Principal Stratification -- Uses and Limitations

VanderWeele, Tyler J.

doi:10.2202/1557-4679.1329

Cited by 87 publications

(85 citation statements)

References 50 publications

(65 reference statements)

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“…Our treatment here will center on several examples in which principal stratification has been used, including noncompliance, other instrumental variables problems, censoring by death, surrogate outcomes, and the effects of partially manipulable variables. The structure here is thus similar to VanderWeele's (2011) accompanying commentary. This essay will sometimes take issue with Pearl's views and sometimes agree or expand on them.…”

Section: Introductionsupporting

confidence: 74%

“…Let Z* denote a dichotomized version of Z. In general, even if the exclusion restriction holds for the original Z, it will not hold for a binary version (Robins and Greenland, 2000;VanderWeele, 2011). The directed acyclic graph (DAG) in figure 1 is useful for illustrating this 1 .…”

Section: Noncompliancementioning

confidence: 99%

“…The causal effects and causal association paradigms may be viewed as complementary. The causal associations paradigm is black box in nature and provides little understanding (VanderWeele, 2011); prediction of effects may be enhanced by considering mechanistic approaches.…”

Section: Effects Of Partially Manipulable Variablesmentioning

confidence: 99%

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Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far

Joffe¹

2011

The International Journal of Biostatistics

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Pearl's article provides a useful springboard for discussing further the benefits and drawbacks of principal stratification and the associated discomfort with attributing effects to post-treatment variables. The basic insights of the approach are important: pay close attention to modification of treatment effects by variables not observable before treatment decisions are made, and be careful in attributing effects to variables when counterfactuals are ill-defined. These insights have often been taken too far in many areas of application of the approach, including instrumental variables, censoring by death, and surrogate outcomes. A novel finding is that the usual principal stratification estimand in the setting of censoring by death is by itself of little practical value in estimating intervention effects.

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Section: Introductionsupporting

confidence: 74%

Section: Noncompliancementioning

confidence: 99%

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Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far

Joffe¹

2011

The International Journal of Biostatistics

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“…Fisher's blunder led Rubin to conclude that "the concepts of direct and indirect causal effects are generally ill-defined and often more deceptive than helpful to clear statistical thinking" [27]. As a result, Frangakis and Rubin [46], proposed alternative definitions of direct and indirect effects based on "principal strata" which, ironically, suffer from at least as many problems as Fisher's [47,48].…”

Section: The Birth Weight Paradoxmentioning

confidence: 99%

Lord’s Paradox Revisited – (Oh Lord! Kumbaya!)

Pearl

2016

Journal of Causal Inference

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Among the many peculiarities that were dubbed "paradoxes" by well meaning statisticians, the one reported by Frederic M. Lord in 1967 has earned a special status. Although it can be viewed, formally, as a version of Simpson's paradox, its reputation has gone much worse. Unlike Simpson's reversal, Lord's is easier to state, harder to disentangle and, for some reason, it has been lingering for almost four decades, under several interpretations and re-interpretations, and it keeps coming up in new situations and under new lights. Most peculiar yet, while some of its variants have received a satisfactory resolution, the original version presented by Lord, to the best of my knowledge, has not been given a proper treatment, not to mention a resolution.The purpose of this paper is to trace back Lord's paradox from its original formulation, resolve it using modern tools of causal analysis, explain why it resisted prior attempts at resolution and, finally, address the general methodological issue of whether adjustments for preexisting conditions is justified in group comparison applications.Keywords: baseline adjustment, birth-weight paradox, differential base-rate, group comparison, Simpson's paradox, sure-thing principle 1 Lord's original dilemma Any attempt to describe Lord's paradox in words other than those used by Lord himself can only do injustice to the clarity and freshness with which it was first enunciated in 1967 [1]. We will begin therefore by listening to Lord's own words."A large university is interested in investigating the effects on the students of the diet provided in the university dining halls and any sex difference in these effects. Various types of data are gathered. In particular, the weight of each student at the time of his arrival in September and his weight the following June are recorded.At the end of the school year, the data are independently examined by two statisticians. Both statisticians divide the students according to sex. The first statistician examines the mean weight of the girls at the beginning of the year and at the end of the year and finds these to be identical. On further investigation, he finds that the frequency distribution of weight for the girls at the end of the year is actually the same as it was at the beginning.He finds the same to be true for the boys. Although the weight of individual boys and girls has usually changed during the course of the year, perhaps by a considerable amount, the group of girls considered as a whole has not changed in weight, nor has the group of boys. A sort of dynamic equilibrium has been maintained during the year.The whole situation is shown by the solid lines in the diagram (Figure 1). Here the two ellipses represent separate scatterplots for the boys and the girls. The frequency distributions of initial weight are indicated at the top of the diagram and the identical distributions of final weight are indicated on the left side. People falling on the solid 45°line through the origin are people whose initial and final weight ar...

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“…In general application of the RHM method may be limited to intermediates with fewer categories and extending the method to the more prevalent continuous compliance may suffer the problem of tractability (VanderWeele, 2011). Although Ma et al (2011) extended the method to continuous compliance in which the joint distribution of the observed and latent/counterfactual compliance are specified by using copula to link the two arm-specific compliance distributions, we note that the underlying spectrum parameter remain unidentified.…”

Section: Discussionmentioning

confidence: 99%

Performance of Principal Stratification Method Adjusting for Treatment Noncompliance in Two Arms of a Randomized Trial

Odondi¹

2013

IJSP

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The method of principal stratification is a unifying framework for modelling cause and effect which is applicable to adjusting for treatment noncompliance in multiple arms of a trial. Baseline covariates which predict compliance with treatment are useful in addressing parameter identification problem associated with principal stratification. Roy, Hogan and Marcus (RHM) (2008) proposed a principal stratification framework in which they used baseline covariates to adjust for imperfect compliance in both arms of a two-active treatments trial. Key to the application of this method is a defining but untestable distributional assumption whose robustness is unknown. The present work uses statistically designed simulation studies in the framework of a clinical trial comparing two active treatments as applied to survival data under both homogeneous and heterogeneous treatment effect assumptions to evaluate the performance of the RHM method in terms of bias and 95% credible intervals. We first apply the standard proportional hazard model to obtain the ITT estimate and evaluate resulting bias if viewed as estimating a causal hazard ratio. We then compare the method's performance in terms of stratum-specific causal relative risk for different specifications of a user-defined spectrum parameter. The results showed no effect of the spectrum parameter on the ITT estimates. The RHM method performed poorly by producing significantly biased efficacy estimates in all strata with wider corresponding 95% credible intervals under heterogeneous treatment effect assumption. The resulting efficacy estimates varied a lot depending on the value of the unknown (user-defined) spectrum parameter.

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Principal Stratification -- Uses and Limitations

Cited by 87 publications

References 50 publications

Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far

Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far

Lord’s Paradox Revisited – (Oh Lord! Kumbaya!)

Performance of Principal Stratification Method Adjusting for Treatment Noncompliance in Two Arms of a Randomized Trial

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