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This paper proposes to embed a class of observational IV data into a cluster-randomized encouragement experiment using nonbipartite matching. Potential outcomes and causal assumptions underpinning the design are formalized and examined. Testing procedures for two commonly used estimands, Fisher’s sharp null hypothesis and the pooled effect ratio (PER), are extended to the current setting. We then introduce a novel cluster-heterogeneous proportional treatment effect model and the relevant estimand: the average cluster effect ratio. This new estimand allows treatment heterogeneity, and is advantageous over the PER estimand in that it does not suffer from Simpson’s paradox. We develop an asymptotically valid randomization-based testing procedure for this new estimand based on solving a mixed-integer quadratically constrained optimization problem.

We propose a general framework of approaching the optimal individualized treatment rules (ITR) estimation problem when a valid IV is allowed to only partially identify the treatment effect. We introduce a novel notion of optimality called ‘IV-optimality’. A treatment rule is said to be IV-optimal if it minimizes the maximum risk with respect to the putative IV and the set of IV identification assumptions. We derive a bound on the risk of an IV-optimal rule that illuminates when an IV-optimal rule has favourable generalization performance. We propose a classification-based statistical learning method that estimates such an IV-optimal rule, design computationally efficient algorithms, and prove theoretical guarantees.

How many healthcare workers have lost their lives fighting coronavirus disease (COVID-19)? We estimate using the capture–recapture method.

A commonly used sensitivity analysis for matched observational studies adopts a worst-case perspective, which assumes that, in each matched set, the unmeasured confounder U is allocated to make the bias worst. This worst-case allocation of U does not correspond to any realistic distribution of U in the population and is difficult to compare with observed covariates. We proposed a new sensitivity analysis method that addresses these concerns. We apply the new method to a study of second-hand smoking and blood lead levels in children and find that, to explain away the association between second-hand smoke exposure and blood lead levels as non-causal, the unmeasured confounder would have to be a bigger confounder than any measured confounder.

It is common to compare individualized treatment rules based on the value function, which is the expected potential outcome under the treatment rule. Although the value function is not point-identified when there is unmeasured confounding, it still defines a partial order among the treatment rules under Rosenbaum’s sensitivity analysis model. We first consider how to compare two treatment rules with unmeasured confounding in the single-decision setting and then use this pairwise test to rank multiple treatment rules. We consider how to, among many treatment rules, select the best rules and select the rules that are better than a control rule. The proposed methods are illustrated using two real examples, one about the benefit of malaria prevention programs to different age groups and another about the effect of late retirement on senior health in different gender and occupation groups. Supplementary materials for this article are available online.

Cerebral malaria (CM) remains a leading cause of mortality and morbidity in children in sub-Saharan Africa. Recent studies using brain magnetic resonance imaging have revealed increased brain volume as a major predictor of death. Similar morphometric predictors of morbidity at discharge are lacking. The aim of this study was to investigate the utility of serial cranial cisternal cerebrospinal fluid (CSF) volume measurements in predicting morbidity at discharge in pediatric CM survivors.