Causal inference for vaccine effects on infectiousness

Assessing intervention effects in a randomized trial within a social network

Studies of social networks provide unique opportunities to assess the causal effects of interventions that may impact more of the population than just those intervened on directly. Such effects are sometimes called peer or spillover effects, and may exist in the presence of interference, that is, when one individual's treatment affects another individual's outcome. Randomization-based inference (RI) methods provide a theoretical basis for causal inference in randomized studies, even in the presence of interference. In this article, we consider RI of the intervention effect in the eX-FLU trial, a randomized study designed to assess the effect of a social distancing intervention on influenza-like-illness transmission in a connected network of college students. The approach considered enables inference about the effect of the social distancing intervention on the per-contact probability of influenza-like-illness transmission in the observed network. The methods allow for interference between connected individuals and for heterogeneous treatment effects. The proposed methods are evaluated empirically via simulation studies, and then applied to data from the eX-FLU trial.

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.

Causal inference, social networks and chain graphs

Traditionally, statistical inference and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where individuals may interact with one another such that treatments may spill over from the treated individual to their social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks of interacting individuals have two major shortcomings. First, they often require a level of granularity in the data that is infeasible in practice to collect in most settings and, second, the models are high dimensional and often too big to fit to the available data. We illustrate and justify a parsimonious parameterization for network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We argue that, in some settings, chain graph models approximate the marginal distribution of a snapshot of a longitudinal data-generating process on interacting units. We illustrate the use of chain graphs for causal inference about collective decision making in social networks by using data from US Supreme Court decisions between 1994 and 2004 and in simulations.

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.

On inverse probability-weighted estimators in the presence of interference

We consider inference about the causal effect of a treatment or exposure in the presence of interference, i.e., when one individual’s treatment affects the outcome of another individual. In the observational setting where the treatment assignment mechanism is not known, inverse probability-weighted estimators have been proposed when individuals can be partitioned into groups such that there is no interference between individuals in different groups. Unfortunately this assumption, which is sometimes referred to as partial interference, may not hold, and moreover existing weighted estimators may have large variances. In this paper we consider weighted estimators that could be employed when interference is present. We first propose a generalized inverse probability-weighted estimator and two Hájek-type stabilized weighted estimators that allow any form of interference. We derive their asymptotic distributions and propose consistent variance estimators assuming partial interference. Empirical results show that one of the Hájek estimators can have substantially smaller finite-sample variance than the other estimators. The different estimators are illustrated using data on the effects of rotavirus vaccination in Nicaragua.

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.

A Bayesian approach to estimating causal vaccine effects on binary post-infection outcomes

To estimate causal effects of vaccine on post-infection outcomes, Hudgens and Halloran (2006) defined a post-infection causal vaccine efficacy estimand VEI based on the principal stratification framework. They also derived closed forms for the maximum likelihood estimators of the causal estimand under some assumptions. Extending their research, we propose a Bayesian approach to estimating the causal vaccine effects on binary post-infection outcomes. The identifiability of the causal vaccine effect VEI is discussed under different assumptions on selection bias. The performance of the proposed Bayesian method is compared with the maximum likelihood method through simulation studies and two case studies - a clinical trial of a rotavirus vaccine candidate and a field study of pertussis vaccination. For both case studies, the Bayesian approach provided similar inference as the frequentist analysis. However, simulation studies with small sample sizes suggest that the Bayesian approach provides smaller bias and shorter confidence interval length.

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.

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.

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.