Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance

Mealli, Fabrizia; Pacini, Barbara

doi:10.1080/01621459.2013.802238

Cited by 78 publications

(82 citation statements)

References 39 publications

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“…() and Frumento et al . ()); additional covariates or secondary outcomes (Ding et al ., ; Mattei and Mealli, ; Mattei et al ., ; Mealli and Pacini, ; Yang and Small, ; Jiang et al ., ).…”

Section: Causal Inference With Intermediate Variablesmentioning

confidence: 98%

Principal Stratification Analysis Using Principal Scores

Ding

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

258

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Practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. However, in many cases we cannot randomize the intermediate variable, resulting in sample selection problems even in randomized experiments.Therefore, we view randomized experiments with intermediate variables as semi-observational studies. In parallel with the analysis of observational studies, we provide a theoretical foundation for conducting objective causal inference with an intermediate variable under the principal stratification framework, with principal strata defined as the joint potential values of the intermediate variable. Our strategy constructs weighted samples based on principal scores, defined as the conditional probabilities of the latent principal strata given covariates, without access to any outcome data. This principal stratification analysis yields robust causal inference without relying on any model assumptions on the outcome distributions. We also propose approaches to conducting sensitivity analysis for violations of the ignorability and monotonicity assumptions, the very crucial but untestable identification assumptions in our theory. When the assumptions required by the classical instrumental variable analysis cannot be justified by background knowledge or cannot be made because of scientific questions of interest, our strategy serves as a useful alternative tool to deal with intermediate variables. We illustrate our methodologies by using two real data examples, and find scientifically meaningful conclusions. (Angrist et al. 1996). When the intermediate variable is the indicator for survival status, the only sensible subgroup causal effect on the outcome is the one for survivors who would potentially survive under both treatment and control (Rubin 2006). When the intermediate variable is a surrogate for the outcome, we want to predict the causal effect on the outcome by the causal effect on the surrogate. An ideal surrogate must satisfy the causal necessity that zero effect on the surrogate implies zero effect on the outcome (Frangakis and Rubin 2002) and the causal sufficiency that positive effect on the surrogate implies positive effect on the outcome (Gilbert and Hudgens 2008). Therefore, we can assess these requirements for an ideal surrogate by conducting a principal stratification analysis. Principal stratification clarifies causal inference with intermediate variables, but it also resultsin inferential difficulties because of the missingness of the principal stratification variable and the consequential mixture distributions of the observed data. We can sharpen inference about causal effects within principal strata only if we impose some of the following structural or modeling assumptions: (1) monotonicity that the treatment has a nonnegative effect on the intermediate variable for each unit (e.g., Angrist et al. 1996;Gilbert and Hudgens 2008); (2) et ...

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“…() and Frumento et al . ()); additional covariates or secondary outcomes (Ding et al ., ; Mattei and Mealli, ; Mattei et al ., ; Mealli and Pacini, ; Yang and Small, ; Jiang et al ., ).…”

Section: Causal Inference With Intermediate Variablesmentioning

confidence: 98%

Principal Stratification Analysis Using Principal Scores

Ding

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

258

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“…The reason for only partial improvement was not addressed. More recent work by Lee (2009) and Mealli and Pacini (2012) indicate the adjusted bounds will never be wider than the unadjusted bounds and sometimes the adjusted bounds will be strictly narrower than the unadjusted bounds. In this paper we characterize the exact circumstances for which adjusting for a baseline covariate leads to improved bounds.…”

Section: Introductionmentioning

confidence: 99%

Sharpening Bounds on Principal Effects with Covariates

Long

Hudgens

2013

Biometrics

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Summary 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, i.e., 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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“…These assumptions translate in our case to stating that strata d & T , d & A , d & C , and d & N do not exist (monotonicity), and strata n & T , n & C , a & T , and a & C are empty and that the distributions of Y in n and a do not depend on Z (exclusion restrictions). Although these assumptions simplify the model, they are not essential from either Bayesian or likelihood perspectives, as illustrated, for example, in the applications of Imbens and Rubin , Hirano et al , Frumento et al , and Mealli and Pacini .…”

Section: Likelihood: Model Specification and Possible Restrictionsmentioning

confidence: 99%

The fragility of standard inferential approaches in principal stratification models relative to direct likelihood approaches

Frumento

Mealli

Pacini

et al. 2015

Statistical Analysis

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Many empirical settings involve the specification of models leading to complicated likelihood functions, for example, finite mixture models that arise in causal inference when using Principal Stratification (PS). Traditional asymptotic results cannot be trusted for the associated likelihood functions, whose logarithms are not close to being quadratic and may be multimodal even with large sample sizes. We first investigate the shape of the likelihood function with models based on PS by providing diagnostic tools for evaluating ellipsoidal approximations based on the second derivatives of the log‐likelihood at a mode. In these settings, inference based on standard approximations is inappropriate, and other forms of inference are required. We explore the use of a direct likelihood approach for parsimonious model selection and, specifically, propose comparing values of scaled maximized likelihood functions under competitive models to select preferred models. An extensive simulation study provides guidelines, for calibrating the use of scaled log‐likelihood ratio statistics, as functions of the complexity of the models being compared.

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Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance

Cited by 78 publications

References 39 publications

Principal Stratification Analysis Using Principal Scores

Principal Stratification Analysis Using Principal Scores

Sharpening Bounds on Principal Effects with Covariates

The fragility of standard inferential approaches in principal stratification models relative to direct likelihood approaches

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