Statistical identifiability and the surrogate endpoint problem, with application to vaccine trials

Four statistical frameworks for assessing an immune correlate of protection (surrogate endpoint) from a randomized, controlled, vaccine efficacy trial

A central goal of vaccine research is to characterize and validate immune correlates of protection (CoPs). In addition to helping elucidate immunological mechanisms, a CoP can serve as a valid surrogate endpoint for an infectious disease clinical outcome and thus qualifies as a primary endpoint for vaccine authorization or approval without requiring resource-intensive randomized, controlled phase 3 trials. Yet, it is challenging to persuasively validate a CoP, because a prognostic immune marker can fail as a reliable basis for predicting/inferring the level of vaccine efficacy against a clinical outcome, and because the statistical analysis of phase 3 trials only has limited capacity to disentangle association from cause. Moreover, the multitude of statistical methods garnered for CoP evaluation in phase 3 trials renders the comparison, interpretation, and synthesis of CoP results challenging. Toward promoting broader harmonization and standardization of CoP evaluation, this article summarizes four complementary statistical frameworks for evaluating CoPs in a phase 3 trial, focusing on the frameworks' distinct scientific objectives as measured and communicated by distinct causal vaccine efficacy parameters. Advantages and disadvantages of the frameworks are considered, dependent on phase 3 trial context, and perspectives are offered on how the frameworks can be applied and their results synthesized.

Can earlier biomarker measurements explain a treatment effect on diabetes incidence? A robust comparison of five surrogate markers

INTRODUCTION

We measured and compared five individual surrogate markers-change from baseline to 1 year after randomization in hemoglobin A1c (HbA1c), fasting glucose, 2-hour postchallenge glucose, triglyceride-glucose index (TyG) index, and homeostatic model assessment of insulin resistance (HOMA-IR)-in terms of their ability to explain a treatment effect on reducing the risk of type 2 diabetes mellitus at 2, 3, and 4 years after treatment initiation.

RESEARCH DESIGN AND METHODS

Study participants were from the Diabetes Prevention Program study, randomly assigned to either a lifestyle intervention (n=1023) or placebo (n=1030). The surrogate markers were measured at baseline and 1 year, and diabetes incidence was examined at 2, 3, and 4 years postrandomization. Surrogacy was evaluated using a robust model-free estimate of the proportion of treatment effect explained (PTE) by the surrogate marker.

RESULTS

Across all time points, change in fasting glucose and HOMA-IR explained higher proportions of the treatment effect than 2-hour glucose, TyG index, or HbA1c. For example, at 2 years, glucose explained the highest (80.1%) proportion of the treatment effect, followed by HOMA-IR (77.7%), 2-hour glucose (76.2%), and HbA1c (74.6%); the TyG index explained the smallest (70.3%) proportion.

CONCLUSIONS

These data suggest that, of the five examined surrogate markers, glucose and HOMA-IR were the superior surrogate markers in terms of PTE, compared with 2-hour glucose, HbA1c, and TyG index.

Mediation and instrumental variable analyses for vaccine-induced antibody titer against influenza B

OBJECTIVE

Immune correlate analyses for vaccine trials have been applied to investigate associations of vaccine efficacy and surrogate markers such as vaccine-induced antibodies. However, the role of antibody as a surrogate marker in predicting the outcome can vary by time, and surrogate-outcome confounding may have resulted in bias even in randomized trials. We provide a framework for surrogate marker assessment to address the aforementioned issues.

STUDY DESIGN AND SETTING

We reanalyzed the vaccine randomized trial for influenza B. We conducted a mediation analysis that enables estimation of vaccine efficacy, mediation effects and proportion of mediation on disease probabilities at various follow-up times. We proposed instrumental variable (IV) analyses with randomized vaccination as an IV accounting for potential unmeasured confounding.

RESULTS

The mediation effect of vaccine efficacy by hemagglutination inhibition (HAI) titer was significantly protective at 181 days after vaccination: 63.2% [95% confidence interval, (CI) = (39.9%, 82.0%)], and HAI titer explained 61.1% [95% CI = (36.7%, 96.2%)] of the protective effect of vaccination.

CONCLUSIONS

Most of vaccine efficacy is mediated by HAI titer, particularly in children 10 years and older. Our contribution is to provide causal analytics for the role of surrogate marker with weaker assumptions regarding surrogate-disease causation.

SENSITIVITY ANALYSIS FOR EVALUATING PRINCIPAL SURROGATE ENDPOINTS RELAXING THE EQUAL EARLY CLINICAL RISK ASSUMPTION

This article addresses the evaluation of post-randomization immune response biomarkers as principal surrogate endpoints of a vaccine's protective effect, based on data from randomized vaccine trials. An important metric for quantifying a biomarker's principal surrogacy in vaccine research is the vaccine efficacy curve, which shows a vaccine's efficacy as a function of potential biomarker values if receiving vaccine, among an 'early-always-at-risk' principal stratum of trial participants who remain disease-free at the time of biomarker measurement whether having received vaccine or placebo. Earlier work in principal surrogate evaluation relied on an 'equal-early-clinical-risk' assumption for identifiability of the vaccine curve, based on observed disease status at the time of biomarker measurement. This assumption is violated in the common setting that the vaccine has an early effect on the clinical endpoint before the biomarker is measured. In particular, a vaccine's early protective effect observed in two phase III dengue vaccine trials (CYD14/CYD15) has motivated our current research development. We relax the 'equal-early-clinical-risk' assumption and propose a new sensitivity analysis framework for principal surrogate evaluation allowing for early vaccine efficacy. Under this framework, we develop inference procedures for vaccine efficacy curve estimators based on the estimated maximum likelihood approach. We then use the proposed methodology to assess the surrogacy of post-randomization neutralization titer in the motivating dengue application.

Translating questions to estimands in randomized clinical trials with intercurrent events

Intercurrent (post-treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight-forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention-to-treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well-defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest.

Informed decision-making: Statistical methodology for surrogacy evaluation and its role in licensing and reimbursement assessments

The desire, by patients and society, for faster access to therapies has driven a long tradition of the use of surrogate endpoints in the evaluation of pharmaceuticals and, more recently, biologics and other innovative medical technologies. The consequent need for statistical validation of potential surrogate outcome measures is a prime example on the theme of statistical support for decision-making in health technology assessment (HTA). Following the pioneering methodology based on hypothesis testing that Prentice presented in 1989, a host of further methods, both frequentist and Bayesian, have been developed to enable the value of a putative surrogate outcome to be determined. This rich methodological seam has generated practical methods for surrogate evaluation, the most recent of which are based on the principles of information theory and bring together ideas from the causal effects and causal association paradigms. Following our synopsis of statistical methods, we then consider how regulatory authorities (on licensing) and payer and HTA agencies (on reimbursement) use clinical trial evidence based on surrogate outcomes. We review existing HTA surrogate outcome evaluative frameworks. We conclude with recommendations for further steps: (1) prioritisation by regulators and payers of the application of formal surrogate outcome evaluative frameworks, (2) application of formal Bayesian decision-analytic methods to support reimbursement decisions, and (3) greater utilization of conditional surrogate-based licensing and reimbursement approvals, with subsequent reassessment of treatments in confirmatory trials based on final patient-relevant outcomes.

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.

Using multiple imputation to classify potential outcomes subgroups

With medical tests becoming increasingly available, concerns about over-testing, over-treatment and health care cost dramatically increase. Hence, it is important to understand the influence of testing on treatment selection in general practice. Most statistical methods focus on average effects of testing on treatment decisions. However, this may be ill-advised, particularly for patient subgroups that tend not to benefit from such tests. Furthermore, missing data are common, representing large and often unaddressed threats to the validity of most statistical methods. Finally, it is often desirable to conduct analyses that can be interpreted causally. Using the Rubin Causal Model framework, we propose to classify patients into four potential outcomes subgroups, defined by whether or not a patient's treatment selection is changed by the test result and by the direction of how the test result changes treatment selection. This subgroup classification naturally captures the differential influence of medical testing on treatment selections for different patients, which can suggest targets to improve the utilization of medical tests. We can then examine patient characteristics associated with patient potential outcomes subgroup memberships. We used multiple imputation methods to simultaneously impute the missing potential outcomes as well as regular missing values. This approach can also provide estimates of many traditional causal quantities of interest. We find that explicitly incorporating causal inference assumptions into the multiple imputation process can improve the precision for some causal estimates of interest. We also find that bias can occur when the potential outcomes conditional independence assumption is violated; sensitivity analyses are proposed to assess the impact of this violation. We applied the proposed methods to examine the influence of 21-gene assay, the most commonly used genomic test in the United States, on chemotherapy selection among breast cancer patients.

On the individual surrogate paradox

When the primary outcome is difficult to collect, a surrogate endpoint is typically used as a substitute. It is possible that for every individual, the treatment has a positive effect on the surrogate, and the surrogate has a positive effect on the primary outcome, but for some individuals, the treatment has a negative effect on the primary outcome. For example, a treatment may be substantially effective in preventing the stroke for everyone, and lowering the risk of stroke is universally beneficial for life expectancy; however, the treatment may still cause death for some individuals. We define such paradoxical phenomenon as the individual surrogate paradox. The individual surrogate paradox is proposed to capture the treatment effect heterogeneity, which is unable to be described by either the surrogate paradox based on average causal effect or that based on distributional causal effect. We investigate the existing surrogate criteria in terms of whether the individual surrogate paradox could manifest. We find that only the strong binary surrogate can avoid such paradox without additional assumptions. Utilizing the sharp bounds, we propose novel criteria to exclude the individual surrogate paradox. Our methods are illustrated in an application to determine the effect of the intensive glycemia on the risk of development or progression of diabetic retinopathy.

Predictive cluster level surrogacy in the presence of interference

Surrogate evaluation is a difficult problem that is made more so by the presence of interference. Our proposed procedure can allow for relatively easy evaluation of surrogates for indirect or spill-over clinical effects at the cluster level. Our definition of surrogacy is based on the causal-association paradigm (Joffe and Greene, 2009. Related causal frameworks for surrogate outcomes. Biometrics65, 530-538), under which surrogates are evaluated by the strength of the association between a causal treatment effect on the clinical outcome and a causal treatment effect on the candidate surrogate. Hudgens and Halloran (2008, Toward causal inference with interference. Journal of the American Statistical Association103, 832-842) introduced estimators that can be used for many of the marginal causal estimands of interest in the presence of interference. We extend these to consider surrogates for not just direct effects, but indirect and total effects at the cluster level. We suggest existing estimators that can be used to evaluate biomarkers under our proposed definition of surrogacy. In our motivating setting of a transmission blocking malaria vaccine, there is expected to be no direct protection to those vaccinated and predictive surrogates are urgently needed. We use a set of simulated data examples based on the proposed Phase IIb/III trial design of transmission blocking malaria vaccine to demonstrate how our definition, proposed criteria and procedure can be used to identify biomarkers as predictive cluster level surrogates in the presence of interference on the clinical outcome.

Evaluation of treatment effect modification by biomarkers measured pre- and post-randomization in the presence of non-monotone missingness

In vaccine studies, an important research question is to study effect modification of clinical treatment efficacy by intermediate biomarker-based principal strata. In settings where participants entering a trial may have prior exposure and therefore variable baseline biomarker values, clinical treatment efficacy may further depend jointly on a biomarker measured at baseline and measured at a fixed time after vaccination. This makes it important to conduct a bivariate effect modification analysis by both the intermediate biomarker-based principal strata and the baseline biomarker values. Existing research allows this assessment if the sampling of baseline and intermediate biomarkers follows a monotone pattern, i.e., if participants who have the biomarker measured post-randomization would also have the biomarker measured at baseline. However, additional complications in study design could happen in practice. For example, in a dengue correlates study, baseline biomarker values were only available from a fraction of participants who have biomarkers measured post-randomization. How to conduct the bivariate effect modification analysis in these studies remains an open research question. In this article, we propose approaches for bivariate effect modification analysis in the complicated sampling design based on an estimated likelihood framework. We demonstrate advantages of the proposed method over existing methods through numerical studies and illustrate our method with data sets from two phase 3 dengue vaccine efficacy trials.

A unified evaluation of differential vaccine efficacy

Many infectious diseases are well prevented by proper vaccination. However, when a vaccine is not completely efficacious, there is great interest in determining how the vaccine effect differs in subgroups conditional on measured immune responses postvaccination and also according to the type of infecting agent (eg, strain of a virus). The former is often called correlate of protection (CoP) analysis, while the latter has been called sieve analysis. We propose a unified framework for simultaneously assessing CoP and sieve effects of a vaccine in a large Phase III randomized trial. We use flexible parametric models treating times to infection from different agents as competing risks and estimated maximum likelihood to fit the models. The parametric models under competing risks allow for estimation of both cumulative incidence-based contrasts and instantaneous rates. We outline the assumptions with which we can link the observable data to the causal contrasts of interest, propose hypothesis testing procedures, and evaluate our proposed methods in an extensive simulation study.

Evaluating the surrogacy of multiple vaccine-induced immune response biomarkers in HIV vaccine trials

Identifying biomarkers as surrogates for clinical endpoints in randomized vaccine trials is useful for reducing study duration and costs, relieving participants of unnecessary discomfort, and understanding vaccine-effect mechanism. In this article, we use risk models with multiple vaccine-induced immune response biomarkers to measure the causal association between a vaccine's effects on these biomarkers and that on the clinical endpoint. In this setup, our main objective is to combine and select markers with high surrogacy from a list of many candidate markers, allowing us to get a more parsimonious model which can potentially increase the predictive quality of the true markers. To address the missing "potential" biomarker value if a subject receives placebo, we utilize the baseline immunogenicity predictor design augmented with a "closeout placebo vaccination" group. We then impute the missing potential marker values and conduct marker selection through a stepwise resampling and imputation method called stability selection. We test our proposed strategy under relevant simulation settings and on (partially simulated) biomarker data from a HIV vaccine trial (RV144).

Simultaneous Inference of Treatment Effect Modification by Intermediate Response Endpoint Principal Strata with Application to Vaccine Trials

In randomized clinical trials, researchers are often interested in identifying an inexpensive intermediate study endpoint (typically a biomarker) that is a strong effect modifier of the treatment effect on a longer-term clinical endpoint of interest. Motivated by randomized placebo-controlled preventive vaccine efficacy trials, within the principal stratification framework a pseudo-score type estimator has been proposed to estimate disease risks conditional on the counter-factual biomarker of interest under each treatment assignment to vaccine or placebo, yielding an estimator of biomarker conditional vaccine efficacy. This method can be used for trial designs that use baseline predictors of the biomarker and/or designs that vaccinate disease-free placebo recipients at the end of the trial. In this article, we utilize the pseudo-score estimator to estimate the biomarker conditional vaccine efficacy adjusting for baseline covariates. We also propose a perturbation resampling method for making simultaneous inference on conditional vaccine efficacy over the values of the biomarker. We illustrate our method with datasets from two phase 3 dengue vaccine efficacy trials.

Evaluation and comparison of predictive individual-level general surrogates

An intermediate response measure that accurately predicts efficacy in a new setting at the individual level could be used both for prediction and personalized medical decisions. In this article, we define a predictive individual-level general surrogate (PIGS), which is an individual-level intermediate response that can be used to accurately predict individual efficacy in a new setting. While methods for evaluating trial-level general surrogates, which are predictors of trial-level efficacy, have been developed previously, few, if any, methods have been developed to evaluate individual-level general surrogates, and no methods have formalized the use of cross-validation to quantify the expected prediction error. Our proposed method uses existing methods of individual-level surrogate evaluation within a given clinical trial setting in combination with cross-validation over a set of clinical trials to evaluate surrogate quality and to estimate the absolute prediction error that is expected in a new trial setting when using a PIGS. Simulations show that our method performs well across a variety of scenarios. We use our method to evaluate and to compare candidate individual-level general surrogates over a set of multi-national trials of a pentavalent rotavirus vaccine.

Likelihood-Based Methods for Assessing Principal Surrogate Endpoints in Vaccine Trials

When evaluating principal surrogate biomarkers in vaccine trials, missingness in potential outcomes requires prediction using auxiliary variables and/or augmented study design with a close-out placebo vaccination (CPV) component. The estimated likelihood approach, which separates the estimation of biomarker distribution from the maximization of the estimated likelihood, has often been adopted. Here we develop a likelihood-based approach that jointly estimates the two parts and describe the methods for selecting auxiliary variables as risk predictors and/or biomarker predictors. Through numerical studies, we observe that in a standard trial design without a CPV component, the two methods achieve similar performance in estimation of the risk model and the marker model. However, for trials augmented with a CPV component, using the likelihood-based method achieves better estimation performance compared to the estimated likelihood method. Moreover, in the presence of a large number of covariates from which to select, the ML method achieves comparable or better performance compared to the EL method in both designs. While the CPV component has not yet been implemented in existing vaccine trials, our results have applications in the planning of future vaccine trials. We illustrate the method using data from a dengue vaccine trial.

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.

Evaluating principal surrogate markers in vaccine trials in the presence of multiphase sampling

This article focuses on the evaluation of vaccine-induced immune responses as principal surrogate markers for predicting a given vaccine's effect on the clinical endpoint of interest. To address the problem of missing potential outcomes under the principal surrogate framework, we can utilize baseline predictors of the immune biomarker(s) or vaccinate uninfected placebo recipients at the end of the trial and measure their immune biomarkers. Examples of good baseline predictors are baseline immune responses when subjects enrolled in the trial have been previously exposed to the same antigen, as in our motivating application of the Zostavax Efficacy and Safety Trial (ZEST). However, laboratory assays of these baseline predictors are expensive and therefore their subsampling among participants is commonly performed. In this article, we develop a methodology for estimating principal surrogate values in the presence of baseline predictor subsampling. Under a multiphase sampling framework, we propose a semiparametric pseudo-score estimator based on conditional likelihood and also develop several alternative semiparametric pseudo-score or estimated likelihood estimators. We derive corresponding asymptotic theories and analytic variance formulas for these estimators. Through extensive numeric studies, we demonstrate good finite sample performance of these estimators and the efficiency advantage of the proposed pseudo-score estimator in various sampling schemes. We illustrate the application of our proposed estimators using data from an immune biomarker study nested within the ZEST trial.

An Introduction to Principal Surrogate Evaluation with the pseval Package

We describe a new package called pseval that implements the core methods for the evaluation of principal surrogates in a single clinical trial. It provides a flexible interface for defining models for the risk given treatment and the surrogate, the models for integration over the missing counterfactual surrogate responses, and the estimation methods. Estimated maximum likelihood and pseudo-score can be used for estimation, and the bootstrap for inference. A variety of post-estimation methods are provided, including print, summary, plot, and testing. We summarize the main statistical methods that are implemented in the package and illustrate its use from the perspective of a novice R user.

An information-theoretic approach for the evaluation of surrogate endpoints based on causal inference

In this work a new metric of surrogacy, the so-called individual causal association (ICA), is introduced using information-theoretic concepts and a causal inference model for a binary surrogate and true endpoint. The ICA has a simple and appealing interpretation in terms of uncertainty reduction and, in some scenarios, it seems to provide a more coherent assessment of the validity of a surrogate than existing measures. The identifiability issues are tackled using a two-step procedure. In the first step, the region of the parametric space of the distribution of the potential outcomes, compatible with the data at hand, is geometrically characterized. Further, in a second step, a Monte Carlo approach is proposed to study the behavior of the ICA on the previous region. The method is illustrated using data from the Collaborative Initial Glaucoma Treatment Study. A newly developed and user-friendly R package Surrogate is provided to carry out the evaluation exercise.

Augmented trial designs for evaluation of principal surrogates

Observation of counterfactual intermediate responses, and evaluation of them as candidate surrogates, is complicated in a standard randomized trial as half of the responses are systematically missing by design. Although some augmentation procedures exist for obtaining counterfactual responses, they are specific to vaccine trials. We outline extensions to the existing augmentations and suggest augmentations of three trial designs outside the setting of vaccines. We outline the assumptions needed to identify the causal estimands of interest under each augmented design, under which standard likelihood-based methods can be used to evaluate intermediate responses as principal surrogates. Two of these designs, crossover and individual stepped-wedge, allow for the observation of clinical endpoints under both treatment and control for some subset of subjects and can therefore improve efficiency over standard parallel trial designs. The third, the treatment run-in design, allows for the observation of a baseline measure that may be as useful a surrogate as the true counterfactual intermediate response. As the evaluation methods rely on several assumptions, we also outline a remediation analysis, which can be used to help overcome assumption violations. We illustrate our suggested methods in an example from a drug-resistant tuberculosis treatment trial.

Surrogate Endpoint Evaluation: Principal Stratification Criteria and the Prentice Definition

A common problem of interest within a randomized clinical trial is the evaluation of an inexpensive response endpoint as a valid surrogate endpoint for a clinical endpoint, where a chief purpose of a valid surrogate is to provide a way to make correct inferences on clinical treatment effects in future studies without needing to collect the clinical endpoint data. Within the principal stratification framework for addressing this problem based on data from a single randomized clinical efficacy trial, a variety of definitions and criteria for a good surrogate endpoint have been proposed, all based on or closely related to the "principal effects" or "causal effect predictiveness (CEP)" surface. We discuss CEP-based criteria for a useful surrogate endpoint, including (1) the meaning and relative importance of proposed criteria including average causal necessity (ACN), average causal sufficiency (ACS), and large clinical effect modification; (2) the relationship between these criteria and the Prentice definition of a valid surrogate endpoint; and (3) the relationship between these criteria and the consistency criterion (i.e., assurance against the "surrogate paradox"). This includes the result that ACN plus a strong version of ACS generally do not imply the Prentice definition nor the consistency criterion, but they do have these implications in special cases. Moreover, the converse does not hold except in a special case with a binary candidate surrogate. The results highlight that assumptions about the treatment effect on the clinical endpoint before the candidate surrogate is measured are influential for the ability to draw conclusions about the Prentice definition or consistency. In addition, we emphasize that in some scenarios that occur commonly in practice, the principal strata sub-populations for inference are identifiable from the observable data, in which cases the principal stratification framework has relatively high utility for the purpose of effect modification analysis, and is closely connected to the treatment marker selection problem. The results are illustrated with application to a vaccine efficacy trial, where ACN and ACS for an antibody marker are found to be consistent with the data and hence support the Prentice definition and consistency.

Likelihood-based methods for evaluating principal surrogacy in augmented vaccine trials

There is growing interest in assessing immune biomarkers, which are quick to measure and potentially predictive of long-term efficacy, as surrogate endpoints in randomized, placebo-controlled vaccine trials. This can be done under a principal stratification approach, with principal strata defined using a subject’s potential immune responses to vaccine and placebo (the latter may be assumed to be zero). In this context, principal surrogacy refers to the extent to which vaccine efficacy varies across principal strata. Because a placebo recipient’s potential immune response to vaccine is unobserved in a standard vaccine trial, augmented vaccine trials have been proposed to produce the information needed to evaluate principal surrogacy. This article reviews existing methods based on an estimated likelihood and a pseudo-score (PS) and proposes two new methods based on a semiparametric likelihood (SL) and a pseudo-likelihood (PL), for analyzing augmented vaccine trials. Unlike the PS method, the SL method does not require a model for missingness, which can be advantageous when immune response data are missing by happenstance. The SL method is shown to be asymptotically efficient, and it performs similarly to the PS and PL methods in simulation experiments. The PL method appears to have a computational advantage over the PS and SL methods.

Comparing and combining biomarkers as principal surrogates for time-to-event clinical endpoints

Principal surrogate endpoints are useful as targets for phase I and II trials. In many recent trials, multiple post-randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates, and none of these methods to our knowledge utilize time-to-event clinical endpoint information. We propose a Weibull model extension of the semi-parametric estimated maximum likelihood method that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time-dependent and surrogate-dependent true and false positive fraction, the time-dependent and the integrated standardized total gain, and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial.

Hard, harder, hardest: principal stratification, statistical identifiability, and the inherent difficulty of finding surrogate endpoints

In many areas of clinical investigation there is great interest in identifying and validating surrogate endpoints, biomarkers that can be measured a relatively short time after a treatment has been administered and that can reliably predict the effect of treatment on the clinical outcome of interest. However, despite dramatic advances in the ability to measure biomarkers, the recent history of clinical research is littered with failed surrogates. In this paper, we present a statistical perspective on why identifying surrogate endpoints is so difficult. We view the problem from the framework of causal inference, with a particular focus on the technique of principal stratification (PS), an approach which is appealing because the resulting estimands are not biased by unmeasured confounding. In many settings, PS estimands are not statistically identifiable and their degree of non-identifiability can be thought of as representing the statistical difficulty of assessing the surrogate value of a biomarker. In this work, we examine the identifiability issue and present key simplifying assumptions and enhanced study designs that enable the partial or full identification of PS estimands. We also present example situations where these assumptions and designs may or may not be feasible, providing insight into the problem characteristics which make the statistical evaluation of surrogate endpoints so challenging.

Fold rise in antibody titers by measured by glycoprotein-based enzyme-linked immunosorbent assay is an excellent correlate of protection for a herpes zoster vaccine, demonstrated via the vaccine efficacy curve

BACKGROUND

The phase III Zostavax Efficacy and Safety Trial of 1 dose of licensed zoster vaccine (ZV; Zostavax; Merck) in 50-59-year-olds showed approximately 70% vaccine efficacy (VE) to reduce the incidence of herpes zoster (HZ). An objective of the trial was to assess immune response biomarkers measuring antibodies to varicella zoster virus (VZV) by glycoprotein-based enzyme-linked immunosorbent assay as correlates of protection (CoPs) against HZ.

METHODS

The principal stratification vaccine efficacy curve framework for statistically evaluating immune response biomarkers as CoPs was applied. The VE curve describes how VE against the clinical end point (HZ) varies across participant subgroups defined by biomarker readout measuring vaccine-induced immune response. The VE curve was estimated using several subgroup definitions.

RESULTS

The fold rise in VZV antibody titers from the time before immunization to 6 weeks after immunization was an excellent CoP, with VE increasing sharply with fold rise: VE was estimated at 0% for the subgroup with no rise and at 90% for the subgroup with 5.26-fold rise. In contrast, VZV antibody titers measured 6 weeks after immunization did not predict VE, with similar estimated VEs across titer subgroups.

CONCLUSIONS

The analysis illustrates the value of the VE curve framework for assessing immune response biomarkers as CoPs in vaccine efficacy trials.

CLINICAL TRIALS REGISTRATION

NCT00534248.

Evaluating principal surrogate endpoints with time-to-event data accounting for time-varying treatment efficacy

Principal surrogate (PS) endpoints are relatively inexpensive and easy to measure study outcomes that can be used to reliably predict treatment effects on clinical endpoints of interest. Few statistical methods for assessing the validity of potential PSs utilize time-to-event clinical endpoint information and to our knowledge none allow for the characterization of time-varying treatment effects. We introduce the time-dependent and surrogate-dependent treatment efficacy curve, ${\mathrm {TE}}(t|s)$, and a new augmented trial design for assessing the quality of a biomarker as a PS. We propose a novel Weibull model and an estimated maximum likelihood method for estimation of the ${\mathrm {TE}}(t|s)$ curve. We describe the operating characteristics of our methods via simulations. We analyze data from the Diabetes Control and Complications Trial, in which we find evidence of a biomarker with value as a PS.

Surrogate measures and consistent surrogates

Surrogates which allow one to predict the effect of the treatment on the outcome of interest from the effect of the treatment on the surrogate are of importance when it is difficult or expensive to measure the primary outcome. Unfortunately, the use of such surrogates can give rise to paradoxical situations in which the effect of the treatment on the surrogate is positive, the surrogate and outcome are strongly positively correlated, but the effect of the treatment on the outcome is negative, a phenomenon sometimes referred to as the "surrogate paradox." New results are given for consistent surrogates that extend the existing literature on sufficient conditions that ensure the surrogate paradox is not manifest. Specifically, it is shown that for the surrogate paradox to be manifest it must be the case that either there is (i) a direct effect of treatment on the outcome not through the surrogate and in the opposite direction as that through the surrogate or (ii) confounding for the effect of the surrogate on the outcome, or (iii) a lack of transitivity so that treatment does not positively affect the surrogate for all the same individuals for whom the surrogate positively affects the outcome. The conditions for consistent surrogates and the results of the article are important because they allow investigators to predict the direction of the effect of the treatment on the outcome simply from the direction of the effect of the treatment on the surrogate. These results on consistent surrogates are then related to the four approaches to surrogate outcomes described by Joffe and Greene (2009, Biometrics 65, 530-538) to assess whether the standard criteria used by these approaches to assess whether a surrogate is "good" suffice to avoid the surrogate paradox.

A threshold method for immunological correlates of protection

Background

Immunological correlates of protection are biological markers such as disease-specific antibodies which correlate with protection against disease and which are measurable with immunological assays. It is common in vaccine research and in setting immunization policy to rely on threshold values for the correlate where the accepted threshold differentiates between individuals who are considered to be protected against disease and those who are susceptible. Examples where thresholds are used include development of a new generation 13-valent pneumococcal conjugate vaccine which was required in clinical trials to meet accepted thresholds for the older 7-valent vaccine, and public health decision making on vaccination policy based on long-term maintenance of protective thresholds for Hepatitis A, rubella, measles, Japanese encephalitis and others. Despite widespread use of such thresholds in vaccine policy and research, few statistical approaches have been formally developed which specifically incorporate a threshold parameter in order to estimate the value of the protective threshold from data.

Methods

We propose a 3-parameter statistical model called the a:b model which incorporates parameters for a threshold and constant but different infection probabilities below and above the threshold estimated using profile likelihood or least squares methods. Evaluation of the estimated threshold can be performed by a significance test for the existence of a threshold using a modified likelihood ratio test which follows a chi-squared distribution with 3 degrees of freedom, and confidence intervals for the threshold can be obtained by bootstrapping. The model also permits assessment of relative risk of infection in patients achieving the threshold or not. Goodness-of-fit of the a:b model may be assessed using the Hosmer-Lemeshow approach. The model is applied to 15 datasets from published clinical trials on pertussis, respiratory syncytial virus and varicella.

Results

Highly significant thresholds with p-values less than 0.01 were found for 13 of the 15 datasets. Considerable variability was seen in the widths of confidence intervals. Relative risks indicated around 70% or better protection in 11 datasets and relevance of the estimated threshold to imply strong protection. Goodness-of-fit was generally acceptable.

Conclusions

The a:b model offers a formal statistical method of estimation of thresholds differentiating susceptible from protected individuals which has previously depended on putative statements based on visual inspection of data.

Design and estimation for evaluating principal surrogate markers in vaccine trials

In vaccine research, immune biomarkers that can reliably predict a vaccine's effect on the clinical endpoint (i.e., surrogate markers) are important tools for guiding vaccine development. This article addresses issues on optimizing two-phase sampling study design for evaluating surrogate markers in a principal surrogate framework, motivated by the design of a future HIV vaccine trial. To address the problem of missing potential outcomes in a standard trial design, novel trial designs have been proposed that utilize baseline predictors of the immune response biomarker(s) and/or augment the trial by vaccinating uninfected placebo recipients at the end of the trial and measuring their immune biomarkers. However, inefficient use of the augmented information can lead to counter-intuitive results on the precision of estimation. To remedy this problem, we propose a pseudo-score type estimator suitable for the augmented design and characterize its asymptotic properties. This estimator has superior performance compared with existing estimators and allows calculation of analytical variances useful for guiding study design. Based on the new estimator we investigate in detail the problem of optimizing the sampling scheme of a biomarker in a vaccine efficacy trial for efficiently estimating its surrogate effect, as characterized by the vaccine efficacy curve (a causal effect predictiveness curve) and by the predicted overall vaccine efficacy using the biomarker.

Bayesian inference for the causal effect of mediation

We propose a nonparametric Bayesian approach to estimate the natural direct and indirect effects through a mediator in the setting of a continuous mediator and a binary response. Several conditional independence assumptions are introduced (with corresponding sensitivity parameters) to make these effects identifiable from the observed data. We suggest strategies for eliciting sensitivity parameters and conduct simulations to assess violations to the assumptions. This approach is used to assess mediation in a recent weight management clinical trial.

Evaluating immune correlates in HIV type 1 vaccine efficacy trials: what RV144 may provide

Since the RV144 vaccine combination showed efficacy in a Phase III trial, it provides an opportunity to generate hypotheses about the immune responses necessary for protection against HIV-1 infection, and these results could help devise vaccine candidates with higher efficacy. Here we describe how researchers can determine the correlates of immune protection for an HIV/AIDS vaccine, particularly in the context of the RV144 trial, and we discuss the terminology used to describe correlates and surrogates.

A Bayesian approach to improved estimation of causal effect predictiveness for a principal surrogate endpoint

The literature on potential outcomes has shown that traditional methods for characterizing surrogate endpoints in clinical trials based only on observed quantities can fail to capture causal relationships between treatments, surrogates, and outcomes. Building on the potential-outcomes formulation of a principal surrogate, we introduce a Bayesian method to estimate the causal effect predictiveness (CEP) surface and quantify a candidate surrogate's utility for reliably predicting clinical outcomes. In considering the full joint distribution of all potentially observable quantities, our Bayesian approach has the following features. First, our approach illuminates implicit assumptions embedded in previously-used estimation strategies that have been shown to result in poor performance. Second, our approach provides tools for making explicit and scientifically-interpretable assumptions regarding associations about which observed data are not informative. Through simulations based on an HIV vaccine trial, we found that the Bayesian approach can produce estimates of the CEP surface with improved performance compared to previous methods. Third, our approach can extend principal-surrogate estimation beyond the previously considered setting of a vaccine trial where the candidate surrogate is constant in one arm of the study. We illustrate this extension through an application to an AIDS therapy trial where the candidate surrogate varies in both treatment arms.

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.

Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.

Comparing biomarkers as principal surrogate endpoints

Recently a new definition of surrogate endpoint, the "principal surrogate," was proposed based on causal associations between treatment effects on the biomarker and on the clinical endpoint. Despite its appealing interpretation, limited research has been conducted to evaluate principal surrogates, and existing methods focus on risk models that consider a single biomarker. How to compare principal surrogate value of biomarkers or general risk models that consider multiple biomarkers remains an open research question. We propose to characterize a marker or risk model's principal surrogate value based on the distribution of risk difference between interventions. In addition, we propose a novel summary measure (the standardized total gain) that can be used to compare markers and to assess the incremental value of a new marker. We develop a semiparametric estimated-likelihood method to estimate the joint surrogate value of multiple biomarkers. This method accommodates two-phase sampling of biomarkers and is more widely applicable than existing nonparametric methods by incorporating continuous baseline covariates to predict the biomarker(s), and is more robust than existing parametric methods by leaving the error distribution of markers unspecified. The methodology is illustrated using a simulated example set and a real data set in the context of HIV vaccine trials.

A Sequential Phase 2b Trial Design for Evaluating Vaccine Efficacy and Immune Correlates for Multiple HIV Vaccine Regimens

Five preventative HIV vaccine efficacy trials have been conducted over the last 12 years, all of which evaluated vaccine efficacy (VE) to prevent HIV infection for a single vaccine regimen versus placebo. Now that one of these trials has supported partial VE of a prime-boost vaccine regimen, there is interest in conducting efficacy trials that simultaneously evaluate multiple prime-boost vaccine regimens against a shared placebo group in the same geographic region, for accelerating the pace of vaccine development. This article proposes such a design, which has main objectives (1) to evaluate VE of each regimen versus placebo against HIV exposures occurring near the time of the immunizations; (2) to evaluate durability of VE for each vaccine regimen showing reliable evidence for positive VE; (3) to expeditiously evaluate the immune correlates of protection if any vaccine regimen shows reliable evidence for positive VE; and (4) to compare VE among the vaccine regimens. The design uses sequential monitoring for the events of vaccine harm, non-efficacy, and high efficacy, selected to weed out poor vaccines as rapidly as possible while guarding against prematurely weeding out a vaccine that does not confer efficacy until most of the immunizations are received. The evaluation of the design shows that testing multiple vaccine regimens is important for providing a well-powered assessment of the correlation of vaccine-induced immune responses with HIV infection, and is critically important for providing a reasonably powered assessment of the value of identified correlates as surrogate endpoints for HIV infection.