Daniel Nevo

Researchers increasingly utilize negative control exposures (NCEs), variables known to have no effect on the outcome, to detect residual confounding. However, an NCE analysis may provide little evidence of confounding despite substantial bias in the estimated exposure effect. We study, analytically and via simulations, how the magnitude and source of exposure-NCE association affect the large-sample NCE coefficient and statistical power of regression-based bias-detection. We show that the power does not always increase with bias, and that stronger confounder-exposure associations can increase bias while reducing the NCE coefficient and power. Furthermore, the correlation between the exposure of interest and the NCE is insufficient to characterize how well the NCE will detect confounding. Additional exposure-NCE common causes that affect the outcome only through the exposure can attenuate the NCE coefficient toward zero or reverse its sign, even when confounding bias remains unchanged. These changes can occur even when the overall exposure-NCE correlation is fixed. Adjusting for such common causes alleviated sign reversal in our simulations but did not uniformly improve power. Negative controls can be a powerful tool to detect unmeasured confounding. Researchers should consider the sources of exposure-NCE association and interpret null or counterintuitive NCE findings with caution.

Background: Seasonality is typically controlled for to mitigate potential confounding by seasonally varying variables in environmental epidemiology research. We aimed to illustrate that correctly specifying the seasonality variable is crucial for effectively controlling confounding by seasonality in the context of prenatal temperature exposure and preterm birth. Methods: We conducted a simulation study based on an Israeli birth cohort of 131 599 births in Southern Israel, 2005–19. Weekly mean temperature exposures throughout pregnancy and last menstrual period (LMP) date were taken from the original cohort, while gestational age at birth was simulated using a Cox model under four causal scenarios: no seasonal confounding and no effect of temperature; seasonal confounding only; causal effect of temperature only; and seasonal confounding and a causal effect. Within each scenario, we compared four seasonality-adjustment approaches: no adjustment; fixed birthdate-based adjustment; fixed LMP-based adjustment; and time-varying seasonal adjustment. Finally, we compared these methods using our original cohort analysis to examine their divergence in real epidemiological study settings. Results: Birthdate-based adjustment induced strong collider bias across all scenarios and in the real study setting. In the absence of seasonal confounding, the other three adjustment methods were comparable and produced valid estimates. In the presence of seasonal confounding, however, fixed LMP-based adjustment was inferior to the use of a time-varying seasonal covariate. Conclusion: Birthdate-based seasonal adjustment in studies of temperature and birth outcomes may introduce severe collider bias and should be avoided, particularly when examining outcomes strongly associated with the duration of pregnancy.

Comparing future antibiotic resistance levels resulting from different antibiotic treatments is challenging because some patients may survive only under one of the antibiotic treatments. We embed this problem within a semi‐competing risks approach to study the causal effect on resistant infection, treated as a nonterminal event time. We argue that existing principal stratification estimands for such problems exclude patients for whom a causal effect is well‐defined and is of clinical interest. Therefore, we present a new principal stratum, the infected‐or‐survivors (). The is the subpopulation of patients who would have survived or been infected under both antibiotic treatments. This subpopulation is more inclusive than previously defined subpopulations. We target the causal effect among these patients, which we term the feasible‐infection causal effect (FICE). We develop large‐sample bounds under novel assumptions, and discuss the plausibility of these assumptions in our application. As an alternative, we derive FICE identification using two illness‐death models with a bivariate frailty random variable. These two models are connected by a cross‐world correlation parameter. Estimation is performed by an expectation‐maximization algorithm followed by a Monte Carlo procedure. We apply our methods to detailed clinical data obtained from a hospital setting.

Egocentric-Network Randomized Trials (ENRTs) are increasingly used to estimate causal effects under interference when measuring complete sociocentric network data is infeasible. ENRTs rely on egocentric network sampling, where a set of egos is first sampled, and each ego recruits a subset of its neighbors as alters. Treatments are then randomized across egos. While the observed ego-networks are disjoint by design, the underlying population network may contain edges connecting them, leading to contamination. Under a design-based framework, we show that the Horvitz-Thompson estimators of direct and indirect effects are biased whenever contamination is present. To address this, we derive bias-corrected estimators and propose a novel sensitivity analysis framework based on sensitivity parameters representing the probability or expected number of missing edges. This framework is implemented via both grid sensitivity analysis and probabilistic bias analysis, providing researchers with a flexible tool to assess the robustness of the causal estimators to contamination. We apply our methodology to the HIV Prevention Trials Network 037 study, finding that ignoring contamination may lead to underestimation of indirect effects and overestimation of direct effects.

Summary: Egocentric-network randomized trials (ENRTs) are increasingly used to estimate causal effects under interference when measuring complete sociocentric network data is infeasible. ENRTs rely on egocentric network sampling, where a set of egos is first sampled, and each ego recruits a subset of its neighbors as alters. Treatments are then randomized across egos. While the observed ego-networks are disjoint by design, the underlying population network may contain edges connecting them, leading to contamination. Under a design-based framework, we show that the Horvitz–Thompson estimators of direct and indirect effects are biased whenever contamination is present. To address this, we derive bias-corrected estimators and propose a novel sensitivity analysis framework based on sensitivity parameters representing the probability or expected number of missing edges. This framework is implemented via both grid sensitivity analysis and probabilistic bias analysis, providing researchers with a flexible tool to assess the robustness of the causal estimators to contamination. We apply our methodology to the HIV Prevention Trials Network 037 study, finding that ignoring contamination may lead to underestimation of indirect effects and overestimation of direct effects.

We thank the discussants for their insightful comments and suggestions. In this rejoinder, we underscore the role of the network specification under interference regardless of the chosen probabilistic regime, revisit the conceptual design-based coupled with exposure mapping framework we pursue in our paper, comment on the welcome extensions and modifications proposed by the discussants, and discuss the promise and perils of multiple networks.

Under interference, the treatment of one unit may affect the outcomes of other units. Such interference patterns between units are typically represented by a network. Correctly specifying this network requires identifying which units can affect others—an inherently challenging task. Nevertheless, most existing approaches assume that a known and accurate network specification is given. In this paper, we study the consequences of such misspecification. We derive bounds on the bias arising from estimating causal effects using a misspecified network, showing that the estimation bias grows with the divergence between the assumed and true networks, quantified through their induced exposure probabilities. To address this challenge, we propose a novel estimator that leverages multiple networks simultaneously and remains unbiased if at least one of the networks is correct, even when we do not know which one. Therefore, the proposed estimator provides robustness to network specification. We illustrate key properties and demonstrate the utility of our proposed estimator through simulations and analysis of a social network field experiment.

Comparing future antibiotic resistance levels resulting from different antibiotic treatments is challenging because some patients may survive only under one of the antibiotic treatments. We embed this problem within a semi-competing risks approach to study the causal effect on resistant infection, treated as a non-terminal event time. We argue that existing principal stratification estimands for such problems exclude patients for whom a causal effect is well-defined and is of clinical interest. Therefore, we present a new principal stratum, the infected-or-survivors (ios). The ios is the subpopulation of patients who would have survived or been infected under both antibiotic treatments. This subpopulation is more inclusive than previously defined subpopulations. We target the causal effect among these patients, which we term the feasible-infection causal effect (FICE). We develop large-sample bounds under novel assumptions, and discuss the plausibility of these assumptions in our application. As an alternative, we derive FICE identification using two illness-death models with a bivariate frailty random variable. These two models are connected by a cross-world correlation parameter. Estimation is performed by an expectation-maximization algorithm followed by a Monte Carlo procedure. We apply our methods to detailed clinical data obtained from a hospital setting.