Single proxy control.

Negative control variables are sometimes used in nonexperimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual confounding bias. For identification, COCA treats the NCO as an error-prone proxy of the treatment-free counterfactual outcome of interest, and involves regressing the NCO on the treatment-free counterfactual, together with a rank-preserving structural model, which assumes a constant individual-level causal effect. In this work, we establish nonparametric COCA identification for the average causal effect for the treated, without requiring rank-preservation, therefore accommodating unrestricted effect heterogeneity across units. This nonparametric identification result has important practical implications, as it provides single-proxy confounding control, in contrast to recently proposed proximal causal inference, which relies for identification on a pair of confounding proxies. For COCA estimation we propose 3 separate strategies: (i) an extended propensity score approach, (ii) an outcome bridge function approach, and (iii) a doubly-robust approach. Finally, we illustrate the proposed methods in an application evaluating the causal impact of a Zika virus outbreak on birth rate in Brazil.

Identification and estimation of causal peer effects using double negative controls for unmeasured network confounding.

Identification and estimation of causal peer effects are challenging in observational studies for two reasons. The first is the identification challenge due to unmeasured network confounding, for example, homophily bias and contextual confounding. The second is network dependence of observations. We establish a framework that leverages a pair of negative control outcome and exposure variables (double negative controls) to non-parametrically identify causal peer effects in the presence of unmeasured network confounding. We then propose a generalised method of moments estimator and establish its consistency and asymptotic normality under an assumption about ψ-network dependence. Finally, we provide a consistent variance estimator.

Real-World Effectiveness of BNT162b2 Against Infection and Severe Diseases in Children and Adolescents.

BACKGROUND: The efficacy of the BNT162b2 vaccine in pediatrics was assessed by randomized trials before the Omicron variant's emergence. The long-term durability of vaccine protection in this population during the Omicron period remains limited. OBJECTIVE: To assess the effectiveness of BNT162b2 in preventing infection and severe diseases with various strains of the SARS-CoV-2 virus in previously uninfected children and adolescents. DESIGN: Comparative effectiveness research accounting for underreported vaccination in 3 study cohorts: adolescents (12 to 20 years) during the Delta phase and children (5 to 11 years) and adolescents (12 to 20 years) during the Omicron phase. SETTING: A national collaboration of pediatric health systems (PEDSnet). PARTICIPANTS: 77 392 adolescents (45 007 vaccinated) during the Delta phase and 111 539 children (50 398 vaccinated) and 56 080 adolescents (21 180 vaccinated) during the Omicron phase. INTERVENTION: First dose of the BNT162b2 vaccine versus no receipt of COVID-19 vaccine. MEASUREMENTS: Outcomes of interest include documented infection, COVID-19 illness severity, admission to an intensive care unit (ICU), and cardiac complications. The effectiveness was reported as (1-relative risk)*100, with confounders balanced via propensity score stratification. RESULTS: During the Delta period, the estimated effectiveness of the BNT162b2 vaccine was 98.4% (95% CI, 98.1% to 98.7%) against documented infection among adolescents, with no statistically significant waning after receipt of the first dose. An analysis of cardiac complications did not suggest a statistically significant difference between vaccinated and unvaccinated groups. During the Omicron period, the effectiveness against documented infection among children was estimated to be 74.3% (CI, 72.2% to 76.2%). Higher levels of effectiveness were seen against moderate or severe COVID-19 (75.5% [CI, 69.0% to 81.0%]) and ICU admission with COVID-19 (84.9% [CI, 64.8% to 93.5%]). Among adolescents, the effectiveness against documented Omicron infection was 85.5% (CI, 83.8% to 87.1%), with 84.8% (CI, 77.3% to 89.9%) against moderate or severe COVID-19, and 91.5% (CI, 69.5% to 97.6%) against ICU admission with COVID-19. The effectiveness of the BNT162b2 vaccine against the Omicron variant declined 4 months after the first dose and then stabilized. The analysis showed a lower risk for cardiac complications in the vaccinated group during the Omicron variant period. LIMITATION: Observational study design and potentially undocumented infection. CONCLUSION: This study suggests that BNT162b2 was effective for various COVID-19-related outcomes in children and adolescents during the Delta and Omicron periods, and there is some evidence of waning effectiveness over time. PRIMARY FUNDING SOURCE: National Institutes of Health.

Universal Difference-in-Differences for Causal Inference in Epidemiology.

Difference-in-differences is undoubtedly one of the most widely used methods for evaluating the causal effect of an intervention in observational (i.e., nonrandomized) settings. The approach is typically used when pre- and postexposure outcome measurements are available, and one can reasonably assume that the association of the unobserved confounder with the outcome has the same absolute magnitude in the two exposure arms and is constant over time; a so-called parallel trends assumption. The parallel trends assumption may not be credible in many practical settings, for example, if the outcome is binary, a count, or polytomous, as well as when an uncontrolled confounder exhibits nonadditive effects on the distribution of the outcome, even if such effects are constant over time. We introduce an alternative approach that replaces the parallel trends assumption with an odds ratio equi-confounding assumption under which an association between treatment and the potential outcome under no treatment is identified with a well-specified generalized linear model relating the pre-exposure outcome and the exposure. Because the proposed method identifies any causal effect that is conceivably identified in the absence of confounding bias, including nonlinear effects such as quantile treatment effects, the approach is aptly called universal difference-in-differences. We describe and illustrate both fully parametric and more robust semiparametric universal difference-in-differences estimators in a real-world application concerning the causal effects of a Zika virus outbreak on birth rate in Brazil. A supplementary digital video is available at: http://links.lww.com/EDE/C90.

The Effect of Family Wealth on Physical Function Among Older Adults in Mpumalanga, South Africa: A Causal Network Analysis.

Objectives: The aging of the South African population could have profound implications for the independence and overall quality of life of older adults as life expectancy increases. While there is evidence that lifetime socio-economic status shapes risks for later function and disability, it is unclear whether, and how, the wealth of family members shapes these outcomes. We investigated the relationship between outcomes activities of daily living (ADL), grip strength, and gait speed, and the household wealth of non-coresident family members. Methods: Using data from Health and Aging in Africa: A Longitudinal Study of an INDEPTH Community in South Africa (HAALSI) and the Agincourt Health and Demographic Surveillance System (AHDSS), we examined the relationship between physical function and household and family wealth in the 13 preceding years. HAALSI is a cohort of 5,059 adults who were 40 years or older at baseline in 2014. Using auto-g-computation-a recently proposed statistical approach to quantify causal effects in the context of a network of interconnected units-we estimated the effect of own and family wealth on the outcomes of interest. Results: We found no evidence of effects of family wealth on physical function and disability. Conclusion: Further research is needed to assess the effect of family wealth in early life on physical function and disability outcomes.

A self-censoring model for multivariate nonignorable nonmonotone missing data.

We introduce an itemwise modeling approach called "self-censoring" for multivariate nonignorable nonmonotone missing data, where the missingness process of each outcome can be affected by its own value and associated with missingness indicators of other outcomes, while conditionally independent of the other outcomes. The self-censoring model complements previous graphical approaches for the analysis of multivariate nonignorable missing data. It is identified under a completeness condition stating that any variability in one outcome can be captured by variability in the other outcomes among complete cases. For estimation, we propose a suite of semiparametric estimators including doubly robust estimators that deliver valid inferences under partial misspecification of the full-data distribution. We also provide a novel and flexible global sensitivity analysis procedure anchored at the self-censoring. We evaluate the performance of the proposed methods with simulations and apply them to analyze a study about the effect of highly active antiretroviral therapy on preterm delivery of HIV-positive mothers.

Estimating the Effect of a Treatment When There Is Nonadherence in a Trial.

Randomized trials offer a powerful strategy for estimating the effect of a treatment on an outcome. However, interpretation of trial results can be complicated when study subjects do not take the treatment to which they were assigned; this is referred to as nonadherence. Prior authors have described instrumental variable approaches to analyze trial data with nonadherence; under their approaches, the initial assignment to treatment is used as an instrument. However, their approaches require the assumption that initial assignment to treatment has no direct effect on the outcome except via the actual treatment received (i.e., the exclusion restriction), which may be implausible. We propose an approach to identification of a causal effect of treatment in a trial with 1-sided nonadherence without assuming exclusion restriction. The proposed approach leverages the study subjects initially assigned to control status as an unexposed reference population; we then employ a bespoke instrumental variable analysis, where the key assumption is "partial exchangeability" of the association between a covariate and an outcome in the treatment and control arms. We provide a formal description of the conditions for identification of causal effects, illustrate the method using simulations, and provide an empirical application.

Generalized Difference-in-Differences.

Difference-in-differences (DID) analyses are used in a variety of research areas as a strategy for estimating the causal effect of a policy, program, intervention, or environmental hazard (hereafter, treatment). The approach offers a strategy for estimating the causal effect of a treatment using observational (i.e., nonrandomized) data in which outcomes on each study unit have been measured both before and after treatment. To identify a causal effect, a DID analysis relies on an assumption that confounding of the treatment effect in the pretreatment period is equivalent to confounding of the treatment effect in the post treatment period. We propose an alternative approach that can yield identification of causal effects under different identifying conditions than those usually required for DID. The proposed approach, which we refer to as generalized DID, has the potential to be used in routine policy evaluation across many disciplines, as it essentially combines two popular quasiexperimental designs, leveraging their strengths while relaxing their usual assumptions. We provide a formal description of the conditions for identification of causal effects, illustrate the method using simulations, and provide an empirical example based on Card and Krueger's landmark study of the impact of an increase in minimum wage in New Jersey on employment.

Semiparametric Inference for Nonmonotone Missing-Not-at-Random Data: The No Self-Censoring Model.

We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called "no self-censoring" or "itemwise conditionally independent nonresponse," which roughly corresponds to the assumption that no partially-observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously-studied data set of HIV-positive mothers in Botswana.

A Bespoke Instrumental Variable Approach to Correction for Exposure Measurement Error.

A covariate-adjusted estimate of an exposure-outcome association may be biased if the exposure variable suffers measurement error. We propose an approach to correct for exposure measurement error in a covariate-adjusted estimate of the association between a continuous exposure variable and outcome of interest. Our proposed approach requires data for a reference population in which the exposure was a priori set to some known level (e.g., 0, and is therefore unexposed); however, our approach does not require an exposure validation study or replicate measures of exposure, which are typically needed when addressing bias due to exposure measurement error. A key condition for this method, which we refer to as "partial population exchangeability," requires that the association between a measured covariate and outcome in the reference population equals the association between that covariate and outcome in the target population in the absence of exposure. We illustrate the approach using simulations and an example.

Bespoke Instruments: A new tool for addressing unmeasured confounders.

Suppose that an investigator is interested in quantifying an exposure-disease causal association in a setting where the exposure, disease, and some potential confounders of the association of interest have been measured. However, there remains concern about residual confounding of the association of interest by unmeasured confounders. We propose an approach to account for residual bias due to unmeasured confounders. The proposed approach uses a measured confounder to derive a "bespoke" instrumental variable that is tailored to the study population and is used to control for bias due to residual confounding. The approach may provide a useful tool for assessing and accounting for bias due to residual confounding. We provide a formal description of the conditions for identification of causal effects, illustrate the method using simulations, and provide an empirical example concerning mortality among Japanese atomic bomb survivors.

Marginal Structural Models for Life-Course Theories and Social Epidemiology: Definitions, Sources of Bias, and Simulated Illustrations.

Social epidemiology aims to identify social structural risk factors, thus informing targets and timing of interventions. Ascertaining which interventions will be most effective and when they should be implemented is challenging because social conditions vary across the life course and are subject to time-varying confounding. Marginal structural models (MSMs) may be useful but can present unique challenges when studying social epidemiologic exposures over the life course. We describe selected MSMs corresponding to common theoretical life-course models and identify key issues for consideration related to time-varying confounding and late study enrollment. Using simulated data mimicking a cohort study evaluating the effects of depression in early, mid-, and late life on late-life stroke risk, we examined whether and when specific study characteristics and analytical strategies may induce bias. In the context of time-varying confounding, inverse-probability-weighted estimation of correctly specified MSMs accurately estimated the target causal effects, while conventional regression models showed significant bias. When no measure of early-life depression was available, neither MSMs nor conventional models were unbiased, due to confounding by early-life depression. To inform interventions, researchers need to identify timing of effects and consider whether missing data regarding exposures earlier in life may lead to biased estimates.

A Semiparametric Approach to Model-Based Sensitivity Analysis in Observational Studies.

When drawing causal inference from observational data, there is almost always concern about unmeasured confounding. One way to tackle this is to conduct a sensitivity analysis. One widely-used sensitivity analysis framework hypothesizes the existence of a scalar unmeasured confounder U and asks how the causal conclusion would change were U measured and included in the primary analysis. Work along this line often makes various parametric assumptions on U, for the sake of mathematical and computational convenience. In this article, we further this line of research by developing a valid sensitivity analysis that leaves the distribution of U unrestricted. Compared to many existing methods in the literature, our method allows for a larger and more flexible family of models, mitigates observable implications (Franks et al., 2019), and works seamlessly with any primary analysis that models the outcome regression parametrically. We construct both pointwise confidence intervals and confidence bands that are uniformly valid over a given sensitivity parameter space, thus formally accounting for unknown sensitivity parameters. We apply our proposed method on an influential yet controversial study of the causal relationship between war experiences and political activeness using observational data from Uganda.

A generalized theory of separable effects in competing event settings.

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.

Auto-G-Computation of Causal Effects on a Network.

Methods for inferring average causal effects have traditionally relied on two key assumptions: (i) the intervention received by one unit cannot causally influence the outcome of another; and (ii) units can be organized into nonoverlapping groups such that outcomes of units in separate groups are independent. In this article, we develop new statistical methods for causal inference based on a single realization of a network of connected units for which neither assumption (i) nor (ii) holds. The proposed approach allows both for arbitrary forms of interference, whereby the outcome of a unit may depend on interventions received by other units with whom a network path through connected units exists; and long range dependence, whereby outcomes for any two units likewise connected by a path in the network may be dependent. Under network versions of consistency and no unobserved confounding, inference is made tractable by an assumption that the networks outcome, treatment and covariate vectors are a single realization of a certain chain graph model. This assumption allows inferences about various network causal effects via the auto-g-computation algorithm, a network generalization of Robins' well-known g-computation algorithm previously described for causal inference under assumptions (i) and (ii). Supplementary materials for this article are available online.

The Causal Interpretation of "Overall Vaccine Effectiveness" in Test-Negative Studies.

Test-negative studies are commonly used to estimate influenza vaccine effectiveness (VE). In a typical study, an "overall VE" estimate based on data from the entire sample may be reported. However, there may be heterogeneity in VE, particularly by age. Therefore, in this article we discuss the potential for a weighted average of age-specific VE estimates to provide a more meaningful measure of overall VE. We illustrate this perspective first using simulations to evaluate how overall VE would be biased when certain age groups are overrepresented. We found that unweighted overall VE estimates tended to be higher than weighted VE estimates when children were overrepresented and lower when elderly persons were overrepresented. Then we extracted published estimates from the US Flu VE network, in which children are overrepresented, and some discrepancy between unweighted and weighted overall VE was observed. Differences in weighted versus unweighted overall VE estimates could translate to substantial differences in the interpretation of individual risk reduction among vaccinated persons and in the total averted disease burden at the population level. Weighting of overall estimates should be considered in VE studies in the future.

Effect of reductions in amyloid levels on cognitive change in randomized trials: instrumental variable meta-analysis.

OBJECTIVE: To evaluate trials of drugs that target amyloid to determine whether reductions in amyloid levels are likely to improve cognition. DESIGN: Instrumental variable meta-analysis. SETTING: 14 randomized controlled trials of drugs for the prevention or treatment of Alzheimer's disease that targeted an amyloid mechanism, identified from ClinicalTrials.gov. POPULATION: Adults enrolled in randomized controlled trials of amyloid targeting drugs. Inclusion criteria for trials vary, but typically include adults aged 50 years or older with a diagnosis of mild cognitive impairment or Alzheimer's disease, and amyloid positivity at baseline. MAIN OUTCOME MEASURES: Analyses included trials for which information could be obtained on both change in brain amyloid levels measured with amyloid positron emission tomography and change in at least one cognitive test score reported for each randomization arm. RESULTS: Pooled results from the 14 randomized controlled trials were more precise than estimates from any single trial. The pooled estimate for the effect of reducing amyloid levels by 0.1 standardized uptake value ratio units was an improvement in the mini-mental state examination score of 0.03 (95% confidence interval -0.06 to 0.1) points. This study provides a web application that allows for the re-estimation of the results when new data become available and illustrates the magnitude of the new evidence that would be necessary to achieve a pooled estimate supporting the benefit of reducing amyloid levels. CONCLUSIONS: Pooled evidence from available trials reporting both reduction in amyloid levels and change in cognition suggests that amyloid reduction strategies do not substantially improve cognition.