Bounding the infectiousness effect in vaccine trials

Maternal hybrid immunity and risk of infant COVID-19 hospitalizations: national case-control study in Israel

Hybrid immunity, acquired through vaccination followed or preceded by a COVID-19 infection, elicits robust antibody augmentation. We hypothesize that maternal hybrid immunity will provide greater infant protection than other forms of COVID-19 immunity in the first 6 months of life. We conducted a case-control study in Israel, enrolling 661 infants up to 6 months of age, hospitalized with COVID-19 (cases) and 59,460 age-matched non-hospitalized infants (controls) between August 24, 2021, and March 15, 2022. Infants were grouped by maternal immunity status at delivery: Naïve (never vaccinated or tested positive, reference group), Hybrid-immunity (vaccinated and tested positive), Natural-immunity (tested positive before or during the study period), Full-vaccination (two-shot regimen plus 1 booster), and Partial-vaccination (less than full three shot regimen). Applying Cox proportional hazards models to estimate the hazard ratios, which was then converted to percent vaccine effectiveness, and using the Naïve group as the reference, maternal hybrid-immunity provided the highest protection (84% [95% CI 75-90]), followed by full-vaccination (66% [95% CI 56-74]), natural-immunity (56% [95% CI 39-68]), and partial-vaccination (29% [95% CI 15-41]). Maternal hybrid-immunity was associated with a reduced risk of infant hospitalization for Covid-19, as compared to natural-immunity, regardless of exposure timing or sequence. These findings emphasize the benefits of vaccinating previously infected individuals during pregnancy to reduce COVID-19 hospitalizations in early infancy.

Maternal third dose of BNT162b2 mRNA vaccine and risk of infant COVID-19 hospitalization

Infants are at a higher risk of Coronavirus Disease 2019 (COVID-19)-related hospitalizations compared to older children. In this study, we investigated the effect of the recommended third maternal dose of BNT162b2 COVID-19 vaccine during pregnancy on rates of infant COVID-19-related hospitalizations. We conducted a nationwide cohort study of all live-born infants delivered in Israel between 24 August 2021 and 15 March 2022 to estimate the effectiveness of the third booster dose versus the second dose against infant COVID-19-related hospitalizations. Data were analyzed for the overall study period, and the Delta and Omicron periods were analyzed separately. Cox proportional hazard regression models estimated hazard ratios and 95% confidence intervals (CIs) for infant hospitalizations according to maternal vaccination status at delivery. Among 48,868 live-born infants included in the analysis, rates of COVID-19 hospitalization were 0.4%, 0.6% and 0.7% in the third-dose, second-dose and unvaccinated groups, respectively. Compared to the second dose, the third dose was associated with reduced infant hospitalization with estimated effectiveness of 53% (95% CI: 36-65%). Greater protection was associated with a shorter interval between vaccination and delivery. A third maternal dose during pregnancy reduced the risk of infant hospitalization for COVID-19 during the first 4 months of life, supporting clinical and public health guidance for maternal booster vaccination to prevent infant COVID-19 hospitalization.

Regression-based negative control of homophily in dyadic peer effect analysis

A prominent threat to causal inference about peer effects in social science studies is the presence of homophily bias , that is, social influence between friends and families is entangled with common characteristics or underlying similarities that form close connections. Analysis of social study data has suggested that certain health conditions such as obesity and psychological states including happiness and loneliness can spread between friends and relatives. However, such analyses of peer effects or contagion effects have come under criticism because homophily bias may compromise the causal statement. We develop a regression-based approach which leverages a negative control exposure for identification and estimation of contagion effects on additive or multiplicative scales, in the presence of homophily bias. We apply our methods to evaluate the peer effect of obesity in Framingham Offspring Study.

Disseminated Effects in Agent-Based Models: A Potential Outcomes Framework and Application to Inform Preexposure Prophylaxis Coverage Levels for HIV Prevention

Preexposure prophylaxis (PrEP) for prevention of human immunodeficiency virus (HIV) infection may benefit not only the person who uses it but also their uninfected sexual risk contacts. We developed an agent-based model using a novel trial emulation approach to quantify disseminated effects of PrEP use among men who have sex with men in Atlanta, Georgia, from 2015 to 2017. Model components (subsets of agents connected through partnerships in a sexual network but not sharing partnerships with any other agents) were first randomized to an intervention coverage level or the control group; then, within intervention components, eligible agents were randomized to receive or not receive PrEP. We calculated direct and disseminated (indirect) effects using randomization-based estimators and report corresponding 95% simulation intervals across scenarios ranging from 10% coverage in the intervention components to 90% coverage. A population of 11,245 agents was simulated, with an average of 1,551 components identified. When comparing agents randomized to no PrEP in 70% coverage components with control agents, there was a 15% disseminated risk reduction in HIV incidence (risk ratio = 0.85, 95% simulation interval: 0.65, 1.05). Persons not on PrEP may receive a protective benefit by being in a sexual network with higher PrEP coverage. Agent-based models are useful for evaluating possible direct and disseminated effects of HIV prevention modalities in sexual networks.

Identification of causal intervention effects under contagion

Defining and identifying causal intervention effects for transmissible infectious disease outcomes is challenging because a treatment - such as a vaccine - given to one individual may affect the infection outcomes of others. Epidemiologists have proposed causal estimands to quantify effects of interventions under contagion using a two-person partnership model. These simple conceptual models have helped researchers develop causal estimands relevant to clinical evaluation of vaccine effects. However, many of these partnership models are formulated under structural assumptions that preclude realistic infectious disease transmission dynamics, limiting their conceptual usefulness in defining and identifying causal treatment effects in empirical intervention trials. In this paper, we propose causal intervention effects in two-person partnerships under arbitrary infectious disease transmission dynamics, and give nonparametric identification results showing how effects can be estimated in empirical trials using time-to-infection or binary outcome data. The key insight is that contagion is a causal phenomenon that induces conditional independencies on infection outcomes that can be exploited for the identification of clinically meaningful causal estimands. These new estimands are compared to existing quantities, and results are illustrated using a realistic simulation of an HIV vaccine trial.

Spillover effects in epidemiology: parameters, study designs and methodological considerations

Many public health interventions provide benefits that extend beyond their direct recipients and impact people in close physical or social proximity who did not directly receive the intervention themselves. A classic example of this phenomenon is the herd protection provided by many vaccines. If these 'spillover effects' (i.e. 'herd effects') are present in the same direction as the effects on the intended recipients, studies that only estimate direct effects on recipients will likely underestimate the full public health benefits of the intervention. Causal inference assumptions for spillover parameters have been articulated in the vaccine literature, but many studies measuring spillovers of other types of public health interventions have not drawn upon that literature. In conjunction with a systematic review we conducted of spillovers of public health interventions delivered in low- and middle-income countries, we classified the most widely used spillover parameters reported in the empirical literature into a standard notation. General classes of spillover parameters include: cluster-level spillovers; spillovers conditional on treatment or outcome density, distance or the number of treated social network links; and vaccine efficacy parameters related to spillovers. We draw on high quality empirical examples to illustrate each of these parameters. We describe study designs to estimate spillovers and assumptions required to make causal inferences about spillovers. We aim to advance and encourage methods for spillover estimation and reporting by standardizing spillover parameter nomenclature and articulating the causal inference assumptions required to estimate spillovers.

Risk ratios for contagious outcomes

Epidemiologists commonly use the risk ratio to summarize the relationship between a binary covariate and outcome, even when outcomes may be dependent. Investigations of transmissible diseases in clusters-households, villages or small groups-often report risk ratios. Epidemiologists have warned that risk ratios may be misleading when outcomes are contagious, but the nature of this error is poorly understood. In this study, we assess the meaning of the risk ratio when outcomes are contagious. We provide a mathematical definition of infectious disease transmission within clusters, based on the canonical stochastic susceptible-infective model. From this characterization, we define the individual-level ratio of instantaneous infection risks as the inferential target, and evaluate the properties of the risk ratio as an approximation of this quantity. We exhibit analytically and by simulation the circumstances under which the risk ratio implies an effect whose direction is opposite that of the true effect of the covariate. In particular, the risk ratio can be greater than one even when the covariate reduces both individual-level susceptibility to infection, and transmissibility once infected. We explain these findings in the epidemiologic language of confounding and Simpson's paradox, underscoring the pitfalls of failing to account for transmission when outcomes are contagious.

Dependent Happenings: A Recent Methodological Review

One hundred years ago Sir Ronald Ross published his treatise on a general Theory of Happenings. Dependent happenings are those in which the frequency depends on the number already affected. When there is dependency of events, interventions can have different types of effects. Interventions such as vaccination can have direct protective effects for the person receiving the treatment, as well as indirect/spillover effects for others in the population. Causal inference is a framework for carefully defining the causal effect of a treatment, exposure, or policy, and then determining conditions under which such effects can be estimated from the observed data. We consider here scenarios in which the potential outcomes of an individual can depend on the treatment of other individuals in the population, known as causal inference with interference. Much of the research so far has assumed the population is divided into groups or clusters, and individuals can interfere with others within their clusters but not across clusters. Recent developments have assumed more general forms of interference. We review some of the different types of effects that have been defined for dependent happenings, particularly using the methods of causal inference with interference. Many of the methods are applicable across disciplines, such as infectious diseases, social sciences, and economics.

Vaccination and all-cause child mortality from 1985 to 2011: global evidence from the Demographic and Health Surveys

Based on models with calibrated parameters for infection, case fatality rates, and vaccine efficacy, basic childhood vaccinations have been estimated to be highly cost effective. We estimated the association of vaccination with mortality directly from survey data. Using 149 cross-sectional Demographic and Health Surveys, we determined the relationship between vaccination coverage and the probability of dying between birth and 5 years of age at the survey cluster level. Our data included approximately 1 million children in 68,490 clusters from 62 countries. We considered the childhood measles, bacillus Calmette-Guérin, diphtheria-pertussis-tetanus, polio, and maternal tetanus vaccinations. Using modified Poisson regression to estimate the relative risk of child mortality in each cluster, we also adjusted for selection bias that resulted from the vaccination status of dead children not being reported. Childhood vaccination, and in particular measles and tetanus vaccination, is associated with substantial reductions in childhood mortality. We estimated that children in clusters with complete vaccination coverage have a relative risk of mortality that is 0.73 (95% confidence interval: 0.68, 0.77) times that of children in a cluster with no vaccinations. Although widely used, basic vaccines still have coverage rates well below 100% in many countries, and our results emphasize the effectiveness of increasing coverage rates in order to reduce child mortality.

Interference and Sensitivity Analysis

Causal inference with interference is a rapidly growing area. The literature has begun to relax the "no-interference" assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper we briefly review the literature on causal inference in the presence of interference when treatments have been randomized. We then consider settings in which causal effects in the presence of interference are not identified, either because randomization alone does not suffice for identification, or because treatment is not randomized and there may be unmeasured confounders of the treatment-outcome relationship. We develop sensitivity analysis techniques for these settings. We describe several sensitivity analysis techniques for the infectiousness effect which, in a vaccine trial, captures the effect of the vaccine of one person on protecting a second person from infection even if the first is infected. We also develop two sensitivity analysis techniques for causal effects in the presence of unmeasured confounding which generalize analogous techniques when interference is absent. These two techniques for unmeasured confounding are compared and contrasted.

Identification of natural direct effects when a confounder of the mediator is directly affected by exposure

Natural direct and indirect effects formalize traditional notions of mediation analysis into a rigorous causal framework and have recently received considerable attention in epidemiology and in social sciences. Sufficient conditions for the identification of natural direct effects were formulated by Judea Pearl under a nonparametric structural equations model, which assumes certain independencies between potential outcomes. A common situation in epidemiology is that a confounder of the mediator-outcome relationship is itself affected by the exposure, in which case natural direct effects fail to be nonparametrically identified without additional assumptions, even under Pearl's nonparametric structural equations model. In this article, we show that when a single binary confounder of the mediator is affected by the exposure, the natural direct effect is nonparametrically identified under the model, assuming monotonicity about the effect of the exposure on the confounder. A similar result is shown to hold for a vector of binary confounders of the mediator under a certain independence assumption about the confounders. Finally, we show that natural direct effects are more generally identified if there is no additive mean interaction between the mediator and the confounders of the mediator affected by exposure. When correct, this latter assumption is particularly appealing because it does not require monotonicity of effects of the exposure. In addition, it places no restriction on the nature of the confounders of the mediator, which can be continuous or polytomous.

Causal Inference Under Multiple Versions of Treatment

Abstract: In this article, we discuss causal inference when there are multiple versions of treatment. The potential outcomes framework, as articulated by Rubin, makes an assumption of no multiple versions of treatment, and here we discuss an extension of this potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which the version precedes the treatment as when an underlying treatment variable is coarsened or dichotomized to create a new treatment variable for which there are effectively “multiple versions”. Results are also given for effects defined by setting the version of treatment to a prespecified distribution. Some of the identification results bear resemblance to identification results in the literature on direct and indirect effects. We describe some settings in which ignoring multiple versions of treatment, even when present, will not lead to incorrect inferences.

Estimating the Effect of a Community-Based Intervention with Two Communities

Due to the need to evaluate the effectiveness of community-based programs in practice, there is substantial interest in methods to estimate the causal effects of community-level treatments or exposures on individual level outcomes. The challenge one is confronted with is that different communities have different environmental factors affecting the individual outcomes, and all individuals in a community share the same environment and intervention. In practice, data are often available from only a small number of communities, making it difficult if not impossible to adjust for these environmental confounders. In this paper we consider an extreme version of this dilemma, in which two communities each receives a different level of the intervention, and covariates and outcomes are measured on a random sample of independent individuals from each of the two populations; the results presented can be straightforwardly generalized to settings in which more than two communities are sampled. We address the question of what conditions are needed to estimate the causal effect of the intervention, defined in terms of an ideal experiment in which the exposed level of the intervention is assigned to both communities and individual outcomes are measured in the combined population, and then the clock is turned back and a control level of the intervention is assigned to both communities and individual outcomes are measured in the combined population. We refer to the difference in the expectation of these outcomes as the marginal (overall) treatment effect. We also discuss conditions needed for estimation of the treatment effect on the treated community. We apply a nonparametric structural equation model to define these causal effects and to establish conditions under which they are identified. These identifiability conditions provide guidance for the design of studies to investigate community level causal effects and for assessing the validity of causal interpretations when data are only available from a few communities. When the identifiability conditions fail to hold, the proposed statistical parameters still provide nonparametric treatment effect measures (albeit non-causal) whose statistical interpretations do not depend on model specifications. In addition, we study the use of a matched cohort sampling design in which the units of different communities are matched on individual factors. Finally, we provide semiparametric efficient and doubly robust targeted MLE estimators of the community level causal effect based on i.i.d. sampling and matched cohort sampling.

Components of the indirect effect in vaccine trials: identification of contagion and infectiousness effects

Vaccination of one person may prevent the infection of another either because the vaccine prevents the first from being infected and from infecting the second, or because, even if the first person is infected, the vaccine may render the infection less infectious. We might refer to the first of these mechanisms as a contagion effect and the second as an infectiousness effect. In the simple setting of a randomized vaccine trial with households of size two, we use counterfactual theory under interference to provide formal definitions of a contagion effect and an unconditional infectiousness effect. Using ideas analogous to mediation analysis, we show that the indirect effect (the effect of one person's vaccine on another's outcome) can be decomposed into a contagion effect and an unconditional infectiousness effect on the risk difference, risk ratio, odds ratio, and vaccine efficacy scales. We provide identification assumptions for such contagion and unconditional infectiousness effects and describe a simple statistical technique to estimate these effects when they are identified. We also give a sensitivity analysis technique to assess how inferences would change under violations of the identification assumptions. The concepts and results of this paper are illustrated with hypothetical vaccine trial data.

The Minicommunity Design to Assess Indirect Effects of Vaccination

We propose the minicommunity design to estimate indirect effects of vaccination. Establishing indirect effects of vaccination in unvaccinated subpopulations could have important implications for global vaccine policies. In the minicommunity design, the household or other small transmission unit serves as the cluster in which to estimate indirect effects of vaccination, similar to studies in larger communities to estimate indirect, total, and overall effects. Examples from the literature include studies in small transmission units to estimate indirect effects of pertussis, pneumococcal, influenza, and cholera vaccines. We characterize the minicommunity design by several methodologic considerations, including the assignment mechanism, ascertainment, the role of transmission outside the transmission unit, and the relation of the size of the transmission unit to number of people vaccinated. The minicommunity study for indirect effects is contrasted with studies to estimate vaccine effects on infectiousness and protective effects under conditions of household exposure within small transmission units. The minicommunity design can be easily implemented in individually randomized studies by enrolling and following-up members of households of the randomized individuals. The methodology for the minicommunity design for estimating indirect effects of vaccination deserves much future research.

Mediation analysis with multiple versions of the mediator

The causal inference literature has provided definitions of direct and indirect effects based on counterfactuals that generalize the approach found in the social science literature. However, these definitions presuppose well-defined hypothetical interventions on the mediator. In many settings, there may be multiple ways to fix the mediator to a particular value, and these various hypothetical interventions may have very different implications for the outcome of interest. In this paper, we consider mediation analysis when multiple versions of the mediator are present. Specifically, we consider the problem of attempting to decompose a total effect of an exposure on an outcome into the portion through the intermediate and the portion through other pathways. We consider the setting in which there are multiple versions of the mediator but the investigator has access only to data on the particular measurement, not information on which version of the mediator may have brought that value about. We show that the quantity that is estimated as a natural indirect effect using only the available data does indeed have an interpretation as a particular type of mediated effect; however, the quantity estimated as a natural direct effect, in fact, captures both a true direct effect and an effect of the exposure on the outcome mediated through the effect of the version of the mediator that is not captured by the mediator measurement. The results are illustrated using 2 examples from the literature, one in which the versions of the mediator are unknown and another in which the mediator itself has been dichotomized.

Extending the sufficient component cause model to describe the Stable Unit Treatment Value Assumption (SUTVA)

Causal inference requires an understanding of the conditions under which association equals causation. The exchangeability or no confounding assumption is well known and well understood as central to this task. More recently the epidemiologic literature has described additional assumptions related to the stability of causal effects. In this paper we extend the Sufficient Component Cause Model to represent one expression of this stability assumption--the Stable Unit Treatment Value Assumption. Approaching SUTVA from an SCC model helps clarify what SUTVA is and reinforces the connections between interaction and SUTVA.

A mapping between interactions and interference: implications for vaccine trials

In this paper, we discuss relationships between causal interactions within the counterfactual framework and interference in which the exposure of one person may affect the outcomes of another. We show that the empirical tests for causal interactions can, in fact, all be adapted to empirical tests for particular forms of interference. In the context of interference, by recoding the response as some function of the outcomes of the various persons within a cluster, a wide range of different forms of interference can potentially be detected. The correspondence between causal interactions and forms of interference extends to encompass n-way causal interactions, interference between n persons within a cluster, and multivalued exposures. The theory for causal interactions provides a complete conceptual apparatus for assessing interference as well. The results are illustrated using data from a hypothetical vaccine trial to reason about specific forms of interference and spillover effects that may be present in this vaccine setting. We discuss the implications of this correspondence for our conceptualizations of interaction and for application to vaccine trials and many other settings in which spillover effects may be present.

Causal inference for vaccine effects on infectiousness

If a vaccine does not protect individuals completely against infection, it could still reduce infectiousness of infected vaccinated individuals to others. Typically, vaccine efficacy for infectiousness is estimated based on contrasts between the transmission risk to susceptible individuals from infected vaccinated individuals compared with that from infected unvaccinated individuals. Such estimates are problematic, however, because they are subject to selection bias and do not have a causal interpretation. Here, we develop causal estimands for vaccine efficacy for infectiousness for four different scenarios of populations of transmission units of size two. These causal estimands incorporate both principal stratification, based on the joint potential infection outcomes under vaccine and control, and interference between individuals within transmission units. In the most general scenario, both individuals can be exposed to infection outside the transmission unit and both can be assigned either vaccine or control. The three other scenarios are special cases of the general scenario where only one individual is exposed outside the transmission unit or can be assigned vaccine. The causal estimands for vaccine efficacy for infectiousness are well defined only within certain principal strata and, in general, are identifiable only with strong unverifiable assumptions. Nonetheless, the observed data do provide some information, and we derive large sample bounds on the causal vaccine efficacy for infectiousness estimands. An example of the type of data observed in a study to estimate vaccine efficacy for infectiousness is analyzed in the causal inference framework we developed.

Principal stratification--uses and limitations

Pearl (2011) asked for the causal inference community to clarify the role of the principal stratification framework in the analysis of causal effects. Here, I argue that the notion of principal stratification has shed light on problems of non-compliance, censoring-by-death, and the analysis of post-infection outcomes; that it may be of use in considering problems of surrogacy but further development is needed; that it is of some use in assessing "direct effects"; but that it is not the appropriate tool for assessing "mediation." There is nothing within the principal stratification framework that corresponds to a measure of an "indirect" or "mediated" effect.

Effect partitioning under interference in two-stage randomized vaccine trials

In the presence of interference, the exposure of one individual may affect the outcomes of others. We provide new effect partitioning results under interferences that express the overall effect as a sum of (i) the indirect (or spillover) effect and (ii) a contrast between two direct effects.