Using instruments for selection to adjust for selection bias in Mendelian randomization.

Selection bias is a common concern in epidemiologic studies. In the literature, selection bias is often viewed as a missing data problem. Popular approaches to adjust for bias due to missing data, such as inverse probability weighting, rely on the assumption that data are missing at random and can yield biased results if this assumption is violated. In observational studies with outcome data missing not at random, Heckman's sample selection model can be used to adjust for bias due to missing data. In this paper, we review Heckman's method and a similar approach proposed by Tchetgen Tchetgen and Wirth (2017). We then discuss how to apply these methods to Mendelian randomization analyses using individual-level data, with missing data for either the exposure or outcome or both. We explore whether genetic variants associated with participation can be used as instruments for selection. We then describe how to obtain missingness-adjusted Wald ratio, two-stage least squares and inverse variance weighted estimates. The two methods are evaluated and compared in simulations, with results suggesting that they can both mitigate selection bias but may yield parameter estimates with large standard errors in some settings. In an illustrative real-data application, we investigate the effects of body mass index on smoking using data from the Avon Longitudinal Study of Parents and Children.

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.

Prediction sets adaptive to unknown covariate shift.

Predicting sets of outcomes-instead of unique outcomes-is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift-a prevalent issue in practice-poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is asymptotically probably approximately correct, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.