Principal Stratification Research Articles

Income and substitution effects of a disability insurance reform

Disability insurance (DI) systems are widely criticized for their inherent work disincentives. This paper evaluates the effects of a Swiss DI reform that aims to lower DI benefits for a group of existing DI beneficiaries and introduces an additional level to the DI benefit schedule. The reform has only modest effects on earnings and employment but increases the disability degree of those threatened by a DI benefit decline. We estimate bounds on the income and substitution effects by employing the principal stratification framework. The income effect is quantitatively important, whereas the substitution effect is smaller and has bounds that include zero. The evidence suggests that caseworkers helped the insured with low labor market attachment to maintain a full DI benefit.

Principal ignorability in mediation analysis: through and beyond sequential ignorability

Author(s): Forastiere, L; Mattei, A; Ding, P | Abstract: In causal mediation analysis, the definitions of the natural direct and indirect effects involve potential outcomes that can never be observed, so-called a priori counterfactuals. This conceptual challenge translates into issues in identification, which requires strong and often unverifiable assumptions, including sequential ignorability. Alternatively, we can deal with post-treatment variables using the principal stratification framework, where causal effects are defined as comparisons of observable potential outcomes.We establish a novel bridge between mediation analysis and principal stratification, which helps to clarify and weaken the commonly used identifying assumptions for natural direct and indirect effects. Using principal stratification, we show how sequential ignorability extrapolates from observable potential outcomes to a priori counterfactuals, and propose alternative weaker principal ignorability-type assumptions. We illustrate the key concepts using a clinical trial.

Estimating causal effects of treatment in RCTs with provider and subject noncompliance

Subject noncompliance is a common problem in the analysis of randomized clinical trials (RCTs). With cognitive behavioral interventions, the addition of provider noncompliance further complicates making causal inference. As a motivating example, we consider an RCT of a motivational interviewing (MI)-based behavioral intervention for treating problem drug use. Treatment receipt depends on compliance of both a therapist (provider) and a patient (subject), where MI is received when the therapist adheres to the MI protocol and the patient actively participates in the intervention. However, therapists cannot be forced to follow protocol and patients cannot be forced to cooperate in an intervention. In this article, we (1) define a causal estimand of interest based on a principal stratification framework, the average causal effect of treatment among provider-subject pairs that comply with assignment or ACE(cc); (2) explore possible assumptions that identify ACE(cc); (3) develop novel estimators of ACE(cc); (4) evaluate estimators' statistical properties via simulation; and (5) apply our proposed methods for estimating ACE(cc) to data from our motivating example.

Identifying treatment responders using counterfactual modeling and potential outcomes.

Individualizing treatment according to patients' characteristics is central for personalized or precision medicine. There has been considerable recent research in developing statistical methods to determine optimal personalized treatment strategies by modeling the outcome of patients according to relevant covariates under each of the alternative treatments, and then relying on so-called predicted individual treatment effects. In this paper, we use potential outcomes and principal stratification frameworks and develop a multinomial model for left and right-censored data to estimate the probability that a patient is a responder given a set of baseline covariates. The model can apply to RCT or observational study data. This method is based on the monotonicity assumption, which implies that no patients would respond to the control treatment but not to the experimental one. We conduct a simulation study to evaluate the properties of the proposed estimation method. Results showed that the predictions of the probability of being a responder were well calibrated even if we observed variability and a small bias when many parameters were estimated. We finally applied the method to a cohort study on the selection of patients for additional radiotherapy after resection of a soft-tissue sarcoma.

Cognitive Behavioral Therapy for antipsychotic-free schizophrenia spectrum disorders: Does therapy dose influence outcome?

This study investigated the effect of “dose” and the components of Cognitive Behavioral Therapy (CBT) on treatment effects. It is a secondary analysis of the ACTION (Assessment of Cognitive Therapy Instead of Neuroleptics) trial which investigated CBT for people with schizophrenia spectrum disorders that chose not to take antipsychotic medication. Using instrumental variable methods, we found a “dose-response” such that each CBT session attended, reduced the primary outcome measure (the PANSS total score) by approximately 0.6 points (95% CI −1.20 to −0.06, p = 0.031). This suggests that length of therapy is important for those that receive CBT in the absence of antipsychotic medication. Secondly, using principal stratification we examined the process variables that modified treatment effects. Findings revealed that those who received a longitudinal formulation in the first 4 sessions of CBT had poorer treatment effects than those who did not, however this finding was not statistically significant (95% CI −37.244, 6.677, p = 0.173). However, it is important to note that these findings were evident in an exploratory analysis with a small sample. Future larger scale studies are needed to help understand components of effective treatment.

Estimation of causal effects in clinical endpoint bioequivalence studies in the presence of intercurrent events: noncompliance and missing data

ABSTRACTIn clinical endpoint bioequivalence (BE) studies, the primary analysis for assessing equivalence between a generic and an innovator product is based on the observed per-protocol (PP) population (usually completers and compliers). However, missing data and noncompliance are post-randomization intercurrent events and may introduce selection bias. Therefore, PP analysis is generally not causal. The FDA Missing Data Working Group recommended using “causal estimands of primary interest.” In this paper, we propose a principal stratification causal framework and co-primary causal estimands to test equivalence, which was also recommended by the recently published ICH E9 (R1) addendum to address intercurrent events. We identify three conditions under which the current PP estimator is unbiased for one of the proposed co-primary causal estimands – the “Survivor Average Causal Effect” (SACE) estimand. Simulation shows that when these three conditions are not met, the PP estimator is biased and may inflate Type 1 error and/or change power. We also propose a tipping point sensitivity analysis to evaluate the robustness of the current PP estimator in testing equivalence when the sensitivity parameters deviate from the three identified conditions, but stay within a clinically meaningful range. Our work is the first causal equivalence assessment in equivalence studies with intercurrent events.

Effects in Adherent Subjects

ABSTRACTDropouts confound the treatment effect when the outcome and the dropout process both depend on subject characteristics. If dropout is unrelated to treatment, there is an unconfounded effect, but it is the effect in a principal stratum, rather than a de jure effect. There are at least two different definitions of the effect if all subjects adhered, giving effects different numerically from each other and from the effect in the adherent principal stratum. Estimation of either of these two effects requires an assumption (MAR) different from but sometimes confused with the assumption that dropout is unrelated to treatment.

Factorization of Dirac operators on toric noncommutative manifolds

We factorize the Dirac operator on the Connes–Landi 4-sphere in unbounded KK-theory. We show that a family of Dirac operators along the orbits of the torus action defines an unbounded Kasparov module, while the Dirac operator on the principal orbit space –an open quadrant in the 2-sphere – defines a half-closed chain. We show that the tensor sum of these two operators coincides up to unitary equivalence with the Dirac operator on the Connes–Landi sphere and prove that this tensor sum is an unbounded representative of the internal Kasparov product in bivariant K-theory. We also generalize our results to Dirac operators on all toric noncommutative manifolds subject to a condition on the principal stratum. We find that there is a curvature term that arises as an obstruction for having a tensor sum decomposition in unbounded KK-theory. This curvature term can however not be detected at the level of bounded KK-theory.

Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied systematically in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We also introduce certain modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the (quasi) modular properties of the generating functions arising from weighted counting of torus coverings. These two parts contain little geometry and can be read independently of the rest of the paper. The starting point is the theorem of Bloch and Okounkov saying that certain weighted averages, called q q -brackets, of shifted symmetric functions on partitions are quasimodular forms. In Part II we give an expression for the growth polynomials (a certain polynomial invariant of quasimodular forms) of these q q -brackets in terms of Gaussian integrals, and we use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials, and we prove a surprising formula for the q q -bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial as a linear combination of derivatives of Eisenstein series. This formula gives a quasimodularity statement also for the ( − 2 ) (-2) -nd hook-length moments by an appropriate extrapolation, and this in turn implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. The generating functions have an amusing form in terms of the inversion of a power series (with multiples of Bernoulli numbers as coefficients) that gives the asymptotic expansion of a Hurwitz zeta function. To apply these exact formulas to the Eskin-Zorich conjectures on large genus asymptotics (both for the volume and the Siegel-Veech constant) we provide in a separate appendix a general framework for computing the asymptotics of rapidly divergent power series.

Ergodicity of the absolute period foliation

We show that the absolute period foliation of the principal stratum of abelian differentials on a surface of genus g ≥ 3 is ergodic.

Identifying Mechanisms of Behavior Change in Psychosocial Alcohol Treatment Trials: Improving the Quality of Evidence from Mediational Analyses.

In recent years, a shift has occurred from identifying variables that mediate the effects of psychosocial interventions for problematic alcohol use to trying to identify effective mechanisms of behavior change (MOBCs) that lead to better drinking-related and other outcomes. Although implementing interventions targeting specific MOBCs has considerable conceptual and intuitive appeal, it is important that strong empirical evidence be available that supports such implementation. One aim of this article is to consider some prior mediational analyses of the effects of alcohol-focused psychosocial treatments to illustrate findings and the types of evidence that typically have been presented. A second aim is to consider methodological approaches, specifically certain statistical analyses of observational data and experimental designs, that could provide more rigorous evidence regarding the causal effects of mechanisms of change (mediators) in producing desired drinking-related outcomes. Prior analyses that have examined the association of a mediator with an outcome, or the relationship between a mediator and an outcome with assigned treatment controlled, do not provide strong evidence regarding the causal effects of mediators on outcomes. Unfortunately, experimental designs that directly manipulate mediators seem difficult to apply in the alcohol treatment field as an approach to examine mediator/MOBC effects. To produce more compelling evidence, we need to investigate interventions that target a specific MOBC and then capitalize on random assignment to intervention/control conditions by using principal stratification or instrumental variable analyses to identify the effects of intervention-induced mediator change on outcomes.

Impact of National Ambient Air Quality Standards Nonattainment Designations on Particulate Pollution and Health

Despite dramatic air quality improvement in the United States over the past decades, recent years have brought renewed scrutiny and uncertainty surrounding the effectiveness of specific regulatory programs for continuing to improve air quality and public health outcomes. We employ causal inference methods and a spatial hierarchical regression model to characterize the extent to which a designation of "nonattainment" with the 1997 National Ambient Air Quality Standard for ambient fine particulate matter (PM2.5) in 2005 causally affected ambient PM2.5 and health outcomes among over 10 million Medicare beneficiaries in the Eastern United States in 2009-2012. We found that, on average across all retained study locations, reductions in ambient PM2.5 and Medicare health outcomes could not be conclusively attributed to the nonattainment designations against the backdrop of other regional strategies that impacted the entire Eastern United States. A more targeted principal stratification analysis indicates substantial health impacts of the nonattainment designations among the subset of areas where the designations are estimated to have actually reduced ambient PM2.5 beyond levels achieved by regional measures, with noteworthy reductions in all-cause mortality, chronic obstructive pulmonary disorder, heart failure, ischemic heart disease, and respiratory tract infections. These findings provide targeted evidence of the effectiveness of local control measures after nonattainment designations for the 1997 PM2.5 air quality standard.

Stable Strata of Geodesics in Outer Space

Abstract In this article, we propose an Outer space analog for the principal stratum of the unit tangent bundle to the Teichmüller space ${\mathcal{T}}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichmüller space determined by the principal stratum. We show that the analogous Outer space “principal” periodic geodesics share certain stability properties with the principal stratum geodesics of Teichmüller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichmüller space context.

Evaluation of Language Training Programs in Luxembourg Using Principal Stratification

In a world increasingly globalized, multiple language skills can create more employment opportunities. Several countries include language training programs in active labor market programs for the unemployed. We analyze the effects of a language training program on the re-employment probability and hourly wages of the unemployed simultaneously, using highquality administrative data from Luxembourg. We address selection into training by exploiting the rich administrative information available, and account for the complication that wages are “truncated” by unemployment by adopting a principal stratification framework. Estimation is undertaken with a mixture model likelihood-based approach. To improve inference, we use the individual’s hours worked as a secondary outcome and a stochastic dominance assumption. These two features considerably ameliorate the multimodality problem commonly encountered in mixture models. We also conduct sensitivity analysis to assess the unconfoundedness assumption employed. Our results strongly suggest a positive effect (of up to 12.7 percent) of the language training programs on the re-employment probability, but no effects on wages for those who are observed employed regardless of training participation.

Estimating Causal Effects of Treatment in a Randomized Trial When Some Participants Only Partially Adhere.

The intention-to-treat analysis evaluates the causal effect of treatment assignment in a randomized controlled trial; however, participants do not always adhere to assigned treatment and the intention-to-treat effect may differ from the effect of treatment receipt. Although more recent adherence-based methods assess a well-defined causal effect of receiving treatment, adherence is assumed to be dichotomized as all or none. This approach can lack precision in the real world because adherence is a complex and heterogeneous phenomenon. In this article, we illustrate a simple method that provides estimates of bounds on the causal effect of full adherence to treatment in the presence of partial adherence. We first define three types of partial adherence (delayed, partial-dose, posttreatment). We then use casual diagrams to show that categorizing partial adherence as nonadherence in a sensitivity analysis can lead to a violation of the exclusion restriction principle. Finally, we apply recently published sensitivity analyses related to principal stratification that allow for creating bound estimates around the causal effect of treatment in the presence of partial adherence.

Bounding, An Accessible Method for Estimating Principal Causal Effects, Examined and Explained

ABSTRACTEstimating treatment effects for subgroups defined by posttreatment behavior (i.e., estimating causal effects in a principal stratification framework) can be technically challenging and heavily reliant on strong assumptions. We investigate an alternative path: using bounds to identify ranges of possible effects that are consistent with the data. This simple approach relies on fewer assumptions and yet can result in policy-relevant findings. As we show, even moderately predictive covariates can be used to substantially tighten bounds in a straightforward manner. Via simulation, we demonstrate which types of covariates are maximally beneficial. We conclude with an analysis of a multisite experimental study of Early College High Schools. When examining the program's impact on students completing the ninth grade “on-track” for college, we find little impact for ECHS students who would otherwise attend a high-quality high school, but substantial effects for those who would not. This suggests a potential benefit in expanding these programs in areas primarily served by lower quality schools.

Principal Score Methods: Assumptions, Extensions, and Practical Considerations

Researchers addressing posttreatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for the subsequent estimation of causal effects in this framework is to use methods based on the “principal score,” the conditional probability of belonging to a certain principal stratum given covariates. These methods typically assume that stratum membership is as good as randomly assigned, given these covariates. We clarify the key assumption in this context, known as principal ignorability, and argue that versions of this assumption are quite strong in practice. We describe these concepts in terms of both one- and two-sided noncompliance and propose a novel approach for researchers to “mix and match” principal ignorability assumptions with alternative assumptions, such as the exclusion restriction. Finally, we apply these ideas to randomized evaluations of a job training program and an early childhood education program. O...

Validation of surrogate endpoints in cancer clinical trials via principal stratification with an application to a prostate cancer trial.

Increasing attention has been focused on the use and validation of surrogate endpoints in cancer clinical trials. Previous literature on validation of surrogate endpoints are classified into four approaches: the proportion explained approach; the indirect effects approach; the meta-analytic approach; and the principal stratification approach. The mainstream in cancer research has seen the application of a meta-analytic approach. However, VanderWeele (2013) showed that all four of these approaches potentially suffer from the surrogate paradox. It was also shown that, if a principal surrogate satisfies additional criteria called one-sided average causal sufficiency, the surrogate cannot exhibit a surrogate paradox. Here, we propose a method for estimating principal effects under a monotonicity assumption. Specifically, we consider cancer clinical trials which compare a binary surrogate endpoint and a time-to-event clinical endpoint under two naturally ordered treatments (e.g. combined therapy vs. monotherapy). Estimation based on a mean score estimating equation will be implemented by the expectation-maximization algorithm. We will also apply the proposed method as well as other surrogacy criteria to evaluate the surrogacy of prostate-specific antigen using data from a phase III advanced prostate cancer trial, clarifying the complementary roles of both the principal stratification and meta-analytic approaches in the evaluation of surrogate endpoints in cancer. Copyright © 2017 John Wiley & Sons, Ltd.

The stratum of random mapping classes

We consider random walks on the mapping class group that have finite first moment with respect to the word metric, whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichmüller geodesic is in the principal stratum. For such random walks, we show that mapping classes along almost every infinite sample path are eventually pseudo-Anosov, with invariant Teichmüller geodesics in the principal stratum. This provides an answer to a question of Kapovich and Pfaff [Internat. J. Algebra Comput.25, 2015 (5) 745–798].

Latent Class Survival Models Linked by Principal Stratification to Investigate Heterogenous Survival Subgroups Among Individuals With Early-Stage Kidney Cancer

ABSTRACTRates of kidney cancer have been increasing, with small incidental tumors experiencing the fastest growth rates. Much of the increase could be due to increased use of CT scans, MRIs, and ultrasounds for unrelated conditions. Many tumors might never have been detected or become symptomatic in the past. This suggests that many patients might benefit from less aggressive therapy, such as active surveillance by which tumors are surgically removed only if they become sufficiently large. However, it has been difficult for clinicians to identify subgroups of patients for whom treatment might be especially beneficial or harmful. In this work, we use a principal stratification framework to estimate the proportion and characteristics of individuals who have large or small hazard rates of death in two treatment arms. This allows us to assess who might be helped or harmed by aggressive treatment. We also use Weibull mixture models. This work differs from much previous work in that the survival classes upon which principal stratification is based are latent variables. That is, survival class is not an observed variable. We apply this work using Surveillance Epidemiology and End Results-Medicare claims data. Clinicians can use our methods for investigating treatments with heterogenous effects.