assignment of treatment, and one which indexes deviations from rank invariance. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to deviations in the point identifying assumptions. We derive √ N -consistent sample analog estimators for these frontiers. We then provide an asymptotically valid bootstrap procedure for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, this confidence band can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that conclusions are fairly robust to failure of rank invariance, when random assignment holds, but conclusions are much more sensitive to both assumptions for small deviations from random assignment.JEL classification: C14; C18; C21; C25; C51

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Nonparametric Bounds and Sensitivity Analysis of Treatment Effects

Cited by 53 publications

References 100 publications

Novel criteria to exclude the surrogate paradox and their optimalities

Novel criteria to exclude the surrogate paradox and their optimalities

On the individual surrogate paradox

Inference on breakdown frontiers

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