Causal Vaccine Effects on Binary Postinfection Outcomes

Preventable Fraction in the Context of Disease Progression

The relevance of the epidemiologic concept of preventable fraction to the study of the population-level impact of preventive exposures is unequivocal. Here, we discuss how the preventable fraction can be usefully understood for the class of outcomes that relate to disease progression (e.g., clinical severity given diagnosis), and, under the principal stratification framework, derive an expression for this quantity for this type of outcome. In particular, we show that, in the context of disease progression, the preventable fraction is a function of the effect on the postdiagnosis outcome in the principal stratum in the unexposed group who would have disease regardless of exposure status. This work will facilitate an understanding of the contribution of principal effects to the impact of preventive exposures at the population level.

Causal Inference Over a Subpopulation: The Effect of Malaria Vaccine in Women During Pregnancy

Preventing malaria during pregnancy is of critical importance, yet there are no approved malaria vaccines for pregnant women due to lack of efficacy results within this population. Conducting a randomized trial in pregnant women throughout the entire duration of pregnancy is impractical. Instead, a randomized trial was conducted among women of childbearing potential (WOCBP), and some participants became pregnant during the 2-year study. We explore a statistical method for estimating vaccine effect within the target subpopulation-women who can naturally become pregnant, namely, women who can become pregnant under a placebo condition-within the causal inference framework. Two vaccine effect estimators are employed to effectively utilize baseline characteristics and account for the fact that certain baseline characteristics were only available from pregnant participants. The first estimator considers all participants but can only utilize baseline variables collected from the entire participant pool. In contrast, the second estimator, which includes only pregnant participants, utilizes all available baseline information. Both estimators are evaluated numerically through simulation studies and applied to the WOCBP trial to assess vaccine effect against pregnancy malaria.

Interpretations of Studies on SARS-CoV-2 Vaccination and Post-acute COVID-19 Sequelae

This article discusses causal interpretations of epidemiologic studies of the effects of vaccination on sequelae after acute severe acute respiratory syndrome coronavirus 2 infection. To date, researchers have tried to answer several different research questions on this topic. While some studies assessed the impact of postinfection vaccination on the presence of or recovery from post-acute coronavirus disease 2019 syndrome, others quantified the association between preinfection vaccination and postacute sequelae conditional on becoming infected. However, the latter analysis does not have a causal interpretation, except under the principal stratification framework-that is, this comparison can only be interpreted as causal for a nondiscernible stratum of the population. As the epidemiology of coronavirus disease 2019 is now nearly entirely dominated by reinfections, including in vaccinated individuals, and possibly caused by different Omicron subvariants, it has become even more important to design studies on the effects of vaccination on postacute sequelae that address precise causal questions and quantify effects corresponding to implementable interventions.

Some principles for using epidemiologic study results to parameterize transmission models

Background

Infectious disease models, including individual based models (IBMs), can be used to inform public health response. For these models to be effective, accurate estimates of key parameters describing the natural history of infection and disease are needed. However, obtaining these parameter estimates from epidemiological studies is not always straightforward. We aim to 1) outline challenges to parameter estimation that arise due to common biases found in epidemiologic studies and 2) describe the conditions under which careful consideration in the design and analysis of the study could allow us to obtain a causal estimate of the parameter of interest. In this discussion we do not focus on issues of generalizability and transportability.

Methods

Using examples from the COVID-19 pandemic, we first identify different ways of parameterizing IBMs and describe ideal study designs to estimate these parameters. Given real-world limitations, we describe challenges in parameter estimation due to confounding and conditioning on a post-exposure observation. We then describe ideal study designs that can lead to unbiased parameter estimates. We finally discuss additional challenges in estimating progression probabilities and the consequences of these challenges.

Results

Causal estimation can only occur if we are able to accurately measure and control for all confounding variables that create non-causal associations between the exposure and outcome of interest, which is sometimes challenging given the nature of the variables we need to measure. In the absence of perfect control, non-causal parameter estimates should still be used, as sometimes they are the best available information we have.

Conclusions

Identifying which estimates from epidemiologic studies correspond to the quantities needed to parameterize disease models, and determining whether these parameters have causal interpretations, can inform future study designs and improve inferences from infectious disease models. Understanding the way in which biases can arise in parameter estimation can inform sensitivity analyses or help with interpretation of results if the magnitude and direction of the bias is understood.

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.

Impact of Chemoprophylaxis on Plasmodium vivax and Plasmodium ovale Infection Among Civilian Travelers: A Nested Case-Control Study With a Counterfactual Approach on 862 Patients

BACKGROUND

The impact of chemoprophylaxis targeting Plasmodium falciparum on Plasmodium vivax and Plasmodium ovale, which may remain quiescent as hypnozoites in the liver, is debated.

METHODS

We conducted a nested case-control analysis of the outcomes of P. vivax and P. ovale infections in imported malaria cases in France among civilian travelers from 1 January 2006, to 31 December 2017. Using adjusted logistic regression, we assessed the effect of chemoprophylaxis on the incubation period, time from symptoms to diagnosis, management, blood results, symptoms, and hospitalization duration. We analyzed the effect of blood-stage drugs (doxycycline, mefloquine, chloroquine, chloroquine-proguanil) or atovaquone-proguanil on the incubation period. We used a counterfactual approach to ascertain the causal effect of chemoprophylaxis on postinfection characteristics.

RESULTS

Among 247 P. vivax- and 615 P. ovale-infected travelers, 30% and 47%, respectively, used chemoprophylaxis, and 7 (3%) and 8 (1%) were severe cases. Chemoprophylaxis users had a greater risk of presenting symptoms >2 months after returning for both species (P. vivax odds ratio [OR], 2.91 [95% confidence interval {CI}, 1.22-6.95], P = .02; P. ovale OR, 2.28 [95% CI, 1.47-3.53], P < .001). Using drugs only acting on the blood stage was associated with delayed symptom onset after 60 days, while using atovaquone-proguanil was not.

CONCLUSIONS

Civilian travelers infected with P. vivax or P. ovale reporting chemoprophylaxis use, especially of blood-stage agents, had a greater risk of delayed onset of illness. The impact of chemoprophylaxis on the outcomes of infection with relapse-causing species calls for new chemoprophylaxis acting against erythrocytic and liver stages.

Incorporating baseline covariates to validate surrogate endpoints with a constant biomarker under control arm

A surrogate endpoint S in a clinical trial is an outcome that may be measured earlier or more easily than the true outcome of interest T. In this work, we extend causal inference approaches to validate such a surrogate using potential outcomes. The causal association paradigm assesses the relationship of the treatment effect on the surrogate with the treatment effect on the true endpoint. Using the principal surrogacy criteria, we utilize the joint conditional distribution of the potential outcomes T, given the potential outcomes S. In particular, our setting of interest allows us to assume the surrogate under the placebo, S ( 0 ) , is zero-valued, and we incorporate baseline covariates in the setting of normally distributed endpoints. We develop Bayesian methods to incorporate conditional independence and other modeling assumptions and explore their impact on the assessment of surrogacy. We demonstrate our approach via simulation and data that mimics an ongoing study of a muscular dystrophy gene therapy.

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.

Influenza vaccine effectiveness in reducing severe outcomes over six influenza seasons, a case-case analysis, Spain, 2010/11 to 2015/16

Introduction

When influenza vaccination is ineffective in preventing influenza virus infection, it may still reduce the severity of influenza-associated disease. Here, we estimate the effect of influenza vaccination in preventing severe outcomes e.g. intensive care unit (ICU) admission and death, even though it did not prevent influenza virus infection and subsequent hospitalisation.

Methods

An observational case–case epidemiological study was carried out in 12 sentinel hospitals in Catalonia (Spain) over six influenza seasons 2010/11–2015/16. Cases were individuals with severe laboratory-confirmed influenza virus infection and aged 18 years and older. For each reported case we collected demographic, virological and clinical characteristics. Logistic regression was used to estimate the crude, adjusted odd ratios (aOR) and 95% confidence intervals (CI).

Results

Of 1,727 hospitalised patients included in the study, 799 were female (46.7%), 591 (34.2%) were admitted to the ICU and 223 (12.9%) died. Influenza vaccination uptake was lower in cases that required ICU admission or died (21.2% vs 29.7%, p < 0.001). The adjusted influenza vaccination effectiveness in preventing ICU admission or death was 23% (95% CI: 1 to 40). In an analysis restricted to sex, age group and antiviral treatment, influenza vaccination had a positive effect on disease severity in all age groups and categories.

Conclusions

We found that influenza vaccination reduced the severity of disease even in cases where it did not prevent infection and influenza-associated hospitalisation. Therefore, increased vaccination uptake may reduce complications, ICU admission and death.

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.

Exposure, hazard, and survival analysis of diffusion on social networks

Sociologists, economists, epidemiologists, and others recognize the importance of social networks in the diffusion of ideas and behaviors through human societies. To measure the flow of information on real-world networks, researchers often conduct comprehensive sociometric mapping of social links between individuals and then follow the spread of an "innovation" from reports of adoption or change in behavior over time. The innovation is introduced to a small number of individuals who may also be encouraged to spread it to their network contacts. In conjunction with the known social network, the pattern of adoptions gives researchers insight into the spread of the innovation in the population and factors associated with successful diffusion. Researchers have used widely varying statistical tools to estimate these quantities, and there is disagreement about how to analyze diffusion on fully observed networks. Here, we describe a framework for measuring features of diffusion processes on social networks using the epidemiological concepts of exposure and competing risks. Given a realization of a diffusion process on a fully observed network, we show that classical survival regression models can be adapted to estimate the rate of diffusion, and actor/edge attributes associated with successful transmission or adoption, while accounting for the topology of the social network. We illustrate these tools by applying them to a randomized network intervention trial conducted in Honduras to estimate the rate of adoption of 2 health-related interventions-multivitamins and chlorine bleach for water purification-and determine factors associated with successful social transmission.

Validation of surrogate endpoints in cancer clinical trials via principal stratification with an application to a prostate cancer trial

Increasing attention has been focused on the use and validation of surrogate endpoints in cancer clinical trials. Previous literature on validation of surrogate endpoints are classified into four approaches: the proportion explained approach; the indirect effects approach; the meta-analytic approach; and the principal stratification approach. The mainstream in cancer research has seen the application of a meta-analytic approach. However, VanderWeele (2013) showed that all four of these approaches potentially suffer from the surrogate paradox. It was also shown that, if a principal surrogate satisfies additional criteria called one-sided average causal sufficiency, the surrogate cannot exhibit a surrogate paradox. Here, we propose a method for estimating principal effects under a monotonicity assumption. Specifically, we consider cancer clinical trials which compare a binary surrogate endpoint and a time-to-event clinical endpoint under two naturally ordered treatments (e.g. combined therapy vs. monotherapy). Estimation based on a mean score estimating equation will be implemented by the expectation-maximization algorithm. We will also apply the proposed method as well as other surrogacy criteria to evaluate the surrogacy of prostate-specific antigen using data from a phase III advanced prostate cancer trial, clarifying the complementary roles of both the principal stratification and meta-analytic approaches in the evaluation of surrogate endpoints in cancer. Copyright © 2017 John Wiley & Sons, Ltd.

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.

Nonparametric Bounds and Sensitivity Analysis of Treatment Effects

This paper considers conducting inference about the effect of a treatment (or exposure) on an outcome of interest. In the ideal setting where treatment is assigned randomly, under certain assumptions the treatment effect is identifiable from the observable data and inference is straightforward. However, in other settings such as observational studies or randomized trials with noncompliance, the treatment effect is no longer identifiable without relying on untestable assumptions. Nonetheless, the observable data often do provide some information about the effect of treatment, that is, the parameter of interest is partially identifiable. Two approaches are often employed in this setting: (i) bounds are derived for the treatment effect under minimal assumptions, or (ii) additional untestable assumptions are invoked that render the treatment effect identifiable and then sensitivity analysis is conducted to assess how inference about the treatment effect changes as the untestable assumptions are varied. Approaches (i) and (ii) are considered in various settings, including assessing principal strata effects, direct and indirect effects and effects of time-varying exposures. Methods for drawing formal inference about partially identified parameters are also discussed.

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 and estimation of survivor average causal effects

In longitudinal studies, outcomes ascertained at follow-up are typically undefined for individuals who die prior to the follow-up visit. In such settings, outcomes are said to be truncated by death and inference about the effects of a point treatment or exposure, restricted to individuals alive at the follow-up visit, could be biased even if as in experimental studies, treatment assignment were randomized. To account for truncation by death, the survivor average causal effect (SACE) defines the effect of treatment on the outcome for the subset of individuals who would have survived regardless of exposure status. In this paper, the author nonparametrically identifies SACE by leveraging post-exposure longitudinal correlates of survival and outcome that may also mediate the exposure effects on survival and outcome. Nonparametric identification is achieved by supposing that the longitudinal data arise from a certain nonparametric structural equations model and by making the monotonicity assumption that the effect of exposure on survival agrees in its direction across individuals. A novel weighted analysis involving a consistent estimate of the survival process is shown to produce consistent estimates of SACE. A data illustration is given, and the methods are extended to the context of time-varying exposures. We discuss a sensitivity analysis framework that relaxes assumptions about independent errors in the nonparametric structural equations model and may be used to assess the extent to which inference may be altered by a violation of key identifying assumptions. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Characteristics of vaccine failures in a randomized placebo-controlled trial of inactivated influenza vaccine in children

BACKGROUND

Infections occurring among vaccinated persons (vaccine failures) are known to occur in vaccines with imperfect efficacy. Failures among vaccinated children who were infected with vaccine-matched influenza B virus strain have not been adequately characterized.

METHODS

Taking advantage of a randomized controlled trial of trivalent seasonal influenza vaccine (TIV), the viral shedding and clinical symptoms associated with reverse transcriptase polymerase chain reaction-confirmed influenza B infection and serum hemaggluttination inhibiting antibody response to vaccine were compared between children 6 and 17 years receiving TIV and placebo.

RESULTS

Vaccine failures were observed to show lower antibody response to TIV compared with other vaccine recipients. We did not find any evidence that vaccination reduced the severity or duration of clinical symptoms of reverse transcriptase polymerase chain reaction-confirmed vaccine-matched influenza B infections. Vaccination was not observed to alter viral load or shedding duration.

CONCLUSIONS

TIV was not observed to ameliorate clinical symptoms or viral shedding among vaccine failures compared with infected placebo recipients. Lower antibody response might have explained vaccine failure and also lack of effect in reducing clinical symptoms and viral shedding upon infection. Our results are based on a randomized controlled trial of split virus inactivated vaccine and may not be applicable to other vaccine types. Further studies in vaccine failure among children will be important in future vaccine development.

Sharpening bounds on principal effects with covariates

Estimation of treatment effects in randomized studies is often hampered by possible selection bias induced by conditioning on or adjusting for a variable measured post-randomization. One approach to obviate such selection bias is to consider inference about treatment effects within principal strata, that is, principal effects. A challenge with this approach is that without strong assumptions principal effects are not identifiable from the observable data. In settings where such assumptions are dubious, identifiable large sample bounds may be the preferred target of inference. In practice these bounds may be wide and not particularly informative. In this work we consider whether bounds on principal effects can be improved by adjusting for a categorical baseline covariate. Adjusted bounds are considered which are shown to never be wider than the unadjusted bounds. Necessary and sufficient conditions are given for which the adjusted bounds will be sharper (i.e., narrower) than the unadjusted bounds. The methods are illustrated using data from a recent, large study of interventions to prevent mother-to-child transmission of HIV through breastfeeding. Using a baseline covariate indicating low birth weight, the estimated adjusted bounds for the principal effect of interest are 63% narrower than the estimated unadjusted bounds.

Rank-based principal stratum sensitivity analyses

We describe rank-based approaches to assess principal stratification treatment effects in studies where the outcome of interest is only well-defined in a subgroup selected after randomization. Our methods are sensitivity analyses, in that estimands are identified by fixing a parameter and then we investigate the sensitivity of results by varying this parameter over a range of plausible values. We present three rank-based test statistics and compare their performance through simulations, and provide recommendations. We also study three different bootstrap approaches for determining levels of significance. Finally, we apply our methods to two studies: an HIV vaccine trial and a prostate cancer prevention trial.

The test-negative design for estimating influenza vaccine effectiveness

OBJECTIVE

The test-negative design has emerged in recent years as the preferred method for estimating influenza vaccine effectiveness (VE) in observational studies. However, the methodologic basis of this design has not been formally developed.

METHODS

In this paper we develop the rationale and underlying assumptions of the test-negative study. Under the test-negative design for influenza VE, study subjects are all persons who seek care for an acute respiratory illness (ARI). All subjects are tested for influenza infection. Influenza VE is estimated from the ratio of the odds of vaccination among subjects testing positive for influenza to the odds of vaccination among subjects testing negative.

RESULTS

With the assumptions that (a) the distribution of non-influenza causes of ARI does not vary by influenza vaccination status, and (b) VE does not vary by health care-seeking behavior, the VE estimate from the sample can generalized to the full source population that gave rise to the study sample. Based on our derivation of this design, we show that test-negative studies of influenza VE can produce biased VE estimates if they include persons seeking care for ARI when influenza is not circulating or do not adjust for calendar time.

CONCLUSIONS

The test-negative design is less susceptible to bias due to misclassification of infection and to confounding by health care-seeking behavior, relative to traditional case-control or cohort studies. The cost of the test-negative design is the additional, difficult-to-test assumptions that incidence of non-influenza respiratory infections is similar between vaccinated and unvaccinated groups within any stratum of care-seeking behavior, and that influenza VE does not vary across care-seeking strata.

Comparing competing risk outcomes within principal strata, with application to studies of mother-to-child transmission of HIV

In randomized trials to prevent breast milk transmission of human immunodeficiency virus (HIV) from mother to infant, investigators are often interested in assessing the effect of a treatment or intervention on the cumulative risk of HIV infection by time (age) t in infants who are alive and uninfected at a certain time point τ(0)  < t. Such comparisons are challenging for two reasons. First, infants are typically randomized at birth (time 0 < τ(0) ) such that comparisons between trial arms among the subset of infants alive and uninfected at τ(0) are subject to selection bias. Second, in most mother-to-child transmission (MTCT) trials competing risks are often present, such as death or cessation of breastfeeding prior to HIV infection. In this paper, we present methods for assessing the causal effect of a treatment on competing risk outcomes within principal strata. In MTCT trials, the causal effect of interest is that of treatment on the risk of HIV infection by time t > τ(0) within the principal stratum of infants who would be alive and uninfected by τ(0) regardless of randomization assignment. We develop large sample nonparametric bounds and a semiparametric sensitivity analysis model for drawing inference about this causal effect. We present a simulation study demonstrating that the proposed methods perform well in finite samples. We apply the proposed methods to a large, recent MTCT trial.

Bounding the infectiousness effect in vaccine trials

In vaccine trials, the vaccination of one person might prevent the infection of another; a distinction can be drawn between the ways such a protective effect might arise. Consider a setting with 2 persons per household in which one of the 2 is vaccinated. Vaccinating the first person may protect the second person by preventing the first from being infected and passing the infection on to the second. Alternatively, vaccinating the first person may protect the second by rendering the infection less contagious even if the first is infected. This latter mechanism is sometimes referred to as an "infectiousness effect" of the vaccine. Crude estimators for the infectiousness effect will be subject to selection bias due to stratification on a postvaccination event, namely the infection status of the first person. We use theory concerning causal inference under interference along with a principal-stratification framework to show that, although the crude estimator is biased, it is, under plausible assumptions, conservative for what one might define as a causal infectiousness effect. This applies to bias from selection due to the persons in the comparison, and also to selection due to pathogen virulence. We illustrate our results with an example from the literature.

On causal inference in the presence of interference

Interference is said to be present when the exposure or treatment received by one individual may affect the outcomes of other individuals. Such interference can arise in settings in which the outcomes of the various individuals come about through social interactions. When interference is present, causal inference is rendered considerably more complex, and the literature on causal inference in the presence of interference has just recently begun to develop. In this article we summarise some of the concepts and results from the existing literature and extend that literature in considering new results for finite sample inference, new inverse probability weighting estimators in the presence of interference and new causal estimands of interest.

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.

Does Finasteride Affect the Severity of Prostate Cancer? A Causal Sensitivity Analysis

In 2003 Thompson and colleagues reported that daily use of finasteride reduced the prevalence of prostate cancer by 25% compared to placebo. These results were based on the double-blind randomized Prostate Cancer Prevention Trial (PCPT) which followed 18,882 men with no prior or current indications of prostate cancer annually for seven years. Enthusiasm for the risk reduction afforded by the chemopreventative agent and adoption of its use in clinical practice, however, was severely dampened by the additional finding in the trial of an increased absolute number of high-grade (Gleason score >/= 7) cancers on the finasteride arm. The question arose as to whether this finding truly implied that finasteride increased the risk of more severe prostate cancer or was a study artifact due to a series of possible post-randomization selection biases, including differences among treatment arms in patient characteristics of cancer cases, differences in biopsy verification of cancer status due to increased sensitivity of prostate-specific antigen under finasteride, differential grading by biopsy due to prostate volume reduction by finasteride, and nonignorable drop-out. Via a causal inference approach implementing inverse probability weighted estimating equations, this analysis addresses the question of whether finasteride caused more severe prostate cancer by estimating the mean treatment difference in prostate cancer severity between finasteride and placebo for the principal stratum of participants who would have developed prostate cancer regardless of treatment assignment. We perform sensitivity analyses that sequentially adjust for the numerous potential post-randomization biases conjectured in the PCPT.

Commentary on "Principal stratification - a goal or a tool?" by Judea Pearl

This commentary takes up Pearl's welcome challenge to clearly articulate the scientific value of principal stratification estimands that we and colleagues have investigated, in the area of randomized placebo-controlled preventive vaccine efficacy trials, especially trials of HIV vaccines. After briefly arguing that certain principal stratification estimands for studying vaccine effects on post-infection outcomes are of genuine scientific interest, the bulk of our commentary argues that the "causal effect predictiveness" (CEP) principal stratification estimand for evaluating immune biomarkers as surrogate endpoints is not of ultimate scientific interest, because it evaluates surrogacy restricted to the setting of a particular vaccine efficacy trial, but is nevertheless useful for guiding the selection of primary immune biomarker endpoints in Phase I/II vaccine trials and for facilitating assessment of transportability/bridging surrogacy.

THE POTENTIAL FOR BIAS IN PRINCIPAL CAUSAL EFFECT ESTIMATION WHEN TREATMENT RECEIVED DEPENDS ON A KEY COVARIATE

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.

Sensitivity Analyses Comparing Time-to-Event Outcomes Existing Only in a Subset Selected Postrandomization

In some randomized studies, researchers are interested in determining the effect of treatment assignment on outcomes that may exist only in a subset chosen after randomization. For example, in preventative human immunodeficiency virus (HIV) vaccine efficacy trials, it is of interest to determine whether randomization to vaccine affects postinfection outcomes that may be right-censored. Such outcomes in these trials include time from infection diagnosis to initiation of antiretroviral therapy and time from infection diagnosis to acquired immune deficiency syndrome. Here we present sensitivity analysis methods for making causal comparisons on these postinfection outcomes. We focus on estimating the survival causal effect, defined as the difference between probabilities of not yet experiencing the event in the vaccine and placebo arms, conditional on being infected regardless of treatment assignment. This group is referred to as the always-infected principal stratum. Our key assumption is monotonicity-that subjects randomized to the vaccine arm who become infected would have been infected had they been randomized to placebo. We propose nonparametric, semiparametric, and parametric methods for estimating the survival causal effect. We apply these methods to the first Phase III preventative HIV vaccine trial, VaxGen's trial of AIDSVAX B/B.

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.

Randomization-Based Inference within Principal Strata

In randomized studies, treatment comparisons conditional on intermediate post-randomization outcomes using standard analytic methods do not have a causal interpretation. An alternate approach entails treatment comparisons within principal strata defined by the potential outcomes for the intermediate outcome that would be observed under each treatment assignment. In this paper, we develop methods for randomization-based inference within principal strata. The proposed methods are compared with existing large-sample methods as well as traditional intent-to-treat approaches. This research is motivated by HIV prevention studies where few infections are expected and inference is desired within the always-infected principal stratum, i.e., all individuals who would become infected regardless of randomization assignment.

Lactoferrin Augmentation of the BCG Vaccine Leads to Increased Pulmonary Integrity

The goal of vaccination to prevent tuberculosis disease (TB) is to offer long-term protection to the individual and the community. In addition, the success of any protective TB vaccine should include the ability to limit cavitary formation and disease progression. The current BCG vaccine protects against disseminated TB disease in children by promoting development of antigenic-specific responses. However, its efficacy is limited in preventing postprimary pulmonary disease in adults that is responsible for the majority of disease and transmission. This paper illustrates the use of lactoferrin as an adjuvant to boost efficacy of the BCG vaccine to control organism growth and limit severe manifestation of pulmonary disease. This resulting limitation in pathology may ultimately, limit spread of bacilli and subsequent transmission of organisms between individuals. The current literature is reviewed, and data is presented to support molecular mechanisms underlying lactoferrin's utility as an adjuvant for the BCG vaccine.

A simple method for principal strata effects when the outcome has been truncated due to death

In randomized trials with follow-up, outcomes such as quality of life may be undefined for individuals who die before the follow-up is complete. In such settings, restricting analysis to those who survive can give rise to biased outcome comparisons. An alternative approach is to consider the "principal strata effect" or "survivor average causal effect" (SACE), defined as the effect of treatment on the outcome among the subpopulation that would have survived under either treatment arm. The authors describe a very simple technique that can be used to assess the SACE. They give both a sensitivity analysis technique and conditions under which a crude comparison provides a conservative estimate of the SACE. The method is illustrated using data from the ARDSnet (Acute Respiratory Distress Syndrome Network) clinical trial comparing low-volume ventilation and traditional ventilation methods for individuals with acute respiratory distress syndrome.

Semiparametric estimation of the average causal effect of treatment on an outcome measured after a postrandomization event, with missing outcome data

In the past decade, several principal stratification-based statistical methods have been developed for testing and estimation of a treatment effect on an outcome measured after a postrandomization event. Two examples are the evaluation of the effect of a cancer treatment on quality of life in subjects who remain alive and the evaluation of the effect of an HIV vaccine on viral load in subjects who acquire HIV infection. However, in general the developed methods have not addressed the issue of missing outcome data, and hence their validity relies on a missing completely at random (MCAR) assumption. Because in many applications the MCAR assumption is untenable, while a missing at random (MAR) assumption is defensible, we extend the semiparametric likelihood sensitivity analysis approach of Gilbert and others (2003) and Jemiai and Rotnitzky (2005) to allow the outcome to be MAR. We combine these methods with the robust likelihood-based method of Little and An (2004) for handling MAR data to provide semiparametric estimation of the average causal effect of treatment on the outcome. The new method, which does not require a monotonicity assumption, is evaluated in a simulation study and is applied to data from the first HIV vaccine efficacy trial.

A novel recombinant human lactoferrin augments the BCG vaccine and protects alveolar integrity upon infection with Mycobacterium tuberculosis in mice

Lactoferrin, an iron binding glycoprotein, possesses multiple immune modulatory activities, including the ability to promote antigen specific cell-mediated immunity. Previous studies showed that adding bovine lactoferrin to the BCG vaccine (an attenuated strain of Mycobacterium bovis Bacillus Calmette Guerin) resulted in increased host protective responses upon subsequent challenge with virulent Erdman Mycobacterium tuberculosis (MTB) in mice. The studies outlined here investigate utility of a novel recombinant human lactoferrin to enhance the BCG vaccine and protect against alveolar injury during experimental MTB infection in mice. Sialylated and non-sialylated forms of the recombinant human lactoferrin (rhLF), glycoengineered in yeast (Pichia pastoris) and expressing humanized N-glycosylation patterns, were examined for their ability to enhance efficacy of the BCG vaccine in a murine TB model system. Results indicated that the sialylated form of the recombinant human lactoferrin generated increased antigen specific recall responses to BCG antigens. Furthermore, augmented protection was demonstrated using the sialylated lactoferrin adjuvant with BCG, resulting in significant reduction in associated pathology following challenge with virulent organisms.

A Bayesian model for evaluating influenza antiviral efficacy in household studies with asymptomatic infections

Antiviral agents are an important component in mitigation/containment strategies for pandemic influenza. However, most research for mitigation/containment strategies relies on the antiviral efficacies evaluated from limited data of clinical trials. Which efficacy measures can be reliably estimated from these studies depends on the trial design, the size of the epidemics, and the statistical methods. We propose a Bayesian framework for modeling the influenza transmission dynamics within households. This Bayesian framework takes into account asymptomatic infections and is able to estimate efficacies with respect to protecting against viral infection, infection with clinical disease, and pathogenicity (the probability of disease given infection). We use the method to reanalyze 2 clinical studies of oseltamivir, an influenza antiviral agent, and compare the results with previous analyses. We found significant prophylactic efficacies in reducing the risk of viral infection and infection with disease but no prophylactic efficacy in reducing pathogenicity. We also found significant therapeutic efficacies in reducing pathogenicity and the risk of infection with disease but no therapeutic efficacy in reducing the risk of viral infection in the contacts.

Evaluating a surrogate endpoint at three levels, with application to vaccine development

Identification of an immune response to vaccination that reliably predicts protection from clinically significant infection, i.e. an immunological surrogate endpoint, is a primary goal of vaccine research. Using this problem of evaluating an immunological surrogate as an illustration, we describe a hierarchy of three criteria for a valid surrogate endpoint and statistical analysis frameworks for evaluating them. Based on a placebo-controlled vaccine efficacy trial, the first level entails assessing the correlation of an immune response with a study endpoint in the study groups, and the second level entails evaluating an immune response as a surrogate for the study endpoint that can be used for predicting vaccine efficacy for a setting similar to that of the vaccine trial. We show that baseline covariates, innovative study design, and a potential outcomes formulation can be helpful for this assessment. The third level entails validation of a surrogate endpoint via meta-analysis, where the goal is to evaluate how well the immune response can be used to predict vaccine efficacy for new settings (building bridges). A simulated vaccine trial and two example vaccine trials are presented, one supporting that certain anti-influenza antibody levels are an excellent surrogate for influenza illness and another supporting that certain anti-HIV antibody levels are not useful as a surrogate for HIV infection.

Overview of Vaccine Field Studies: Types of Effects and Designs

Vaccination produces many different types of effects in individuals and in populations. The scientific and public health questions of interest determine the choice of measures of effect and study designs. Here we review some of the various measures and study designs for evaluating different effects of vaccination.