Doubly robust proximal synthetic controls.

To infer the treatment effect for a single treated unit using panel data, synthetic control (SC) methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing SC methods rely on correctly modeling certain aspects of the counterfactual outcome generating mechanism and may require near-perfect matching of the pre-treatment trajectory. Inspired by proximal causal inference, we obtain two novel nonparametric identifying formulas for the average treatment effect for the treated unit: one is based on weighting, and the other combines models for the counterfactual outcome and the weighting function. We introduce the concept of covariate shift to SCs to obtain these identification results conditional on the treatment assignment. We also develop two treatment effect estimators based on these two formulas and generalized method of moments. One new estimator is doubly robust: it is consistent and asymptotically normal if at least one of the outcome and weighting models is correctly specified. We demonstrate the performance of the methods via simulations and apply them to evaluate the effectiveness of a pneumococcal conjugate vaccine on the risk of all-cause pneumonia 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.

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.

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.

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 three study cohorts: adolescents (12 to 20 years) during the Delta phase, 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) in the Delta phase, 111,539 children (50,398 vaccinated) and 56,080 adolescents (21,180 vaccinated) in the Omicron period. Exposures: First dose of the BNT162b2 vaccine vs. 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 BNT162b2 vaccine was 98.4% (95% CI, 98.1 to 98.7) against documented infection among adolescents, with no significant waning after receipt of the first dose. An analysis of cardiac complications did not find an increased risk after vaccination. During the Omicron period, the effectiveness against documented infection among children was estimated to be 74.3% (95% CI, 72.2 to 76.2). Higher levels of effectiveness were observed against moderate or severe COVID-19 (75.5%, 95% CI, 69.0 to 81.0) and ICU admission with COVID-19 (84.9%, 95% CI, 64.8 to 93.5). Among adolescents, the effectiveness against documented Omicron infection was 85.5% (95% CI, 83.8 to 87.1), with 84.8% (95% CI, 77.3 to 89.9) against moderate or severe COVID-19, and 91.5% (95% CI, 69.5 to 97.6)) against ICU admission with COVID-19. The effectiveness of the BNT162b2 vaccine against the Omicron variant declined after 4 months following the first dose and then stabilized. The analysis revealed a lower risk of cardiac complications in the vaccinated group during the Omicron variant period. Limitations: Observational study design and potentially undocumented infection. Conclusions: Our 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.

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.

Impact of family networks on uptake of health interventions: evidence from a community-randomized control trial aimed at increasing HIV testing in South Africa.

INTRODUCTION: While it is widely acknowledged that family relationships can influence health outcomes, their impact on the uptake of individual health interventions is unclear. In this study, we quantified how the efficacy of a randomized health intervention is shaped by its pattern of distribution in the family network. METHODS: The "Home-Based Intervention to Test and Start" (HITS) was a 2×2 factorial community-randomized controlled trial in Umkhanyakude, KwaZulu-Natal, South Africa, embedded in the Africa Health Research Institute's population-based demographic and HIV surveillance platform (ClinicalTrials.gov # NCT03757104). The study investigated the impact of two interventions: a financial micro-incentive and a male-targeted HIV-specific decision support programme. The surveillance area was divided into 45 community clusters. Individuals aged ≥15 years in 16 randomly selected communities were offered a micro-incentive (R50 [$3] food voucher) for rapid HIV testing (intervention arm). Those living in the remaining 29 communities were offered testing only (control arm). Study data were collected between February and November 2018. Using routinely collected data on parents, conjugal partners, and co-residents, a socio-centric family network was constructed among HITS-eligible individuals. Nodes in this network represent individuals and ties represent family relationships. We estimated the effect of offering the incentive to people with and without family members who also received the offer on the uptake of HIV testing. We fitted a linear probability model with robust standard errors, accounting for clustering at the community level. RESULTS: Overall, 15,675 people participated in the HITS trial. Among those with no family members who received the offer, the incentive's efficacy was a 6.5 percentage point increase (95% CI: 5.3-7.7). The efficacy was higher among those with at least one family member who received the offer (21.1 percentage point increase (95% CI: 19.9-22.3). The difference in efficacy was statistically significant (21.1-6.5 = 14.6%; 95% CI: 9.3-19.9). CONCLUSIONS: Micro-incentives appear to have synergistic effects when distributed within family networks. These effects support family network-based approaches for the design of health interventions.

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.

Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution.

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for n-estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.

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.

Double Negative Control Inference in Test-Negative Design Studies of Vaccine Effectiveness.

The test-negative design (TND) has become a standard approach to evaluate vaccine effectiveness against the risk of acquiring infectious diseases in real-world settings, such as Influenza, Rotavirus, Dengue fever, and more recently COVID-19. In a TND study, individuals who experience symptoms and seek care are recruited and tested for the infectious disease which defines cases and controls. Despite TND's potential to reduce unobserved differences in healthcare seeking behavior (HSB) between vaccinated and unvaccinated subjects, it remains subject to various potential biases. First, residual confounding bias may remain due to unobserved HSB, occupation as healthcare worker, or previous infection history. Second, because selection into the TND sample is a common consequence of infection and HSB, collider stratification bias may exist when conditioning the analysis on testing, which further induces confounding by latent HSB. In this paper, we present a novel approach to identify and estimate vaccine effectiveness in the target population by carefully leveraging a pair of negative control exposure and outcome variables to account for potential hidden bias in TND studies. We illustrate our proposed method with extensive simulation and an application to study COVID-19 vaccine effectiveness using data from the University of Michigan Health System.

Structural cumulative survival models for estimation of treatment effects accounting for treatment switching in randomized experiments.

Treatment switching in a randomized controlled trial occurs when a patient in one treatment arm switches to another arm during follow-up. This can occur at the point of disease progression, whereby patients in the control arm may be offered the experimental treatment. It is widely known that failure to account for treatment switching can seriously bias the estimated treatment causal effect. In this paper, we aim to account for the potential impact of treatment switching in a reanalysis evaluating the treatment effect of nucleoside reverse transcriptase inhibitors (NRTIs) on a safety outcome (time to first severe or worse sign or symptom) in participants receiving a new antiretroviral regimen that either included or omitted NRTIs in the optimized treatment that includes or omits NRTIs trial. We propose an estimator of a treatment causal effect for a censored time to event outcome under a structural cumulative survival model that leverages randomization as an instrumental variable to account for selective treatment switching. We establish that the proposed estimator is uniformly consistent and asymptotically Gaussian, with a consistent variance estimator and confidence intervals given, whose finite-sample performance is evaluated via extensive simulations. An R package 'ivsacim' implementing all proposed methods is freely available on R CRAN. Results indicate that adding NRTIs versus omitting NRTIs to a new optimized treatment regime may increase the risk for a safety outcome.

Instrumental variable estimation of the causal hazard ratio.

Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first-stage regression of the treatment on the IV and unmeasured confounders. We propose, to the best of our knowledge, the first consistent estimator of the (population) causal hazard ratio within an instrumental variable framework. A version of our estimator admits a closed-form representation. We derive the asymptotic distribution of our estimator and provide a consistent estimator for its asymptotic variance. Our approach is illustrated via simulation studies and a data application.

Mendelian randomization mixed-scale treatment effect robust identification and estimation for causal inference.

Standard Mendelian randomization (MR) analysis can produce biased results if the genetic variant defining an instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment variable. We provide novel identification conditions for the causal effect of a treatment in the presence of unmeasured confounding by leveraging a possibly invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian randomization mixed-scale treatment effect robust identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the possibly invalid IV on the additive scale; (ii) that the confounding bias does not vary with the possibly invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroskedastic with respect to the possibly invalid IV. Although assumptions (i) and (ii) have, respectively, appeared in the IV literature, assumption (iii) has not; we formally establish that their conjunction can identify a causal effect even with an invalid IV. MR MiSTERI is shown to be particularly advantageous in the presence of pervasive heterogeneity of pleiotropic effects on the additive scale. We propose a simple and consistent three-stage estimator that can be used as a preliminary estimator to a carefully constructed efficient one-step-update estimator. In order to incorporate multiple, possibly correlated, and weak invalid IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved estimation accuracy. Both simulation studies and UK Biobank data analysis results demonstrate the robustness of the proposed methods.

On the double-robustness and semiparametric efficiency of matching-adjusted indirect comparisons.

Matching-adjusted indirect comparison (MAIC) enables indirect comparisons of interventions across separate studies when individual patient-level data (IPD) are available for only one study. Due to its similarity with propensity score weighting, it has been speculated that MAIC can be combined with outcome regression models in the spirit of augmented inverse probability weighting estimators to improve robustness and efficiency. We show that MAIC enjoys intrinsic double-robustness and semiparametric efficiency properties for estimating the average treatment effect on the treated in the limited IPD setting without explicit augmentation. A connection between MAIC and the method of simulated treatment comparisons is highlighted. These results clarify conditions under which MAIC is consistent and efficient, informing appropriate application and interpretation of MAIC analyses.

Rejoinder to discussions on "Instrumental variable estimation of the causal hazard ratio".

In this paper, we respond to comments on our paper, "Instrumental variable estimation of the causal hazard ratio."

Proximal Causal Inference without Uniqueness Assumptions.

We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference. Proximal causal inference requires existence of solutions to at least one of two integral equations. We motivate the existence of solutions to the integral equations from proximal causal inference by demonstrating that, assuming the existence of a solution to one of the integral equations, n-estimability of a mean functional of that solution requires the existence of a solution to the other integral equation. Solutions to the integral equations may not be unique, which complicates estimation and inference. We construct a consistent estimator for the solution set for one of the integral equations and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator for a uniquely defined solution. A debiased estimator is shown to be root-n consistent, regular, and semiparametrically locally efficient under additional regularity conditions.