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1.  Principal Stratification in Causal Inference 
Biometrics  2002;58(1):21-29.
Summary
Many scientific problems require that treatment comparisons be adjusted for posttreatment variables, but the estimands underlying standard methods are not causal effects. To address this deficiency, we propose a general framework for comparing treatments adjusting for posttreatment variables that yields principal effects based on principal stratification. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable under each of the treatments being compared. Principal effects are causal effects within a principal stratum. The key property of principal strata is that they are not affected by treatment assignment and therefore can be used just as any pretreatment covariate, such as age category. As a result, the central property of our principal effects is that they are always causal effects and do not suffer from the complications of standard posttreatment-adjusted estimands. We discuss briefly that such principal causal effects are the link between three recent applications with adjustment for posttreatment variables: (i) treatment noncompliance, (ii) missing outcomes (dropout) following treatment noncompliance, and (iii) censoring by death. We then attack the problem of surrogate or biomarker endpoints, where we show, using principal causal effects, that all current definitions of surrogacy, even when perfectly true, do not generally have the desired interpretation as causal effects of treatment on outcome. We go on to formulate estimands based on principal stratification and principal causal effects and show their superiority.
PMCID: PMC4137767  PMID: 11890317
Biomarker; Causal inference; Censoring by death; Missing data; Posttreatment variable; Principal stratification; Quality of life; Rubin causal model; Surrogate
2.  ASSESSING SURROGATE ENDPOINTS IN VACCINE TRIALS WITH CASE-COHORT SAMPLING AND THE COX MODEL1 
The annals of applied statistics  2008;2(1):386-407.
Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21–29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.
doi:10.1214/07-AOAS132
PMCID: PMC2601643  PMID: 19079758
Clinical trial; discrete failure time model; missing data; potential outcomes; principal stratification; surrogate marker
3.  Statistical identifiability and the surrogate endpoint problem, with application to vaccine trials 
Biometrics  2010;66(4):1153-1161.
Summary
Given a randomized treatment Z, a clinical outcome Y, and a biomarker S measured some fixed time after Z is administered, we may be interested in addressing the surrogate endpoint problem by evaluating whether S can be used to reliably predict the effect of Z on Y. Several recent proposals for the statistical evaluation of surrogate value have been based on the framework of principal stratification. In this paper, we consider two principal stratification estimands: joint risks and marginal risks. Joint risks measure causal associations of treatment effects on S and Y, providing insight into the surrogate value of the biomarker, but are not statistically identifiable from vaccine trial data. While marginal risks do not measure causal associations of treatment effects, they nevertheless provide guidance for future research, and we describe a data collection scheme and assumptions under which the marginal risks are statistically identifiable. We show how different sets of assumptions affect the identifiability of these estimands; in particular, we depart from previous work by considering the consequences of relaxing the assumption of no individual treatment effects on Y before S is measured. Based on algebraic relationships between joint and marginal risks, we propose a sensitivity analysis approach for assessment of surrogate value, and show that in many cases the surrogate value of a biomarker may be hard to establish, even when the sample size is large.
doi:10.1111/j.1541-0420.2009.01380.x
PMCID: PMC3597127  PMID: 20105158
Estimated likelihood; Identifiability; Principal stratification; Sensitivity analysis; Surrogate endpoint; Vaccine trials
4.  Causal Vaccine Effects on Binary Postinfection Outcomes 
The effects of vaccine on postinfection outcomes, such as disease, death, and secondary transmission to others, are important scientific and public health aspects of prophylactic vaccination. As a result, evaluation of many vaccine effects condition on being infected. Conditioning on an event that occurs posttreatment (in our case, infection subsequent to assignment to vaccine or control) can result in selection bias. Moreover, because the set of individuals who would become infected if vaccinated is likely not identical to the set of those who would become infected if given control, comparisons that condition on infection do not have a causal interpretation. In this article we consider identifiability and estimation of causal vaccine effects on binary postinfection outcomes. Using the principal stratification framework, we define a postinfection causal vaccine efficacy estimand in individuals who would be infected regardless of treatment assignment. The estimand is shown to be not identifiable under the standard assumptions of the stable unit treatment value, monotonicity, and independence of treatment assignment. Thus selection models are proposed that identify the causal estimand. Closed-form maximum likelihood estimators (MLEs) are then derived under these models, including those assuming maximum possible levels of positive and negative selection bias. These results show the relations between the MLE of the causal estimand and two commonly used estimators for vaccine effects on postinfection outcomes. For example, the usual intent-to-treat estimator is shown to be an upper bound on the postinfection causal vaccine effect provided that the magnitude of protection against infection is not too large. The methods are used to evaluate postinfection vaccine effects in a clinical trial of a rotavirus vaccine candidate and in a field study of a pertussis vaccine. Our results show that pertussis vaccination has a significant causal effect in reducing disease severity.
doi:10.1198/016214505000000970
PMCID: PMC2603579  PMID: 19096723
Causal inference; Infectious disease; Maximum likelihood; Principal stratification; Sensitivity analysis
5.  Evaluating Candidate Principal Surrogate Endpoints 
Biometrics  2008;64(4):1146-1154.
Summary
Frangakis and Rubin (2002, Biometrics 58, 21–29) proposed a new definition of a surrogate endpoint (a “principal” surrogate) based on causal effects. We introduce an estimand for evaluating a principal surrogate, the causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. Although the CEP surface is not identifiable due to missing potential outcomes, it can be identified by incorporating a baseline covariate(s) that predicts the biomarker. Given case–cohort sampling of such a baseline predictor and the biomarker in a large blinded randomized clinical trial, we develop an estimated likelihood method for estimating the CEP surface. This estimation assesses the “surrogate value” of the biomarker for reliably predicting clinical treatment effects for the same or similar setting as the trial. A CEP surface plot provides a way to compare the surrogate value of multiple biomarkers. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection.
doi:10.1111/j.1541-0420.2008.01014.x
PMCID: PMC2726718  PMID: 18363776
Case cohort; Causal inference; Clinical trial; HIV vaccine; Postrandomization selection bias; Structural model; Prentice criteria; Principal stratification
6.  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.
doi:10.1186/1742-7622-11-14
PMCID: PMC4171402  PMID: 25342953
Surrogate endpoint; Principal stratification; Causal inference; Statistical identifiability
7.  Causal Inference for Vaccine Effects on Infectiousness 
The International Journal of Biostatistics  2012;8(2):10.2202/1557-4679.1354 /j/ijb.2012.8.issue-2/1557-4679.1354/1557-4679.1354.xml.
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.
doi:10.2202/1557-4679.1354
PMCID: PMC3348179  PMID: 22499732
causal inference; principal stratification; interference; infectious disease; vaccine
8.  Sensitivity Analysis of Per-Protocol Time-to-Event Treatment Efficacy in Randomized Clinical Trials 
Journal of the American Statistical Association  2013;108(503):10.1080/01621459.2013.786649.
Summary
Assessing per-protocol treatment effcacy on a time-to-event endpoint is a common objective of randomized clinical trials. The typical analysis uses the same method employed for the intention-to-treat analysis (e.g., standard survival analysis) applied to the subgroup meeting protocol adherence criteria. However, due to potential post-randomization selection bias, this analysis may mislead about treatment efficacy. Moreover, while there is extensive literature on methods for assessing causal treatment effects in compliers, these methods do not apply to a common class of trials where a) the primary objective compares survival curves, b) it is inconceivable to assign participants to be adherent and event-free before adherence is measured, and c) the exclusion restriction assumption fails to hold. HIV vaccine efficacy trials including the recent RV144 trial exemplify this class, because many primary endpoints (e.g., HIV infections) occur before adherence is measured, and nonadherent subjects who receive some of the planned immunizations may be partially protected. Therefore, we develop methods for assessing per-protocol treatment efficacy for this problem class, considering three causal estimands of interest. Because these estimands are not identifiable from the observable data, we develop nonparametric bounds and semiparametric sensitivity analysis methods that yield estimated ignorance and uncertainty intervals. The methods are applied to RV144.
doi:10.1080/01621459.2013.786649
PMCID: PMC3811958  PMID: 24187408
As-treated; Bounds; Causal inference; Exclusion restriction; Ignorance region; Intention to treat; Principal stratification; Selection bias; Survival analysis
9.  Partially hidden Markov model for time-varying principal stratification in HIV prevention trials 
It is frequently of interest to estimate the intervention effect that adjusts for post-randomization variables in clinical trials. In the recently completed HPTN 035 trial, there is differential condom use between the three microbicide gel arms and the No Gel control arm, so that intention to treat (ITT) analyses only assess the net treatment effect that includes the indirect treatment effect mediated through differential condom use. Various statistical methods in causal inference have been developed to adjust for post-randomization variables. We extend the principal stratification framework to time-varying behavioral variables in HIV prevention trials with a time-to-event endpoint, using a partially hidden Markov model (pHMM). We formulate the causal estimand of interest, establish assumptions that enable identifiability of the causal parameters, and develop maximum likelihood methods for estimation. Application of our model on the HPTN 035 trial reveals an interesting pattern of prevention effectiveness among different condom-use principal strata.
doi:10.1080/01621459.2011.643743
PMCID: PMC3649016  PMID: 23667279
microbicide; causal inference; posttreatment variables; direct effect
10.  Principal Stratification and Attribution Prohibition: Good Ideas Taken Too Far 
Pearl’s article provides a useful springboard for discussing further the benefits and drawbacks of principal stratification and the associated discomfort with attributing effects to post-treatment variables. The basic insights of the approach are important: pay close attention to modification of treatment effects by variables not observable before treatment decisions are made, and be careful in attributing effects to variables when counterfactuals are ill-defined. These insights have often been taken too far in many areas of application of the approach, including instrumental variables, censoring by death, and surrogate outcomes. A novel finding is that the usual principal stratification estimand in the setting of censoring by death is by itself of little practical value in estimating intervention effects.
doi:10.2202/1557-4679.1367
PMCID: PMC3204670  PMID: 22049269
principal stratification; causal inference
11.  Accommodating Missingness When Assessing Surrogacy Via Principal Stratification 
Clinical trials (London, England)  2013;10(3):363-377.
Background
When an outcome of interest in a clinical trial is late-occurring or difficult to obtain, surrogate markers can extract information about the effect of the treatment on the outcome of interest. Understanding associations between the causal effect of treatment on the outcome and the causal effect of treatment on the surrogate is critical to understanding the value of a surrogate from a clinical perspective.
Purpose
Traditional regression approaches to determine the proportion of the treatment effect explained by surrogate markers suffer from several shortcomings: they can be unstable, and can lie outside of the 0–1 range. Further, they do not account for the fact that surrogate measures are obtained post-randomization, and thus the surrogate-outcome relationship may be subject to unmeasured confounding. Methods to avoid these problem are of key importance.
Methods
Frangakis C, Rubin DM. Principal stratification in causal inference. Biometrics 2002; 58:21–9 suggested assessing the causal effect of treatment within pre-randomization “principal strata” defined by the counterfactual joint distribution of the surrogate marker under the different treatment arms, with the proportion of the overall outcome causal effect attributable to subjects for whom the treatment affects the proposed surrogate as the key measure of interest. Li Y, Taylor JMG, Elliott MR. Bayesian approach to surrogacy assessment using principal stratification in clinical trials. Biometrics 2010; 66:523–31 developed this “principal surrogacy” approach for dichotomous markers and outcomes, utilizing Bayesian methods that accommodated non-identifiability in the model parameters. Because the surrogate marker is typically observed early, outcome data is often missing. Here we extend Li, Taylor, and Elliott to accommodate missing data in the observable final outcome under ignorable and non-ignorable settings. We also allow for the possibility that missingness has a counterfactual component, a feature that previous literature has not addressed.
Results
We apply the proposed methods to a trial of glaucoma control comparing surgery versus medication, where intraocular pressure (IOP) control at 12 months is a surrogate for IOP control at 96 months. We also conduct a series of simulations to consider the impacts of non-ignorability, as well as sensitivity to priors and the ability of the Decision Information Criterion to choose the correct model when parameters are not fully identified.
Limitations
Because model parameters cannot be fully identified from data, informative priors can introduce non-trivial bias in moderate sample size settings, while more non-informative priors can yield wide credible intervals.
Conclusions
Assessing the linkage between causal effects of treatment on a surrogate marker and causal effects of a treatment on an outcome is important to understanding the value of a marker. These causal effects are not fully identifiable: hence we explore the sensitivity and identifiability aspects of these models and show that relatively weak assumptions can still yield meaningful results.
doi:10.1177/1740774513479522
PMCID: PMC4096330  PMID: 23553326
Causal Inference; Surrogate Marker; Bayesian Analysis; dentifiability; Non-response; Counterfactual
12.  Estimating Causal Effects in Trials Involving Multi-Treatment Arms Subject to Non-compliance: A Bayesian framework 
Summary
Data analysis for randomized trials including multi-treatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multi-treatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect (CACE) (Angrist et al. 1996), which is defined as the treatment effect for subjects who would comply regardless of the assigned treatment. Following the idea of principal stratification (Frangakis & Rubin 2002), we define principal compliance (Little et al. 2009) in trials with three treatment arms, extend CACE and define causal estimands of interest in this setting. In addition, we discuss structural assumptions needed for estimation of causal effects and the identifiability problem inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method of moments approach proposed by Cheng & Small (2006) using a hypothetical data set, and further illustrate our approach with an application to a behavioral intervention study (Janevic et al. 2003).
doi:10.1111/j.1467-9876.2009.00709.x
PMCID: PMC3104736  PMID: 21637737
Causal Inference; Complier Average Causal Effect; Multi-arm Trials; Non-compliance; Principal Compliance; Principal Stratification
13.  Design and Estimation for Evaluating Principal Surrogate Markers in Vaccine Trials 
Biometrics  2013;69(2):301-309.
Summary
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 paper 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 counterintuitive 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.
doi:10.1111/biom.12014
PMCID: PMC3713795  PMID: 23409839
Closeout placebo vaccination; Estimated likelihood; Immune correlate; Principal surrogate; Pseudo-score; Two-phase sampling design
14.  Is blood pressure reduction a valid surrogate endpoint for stroke prevention? an analysis incorporating a systematic review of randomised controlled trials, a by-trial weighted errors-in-variables regression, the surrogate threshold effect (STE) and the biomarker-surrogacy (BioSurrogate) evaluation schema (BSES) 
Background
Blood pressure is considered to be a leading example of a valid surrogate endpoint. The aims of this study were to (i) formally evaluate systolic and diastolic blood pressure reduction as a surrogate endpoint for stroke prevention and (ii) determine what blood pressure reduction would predict a stroke benefit.
Methods
We identified randomised trials of at least six months duration comparing any pharmacologic anti-hypertensive treatment to placebo or no treatment, and reporting baseline blood pressure, on-trial blood pressure, and fatal and non-fatal stroke. Trials with fewer than five strokes in at least one arm were excluded. Errors-in-variables weighted least squares regression modelled the reduction in stroke as a function of systolic blood pressure reduction and diastolic blood pressure reduction respectively. The lower 95% prediction band was used to determine the minimum systolic blood pressure and diastolic blood pressure difference, the surrogate threshold effect (STE), below which there would be no predicted stroke benefit. The STE was used to generate the surrogate threshold effect proportion (STEP), a surrogacy metric, which with the R-squared trial-level association was used to evaluate blood pressure as a surrogate endpoint for stroke using the Biomarker-Surrogacy Evaluation Schema (BSES3).
Results
In 18 qualifying trials representing all pharmacologic drug classes of antihypertensives, assuming a reliability coefficient of 0.9, the surrogate threshold effect for a stroke benefit was 7.1 mmHg for systolic blood pressure and 2.4 mmHg for diastolic blood pressure. The trial-level association was 0.41 and 0.64 and the STEP was 66% and 78% for systolic and diastolic blood pressure respectively. The STE and STEP were more robust to measurement error in the independent variable than R-squared trial-level associations. Using the BSES3, assuming a reliability coefficient of 0.9, systolic blood pressure was a B + grade and diastolic blood pressure was an A grade surrogate endpoint for stroke prevention. In comparison, using the same stroke data sets, no STEs could be estimated for cardiovascular (CV) mortality or all-cause mortality reduction, although the STE for CV mortality approached 25 mmHg for systolic blood pressure.
Conclusions
In this report we provide the first surrogate threshold effect (STE) values for systolic and diastolic blood pressure. We suggest the STEs have face and content validity, evidenced by the inclusivity of trial populations, subject populations and pharmacologic intervention populations in their calculation. We propose that the STE and STEP metrics offer another method of evaluating the evidence supporting surrogate endpoints. We demonstrate how surrogacy evaluations are strengthened if formally evaluated within specific-context evaluation frameworks using the Biomarker- Surrogate Evaluation Schema (BSES3), and we discuss the implications of our evaluation of blood pressure on other biomarkers and patient-reported instruments in relation to surrogacy metrics and trial design.
doi:10.1186/1471-2288-12-27
PMCID: PMC3388460  PMID: 22409774
Blood pressure; Stroke; Surrogate Endpoint; Biomarker
15.  Clarifying the Role of Principal Stratification in the Paired Availability Design 
The paired availability design for historical controls postulated four classes corresponding to the treatment (old or new) a participant would receive if arrival occurred during either of two time periods associated with different availabilities of treatment. These classes were later extended to other settings and called principal strata. Judea Pearl asks if principal stratification is a goal or a tool and lists four interpretations of principal stratification. In the case of the paired availability design, principal stratification is a tool that falls squarely into Pearl's interpretation of principal stratification as “an approximation to research questions concerning population averages.” We describe the paired availability design and the important role played by principal stratification in estimating the effect of receipt of treatment in a population using data on changes in availability of treatment. We discuss the assumptions and their plausibility. We also introduce the extrapolated estimate to make the generalizability assumption more plausible. By showing why the assumptions are plausible we show why the paired availability design, which includes principal stratification as a key component, is useful for estimating the effect of receipt of treatment in a population. Thus, for our application, we answer Pearl's challenge to clearly demonstrate the value of principal stratification.
doi:10.2202/1557-4679.1338
PMCID: PMC3114955  PMID: 21686085
principal stratification; causal inference; paired availability design
16.  Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials 
Biostatistics (Oxford, England)  2011;12(3):478-492.
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.
doi:10.1093/biostatistics/kxq082
PMCID: PMC3114655  PMID: 21252079
Bayesian estimation; Counterfactual model; Identifiability; Multiple trials; Principal stratification; Surrogate marker
17.  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.
doi:10.2202/1557-4679.1329
PMCID: PMC3154088  PMID: 21841939
causal inference; mediation; non-compliance; potential outcomes; principal stratification; surrogates
18.  A Bayesian Approach to Improved Estimation of Causal Effect Predictiveness for a Principal Surrogate Endpoint 
Biometrics  2012;68(3):10.1111/j.1541-0420.2011.01736.x.
Summary
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.
doi:10.1111/j.1541-0420.2011.01736.x
PMCID: PMC3860118  PMID: 22348277
Biomarker; Causal effect predictiveness; principal stratification; surrogate endpoint
19.  Evaluating a surrogate endpoint at three levels, with application to vaccine development 
Statistics in medicine  2008;27(23):4758-4778.
SUMMARY
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.
doi:10.1002/sim.3122
PMCID: PMC2646675  PMID: 17979212
clinical trial; counterfactual; immune correlate; meta-analysis; potential outcomes; principal surrogate; statistical surrogate
20.  Invited Commentary: Decomposing with a Lot of Supposing 
American Journal of Epidemiology  2010;172(12):1349-1351.
In this issue of the Journal, VanderWeele and Vansteelandt (Am J Epidemiol. 2010;172(12):1339–1348) provide simple formulae for estimation of direct and indirect effects using standard logistic regression when the exposure and outcome are binary, the mediator is continuous, and the odds ratio is the chosen effect measure. They also provide concisely stated lists of assumptions necessary for estimation of these effects, including various conditional independencies and homogeneity of exposure and mediator effects over covariate strata. They further suggest that this will allow effect decomposition in case-control studies if the sampling fractions and population outcome prevalence are known with certainty. In this invited commentary, the author argues that, in a well-designed case-control study in which the sampling fraction is known, it should not be necessary to rely on the odds ratio. The odds ratio has well-known deficiencies as a causal parameter, and its use severely complicates evaluation of confounding and effect homogeneity. Although VanderWeele and Vansteelandt propose that a rare disease assumption is not necessary for estimation of controlled direct effects using their approach, collapsibility concerns suggest otherwise when the goal is causal inference rather than merely measuring association. Moreover, their clear statement of assumptions necessary for the estimation of natural/pure effects suggests that these quantities will rarely be viable estimands in observational epidemiology.
doi:10.1093/aje/kwq329
PMCID: PMC3139971  PMID: 21036956
causal inference; conditional independence; confounding; decomposition; estimation; interaction; logistic regression; odds ratio
21.  Losartan and diabetic nephropathy: commentaries on the RENAAL study 
The RENAAL (Reduction of Endpoints in NIDDM with the Angiotensin II Antagonist Losartan) study is a multinational, double-blind, randomized, placebo controlled trial which was recently published. It was aimed to evaluate the effect of the angiotensin receptor blocker losartan in patients with diabetic nephropathy. The primary efficacy measure was the time to the first event of the composite end point of a doubling of serum creatinine, end-stage renal disease, or death. The conclusion was that losartan led to significant improvement in renal outcomes, that was beyond that attributable to blood pressure control in patients with type 2 diabetes and nephropathy.
The perusal of the report raises concern, regarding to both the patient population as well as the outcome measures. At randomization, the placebo group included more patients with angina, myocardial infarction and lipid disorders than the losartan group. Information on glucose metabolism was disregarded, and data on antihyperglycemic therapy – which may have undesirable influences on cardiac performance – were not included in a multivariate analysis. In addition, only data on first hospitalization were reported, whilst information on total specific-cause hospitalizations was disregarded, thus potentially masking further unfavorable events. Furthermore, creatinine seems not to be a reliable surrogate end point. Based on its mechanism of action, losartan may possess favorable renoprotective properties. However, due to the methodological flaws and the incomplete data in the RENAAL study, the question of the effectiveness and safety of this drug in diabetic nephropathy remains yet unanswered.
doi:10.1186/1475-2840-1-2
PMCID: PMC116616  PMID: 12119058
Angiotensin receptor blockers; Clinical trials; Diabetes mellitus; Losartan; Nephropathy; RENAAL study
22.  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.
PMCID: PMC3502884  PMID: 23181167
HIV vaccine efficacy clinical trial; immune correlate of protection; one-way crossover design; surrogate endpoint for HIV infection; two-phase sampling
23.  Effects of Community-Wide Vaccination with PCV-7 on Pneumococcal Nasopharyngeal Carriage in The Gambia: A Cluster-Randomized Trial 
PLoS Medicine  2011;8(10):e1001107.
In a cluster-randomized trial conducted in Gambian villages, Anna Roca and colleagues find that vaccination of children with pneumococcal conjugate vaccines reduced vaccine-type pneumococcal carriage even among nonvaccinated older children and adults.
Background
Introduction of pneumococcal conjugate vaccines (PCVs) of limited valency is justified in Africa by the high burden of pneumococcal disease. Long-term beneficial effects of PCVs may be countered by serotype replacement. We aimed to determine the impact of PCV-7 vaccination on pneumococcal carriage in rural Gambia.
Methods and Findings
A cluster-randomized (by village) trial of the impact of PCV-7 on pneumococcal nasopharyngeal carriage was conducted in 21 Gambian villages between December 2003 to June 2008 (5,441 inhabitants in 2006). Analysis was complemented with data obtained before vaccination. Because efficacy of PCV-9 in young Gambian children had been shown, it was considered unethical not to give PCV-7 to young children in all of the study villages. PCV-7 was given to children below 30 mo of age and to those born during the trial in all study villages. Villages were randomized (older children and adults) to receive one dose of PCV-7 (11 vaccinated villages) or meningococcal serogroup C conjugate vaccine (10 control villages). Cross-sectional surveys (CSSs) to collect nasopharyngeal swabs were conducted before vaccination (2,094 samples in the baseline CSS), and 4–6, 12, and 22 mo after vaccination (1,168, 1,210, and 446 samples in CSS-1, -2, and -3, respectively).
A time trend analysis showed a marked fall in the prevalence of vaccine-type pneumococcal carriage in all age groups following vaccination (from 23.7% and 26.8% in the baseline CSS to 7.1% and 8.5% in CSS-1, in vaccinated and control villages, respectively). The prevalence of vaccine-type pneumococcal carriage was lower in vaccinated than in control villages among older children (5 y to <15 y of age) and adults (≥15 y of age) at CSS-2 (odds ratio [OR] = 0.15 [95% CI 0.04–0.57] and OR = 0.32 [95% CI 0.10–0.98], respectively) and at CSS-3 (OR = 0.37 [95% CI 0.15–0.90] for older children, and 0% versus 7.6% for adults in vaccinated and control villages, respectively). Differences in the prevalence of non-vaccine-type pneumococcal carriage between vaccinated and control villages were small.
Conclusions
Vaccination of Gambian children reduced vaccine-type pneumococcal carriage across all age groups, indicating a “herd effect” in non-vaccinated older children and adults. No significant serotype replacement was detected.
Please see later in the article for the Editors' Summary
Editors' Summary
Background
The prevention of pneumococcal disease, especially in children in developing countries, is a major international public health priority. Despite all the international attention on the UN's Millennium Development Goal 4—to reduce deaths in children under five years by two-thirds between 1990 and 2015—pneumonia, sepsis, and meningitis together compose more than 25% of the 10 million deaths occurring in children less than five years of age. Streptococcus pneumoniae is a leading bacterial cause of these diseases, and the World Health Organization estimates that approximately 800,000 children die each year of invasive pneumococcal disease.
Pneumococcal conjugate vaccines are currently available and protect against the serotypes that most commonly cause invasive pneumococcal disease in young children in North America and Europe. Such vaccines have been highly successful in reducing the incidence of invasive pneumococcal disease in both vaccinated children and in the non-vaccinated older population by reducing nasopharyngeal carriage (presence of pneumococcal bacteria in the back of the nose) in vaccinated infants, resulting in decreased transmission to contacts—the so-called herd effect. However, few countries with the highest burden of invasive pneumococcal disease, especially those in sub-Saharan Africa, have introduced the vaccine into their national immunization programs.
Why Was This Study Done?
The features of pneumococcal nasopharyngeal carriage and invasive pneumococcal disease in sub-Saharan Africa are different than in other regions. Therefore, careful evaluation of the immune effects of vaccination requires long-term, longitudinal studies. As an alternative to such long-term observational studies, and to anticipate the potential long-term effects of the introduction of pneumococcal conjugate vaccination in sub-Saharan Africa, the researchers conducted a cluster-randomized (by village) trial in The Gambia in which the whole populations of some villages were immunized with the vaccine PCV-7, and other villages received a control.
What Did the Researchers Do and Find?
With full consent from communities, the researchers randomized 21 similar villages in a rural region of western Gambia to receive pneumococcal conjugate vaccine or a control—meningococcal serogroup C conjugated vaccine, which is unlikely to affect pneumococcal carriage rates. For ethical reasons, the researchers only randomized residents aged over 30 months—all young infants received PCV-7, as a similar vaccine had already been shown to be effective in young infants. Before immunization began, the researchers took nasopharyngeal swabs from a random selection of village residents to determine the baseline pneumococcal carriage rates of both the serotypes of pneumococci covered by the vaccine (vaccine types, VTs) and the serotypes of pneumococci not covered in the vaccine (non-vaccine types, NVTs). The researchers then took nasopharyngeal swabs from a random sample of 1,200 of village residents in both groups of villages in cross-sectional surveys at 4–6, 12, and 22 months after vaccination. Villagers and laboratory staff were unaware of which vaccine was which (that is, they were blinded).
Before immunization, the overall prevalence of pneumococcal carriage in both groups was high, at 71.1%, and decreased with age. After vaccination, the overall prevalence of pneumococcal carriage in all three surveys was similar between vaccinated and control villages, showing a marked fall. However, the prevalence of carriage of VT pneumococci was significantly lower in vaccinated than in control villages in all surveys for all age groups. The prevalence of carriage of NVT pneumococci was similar in vaccinated and in control villages, except for a slightly higher prevalence of NVT pneumococci among vaccinated communities in adults at 4–6 months after vaccination. The researchers also found that the overall prevalence of pneumococcal carriage fell markedly after vaccination and reached minimum levels at 12 months in both study arms and in all age groups.
What Do These Findings Mean?
These findings show that vaccination of young Gambian children reduced carriage of VT pneumococci in vaccinated children but also in vaccinated and non-vaccinated older children and adults, revealing a potential herd effect from vaccination of young children. Furthermore, the immunological pressure induced by vaccinating whole communities did not lead to a community-wide increase in carriage of NVT pneumococci during a two-year period after vaccination. The researchers plan to conduct more long-term follow-up studies to determine nasopharyngeal carriage in these communities.
Additional Information
Please access these websites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.1001107.
The World Health Organization has information about pneumococcus
The US Centers for Disease Control and Prevention provides information about pneumococcal conjugate vaccination
doi:10.1371/journal.pmed.1001107
PMCID: PMC3196470  PMID: 22028630
24.  Tumor Response and Progression-Free Survival as Potential Surrogate Endpoints for Overall Survival in Extensive-Stage Small Cell Lung Cancer (ES-SCLC): Findings Based on North Central Cancer Treatment Group (NCCTG) Trials 
Cancer  2010;117(6):1262-1271.
Purpose
We investigated the putative surrogate endpoints (PSEs) of best response (BR), complete response (CR), confirmed response (CoR), and progression-free survival (PFS) for associations with Overall Survival (OS), and as possible surrogate endpoints for OS.
Methods
Individual patient (pt) data from 870 untreated ES-SCLC pts participating in 6 single-arm (274 pts) and 3 randomized trials (596 pts) were pooled. Patient-level associations between PSEs and OS were assessed by Cox models using landmark analyses. Trial-level surrogacy of PSEs assessed by the association of treatment effects on OS and individual PSEs. Trial-level surrogacy measures included: R2 from weighted least squares regression model (WLS R2), Spearman's correlation coefficient, and R2 from bivariate survival model (Copula R2).
Results
Median OS and PFS were 9.6 (95% CI: 9.1-10.0) and 5.5 (95% CI: 5.2-5.9) months, respectively; BR, CR, and CoR rates were 44%, 22%, and 34%, respectively. Patient-level associations showed that PFS status at 4 months was a strong predictor of subsequent survival (HR=0.42 (95% CI: 0.35-0.51); concordance index=0.63; p<0.01), with 6-month PFS being the strongest (HR=0.41 (95% CI: 0.35-0.49); concordance index=0.66; p<0.01). At the trial-level, PFS showed the highest level of surrogacy for OS (WLS R2=0.79; Copula R2=0.80), explaining 79% of the variance in OS. Tumor response endpoints showed lower surrogacy levels (WLS R2≤0.48).
Conclusion
PFS was strongly associated with OS at both the patient and trial-level. PFS also shows promise as a potential surrogate for OS, but further validation is needed using data from a larger number of randomized phase III trials.
doi:10.1002/cncr.25526
PMCID: PMC3025267  PMID: 20960500
extensive-stage small cell lung cancer; surrogate endpoints; pooled analysis; progression-free survival; tumor response
25.  Surrogate endpoints for overall survival in digestive oncology trials: which candidates? A questionnaires survey among clinicians and methodologists 
BMC Cancer  2010;10:277.
Background
Overall survival (OS) is the gold standard for the demonstration of a clinical benefit in cancer trials. Replacement of OS by a surrogate endpoint allows to reduce trial duration. To date, few surrogate endpoints have been validated in digestive oncology. The aim of this study was to draw up an ordered list of potential surrogate endpoints for OS in digestive cancer trials, by way of a survey among clinicians and methodologists. Secondary objective was to obtain their opinion on surrogacy and quality of life (QoL).
Methods
In 2007 and 2008, self administered sequential questionnaires were sent to a panel of French clinicians and methodologists involved in the conduct of cancer clinical trials. In the first questionnaire, panellists were asked to choose the most important characteristics defining a surrogate among six proposals, to give advantages and drawbacks of the surrogates, and to answer questions about their validation and use. Then they had to suggest potential surrogate endpoints for OS in each of the following tumour sites: oesophagus, stomach, liver, pancreas, biliary tract, lymphoma, colon, rectum, and anus. They finally gave their opinion on QoL as surrogate endpoint. In the second questionnaire, they had to classify the previously proposed candidate surrogates from the most (position #1) to the least relevant in their opinion.
Frequency at which the endpoints were chosen as first, second or third most relevant surrogates was calculated and served as final ranking.
Results
Response rate was 30% (24/80) in the first round and 20% (16/80) in the second one. Participants highlighted key points concerning surrogacy. In particular, they reminded that a surrogate endpoint is expected to predict clinical benefit in a well-defined therapeutic situation. Half of them thought it was not relevant to study QoL as surrogate for OS.
DFS, in the neoadjuvant settings or early stages, and PFS, in the non operable or metastatic settings, were ranked first, with a frequency of more than 69% in 20 out of 22 settings. PFS was proposed in association with QoL in metastatic primary liver and stomach cancers (both 81%). This composite endpoint was ranked second in metastatic oesophageal (69%), colorectal (56%) and anal (56%) cancers, whereas QoL alone was also suggested in most metastatic situations.
Other endpoints frequently suggested were R0 resection in the neoadjuvant settings (oesophagus (69%), stomach (56%), pancreas (75%) and biliary tract (63%)) and response. An unexpected endpoint was metastatic PFS in non operable oesophageal (31%) and pancreatic (44%) cancers. Quality and results of surgical procedures like sphincter preservation were also cited as eligible surrogate endpoints in rectal (19%) and anal (50% in case of localized disease) cancers. Except for alpha-FP kinetic in hepatocellular carcinoma (13%) and CA19-9 decline (6%) in pancreas, few endpoints based on biological or tumour markers were proposed.
Conclusion
The overall results should help prioritise the endpoints to be statistically evaluated as surrogate for OS, so that trialists and clinicians can rely on endpoints that ensure relevant clinical benefit to the patient.
doi:10.1186/1471-2407-10-277
PMCID: PMC2904280  PMID: 20537166

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