Sensitivity analysis for the assessment of causal vaccine effects on viral load in HIV vaccine trials

Vaccines with limited ability to prevent HIV infection may positively impact the HIV/AIDS pandemic by preventing secondary transmission and disease in vaccine recipients who become infected. To evaluate the impact of vaccination on secondary transmission and disease, efficacy trials assess vaccine effects on HIV viral load and other surrogate endpoints measured after infection. A standard test that compares the distribution of viral load between the infected subgroups of vaccine and placebo recipients does not assess a causal effect of vaccine, because the comparison groups are selected after randomization. To address this problem, we formulate clinically relevant causal estimands using the principal stratification framework developed by Frangakis and Rubin (2002, Biometrics 58, 21-29), and propose a class of logistic selection bias models whose members identify the estimands. Given a selection model in the class, procedures are developed for testing and estimation of the causal effect of vaccination on viral load in the principal stratum of subjects who would be infected regardless of randomization assignment. We show how the procedures can be used for a sensitivity analysis that quantifies how the causal effect of vaccination varies with the presumed magnitude of selection bias.     

Principal stratification designs to estimate input data missing due to death

We consider studies of cohorts of individuals after a critical event, such as an injury, with the following characteristics. First, the studies are designed to measure "input" variables, which describe the period before the critical event, and to characterize the distribution of the input variables in the cohort. Second, the studies are designed to measure "output" variables, primarily mortality after the critical event, and to characterize the predictive (conditional) distribution of mortality given the input variables in the cohort. Such studies often possess the complication that the input data are missing for those who die shortly after the critical event because the data collection takes place after the event. Standard methods of dealing with the missing inputs, such as imputation or weighting methods based on an assumption of ignorable missingness, are known to be generally invalid when the missingness of inputs is nonignorable, that is, when the distribution of the inputs is different between those who die and those who live. To address this issue, we propose a novel design that obtains and uses information on an additional key variable-a treatment or externally controlled variable, which if set at its "effective" level, could have prevented the death of those who died. We show that the new design can be used to draw valid inferences for the marginal distribution of inputs in the entire cohort, and for the conditional distribution of mortality given the inputs, also in the entire cohort, even under nonignorable missingness. The crucial framework that we use is principal stratification based on the potential outcomes, here mortality under both levels of treatment. We also show using illustrative preliminary injury data that our approach can reveal results that are more reasonable than the results of standard methods, in relatively dramatic ways. Thus, our approach suggests that the routine collection of data on variables that could be used as possible treatments in such studies of inputs and mortality should become common.     

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

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.     

Sensitivity analyses comparing outcomes only existing in a subset selected post-randomization, conditional on covariates, with application to HIV vaccine trials

In many experiments, researchers would like to compare between treatments and outcome that only exists in a subset of participants selected after randomization. For example, in preventive HIV vaccine efficacy trials it is of interest to determine whether randomization to vaccine causes lower HIV viral load, a quantity that only exists in participants who acquire HIV. To make a causal comparison and account for potential selection bias we propose a sensitivity analysis following the principal stratification framework set forth by Frangakis and Rubin (2002, Biometrics58, 21-29). Our goal is to assess the average causal effect of treatment assignment on viral load at a given baseline covariate level in the always infected principal stratum (those who would have been infected whether they had been assigned to vaccine or placebo). We assume stable unit treatment values (SUTVA), randomization, and that subjects randomized to the vaccine arm who became infected would also have become infected if randomized to the placebo arm (monotonicity). It is not known which of those subjects infected in the placebo arm are in the always infected principal stratum, but this can be modeled conditional on covariates, the observed viral load, and a specified sensitivity parameter. Under parametric regression models for viral load, we obtain maximum likelihood estimates of the average causal effect conditional on covariates and the sensitivity parameter. We apply our methods to the world's first phase III HIV vaccine trial.     

Multiple imputation methods for treatment noncompliance and nonresponse in randomized clinical trials

Summary .  Randomized clinical trials are a powerful tool for investigating causal treatment effects, but in human trials there are oftentimes problems of noncompliance which standard analyses, such as the intention-to-treat or as-treated analysis, either ignore or incorporate in such a way that the resulting estimand is no longer a causal effect. One alternative to these analyses is the complier average causal effect (CACE) which estimates the average causal treatment effect among a subpopulation that would comply under any treatment assigned. We focus on the setting of a randomized clinical trial with crossover treatment noncompliance (e.g., control subjects could receive the intervention and intervention subjects could receive the control) and outcome nonresponse. In this article, we develop estimators for the CACE using multiple imputation methods, which have been successfully applied to a wide variety of missing data problems, but have not yet been applied to the potential outcomes setting of causal inference. Using simulated data we investigate the finite sample properties of these estimators as well as of competing procedures in a simple setting. Finally we illustrate our methods using a real randomized encouragement design study on the effectiveness of the influenza vaccine.     

Principal stratification in causal inference

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 tinder 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 forrmulate estimands based on principal stratification and principal causal effects and show their superiority.     

Sensitivity analyses comparing time-to-event outcomes only existing in a subset selected postrandomization and relaxing monotonicity

In randomized studies researchers may be interested in the effect of treatment assignment on a time-to-event outcome that only exists in a subset selected after randomization. For example, in preventative HIV vaccine trials, it is of interest to determine whether randomization to vaccine affects the time from infection diagnosis until initiation of antiretroviral therapy. Earlier work assessed the effect of treatment on outcome among the principal stratum of individuals who would have been selected regardless of treatment assignment. These studies assumed monotonicity, that one of the principal strata was empty (e.g., every person infected in the vaccine arm would have been infected if randomized to placebo). Here, we present a sensitivity analysis approach for relaxing monotonicity with a time-to-event outcome. We also consider scenarios where selection is unknown for some subjects because of noninformative censoring (e.g., infection status k years after randomization is unknown for some because of staggered study entry). We illustrate our method using data from an HIV vaccine trial.     

Assessing Vaccine Effects in Repeated Low‐Dose Challenge Experiments

Summary Evaluation of HIV vaccine candidates in nonhuman primates (NHPs) is a critical step toward developing a successful vaccine to control the HIV pandemic. Historically, HIV vaccine regimens have been tested in NHPs by administering a single high dose of the challenge virus. More recently, evaluation of candidate HIV vaccines has entailed repeated low‐dose challenges, which more closely mimic typical exposure in natural transmission settings. In this article, we consider evaluation of the type and magnitude of vaccine efficacy from such experiments. Based on the principal stratification framework, we also address evaluation of potential immunological surrogate endpoints for infection.     

Identifiability and estimation of causal effects in randomized trials with noncompliance and completely nonignorable missing data

Summary .  In this article, we first study parameter identifiability in randomized clinical trials with noncompliance and missing outcomes. We show that under certain conditions the parameters of interest are identifiable even under different types of completely nonignorable missing data: that is, the missing mechanism depends on the outcome. We then derive their maximum likelihood and moment estimators and evaluate their finite-sample properties in simulation studies in terms of bias, efficiency, and robustness. Our sensitivity analysis shows that the assumed nonignorable missing-data model has an important impact on the estimated complier average causal effect (CACE) parameter. Our new method provides some new and useful alternative nonignorable missing-data models over the existing latent ignorable model, which guarantees parameter identifiability, for estimating the CACE in a randomized clinical trial with noncompliance and missing data.     

A comparison of methods for estimating the causal effect of a treatment in randomized clinical trials subject to noncompliance

Summary .  We consider the analysis of clinical trials that involve randomization to an active treatment ( T  = 1) or a control treatment ( T  = 0), when the active treatment is subject to all-or-nothing compliance. We compare three approaches to estimating treatment efficacy in this situation: as-treated analysis, per-protocol analysis, and instrumental variable (IV) estimation, where the treatment effect is estimated using the randomization indicator as an IV. Both model- and method-of-moment based IV estimators are considered. The assumptions underlying these estimators are assessed, standard errors and mean squared errors of the estimates are compared, and design implications of the three methods are examined. Extensions of the methods to include observed covariates are then discussed, emphasizing the role of compliance propensity methods and the contrasting role of covariates in these extensions. Methods are illustrated on data from the Women Take Pride study, an assessment of behavioral treatments for women with heart disease.     

A comparison of eight methods for the dual-endpoint evaluation of efficacy in a proof-of-concept HIV vaccine trial

To support the design of the world's first proof-of-concept (POC) efficacy trial of a cell-mediated immunity-based HIV vaccine, we evaluate eight methods for testing the composite null hypothesis of no-vaccine effect on either the incidence of HIV infection or the viral load set point among those infected, relative to placebo. The first two methods use a single test applied to the actual values or ranks of a burden-of-illness (BOI) outcome that combines the infection and viral load endpoints. The other six methods combine separate tests for the two endpoints using unweighted or weighted versions of the two-part z, Simes', and Fisher's methods. Based on extensive simulations that were used to design the landmark POC trial, the BOI methods are shown to have generally low power for rejecting the composite null hypothesis (and hence advancing the vaccine to a subsequent large-scale efficacy trial). The unweighted Simes' and Fisher's combination methods perform best overall. Importantly, this conclusion holds even after the test for the viral load component is adjusted for bias that can be introduced by conditioning on a postrandomization event (HIV infection). The adjustment is derived using a selection bias model based on the principal stratification framework of causal inference.     

Semiparametric methods for multiple exposure mismeasurement and a bivariate outcome in HIV vaccine trials

Exposure to infection information is important for estimating vaccine efficacy, but it is difficult to collect and prone to missingness and mismeasurement. We discuss study designs that collect detailed exposure information from only a small subset of participants while collecting crude exposure information from all participants and treat estimation of vaccine efficacy in the missing data/measurement error framework. We extend the discordant partner design for HIV vaccine trials of Golm, Halloran, and Longini (1998, Statistics in Medicine, 17, 2335-2352.) to the more complex augmented trial design of Longini, Datta, and Halloran (1996, Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 13, 440-447) and Datta, Halloran, and Longini (1998, Statistics in Medicine 17, 185-200). The model for this design includes three exposure covariates and both univariate and bivariate outcomes. We adapt recently developed semiparametric missing data methods of Reilly and Pepe (1995, Biometrika 82, 299 314), Carroll and Wand (1991, Journal of the Royal Statistical Society, Series B 53, 573-585), and Pepe and Fleming (1991, Journal of the American Statistical Association 86, 108-113) to the augmented vaccine trial design. We demonstrate with simulated HIV vaccine trial data the improvements in bias and efficiency when combining the different levels of exposure information to estimate vaccine efficacy for reducing both susceptibility and infectiousness. We show that the semiparametric methods estimate both efficacy parameters without bias when the good exposure information is either missing completely at random or missing at random. The pseudolikelihood method of Carroll and Wand (1991) and Pepe and Fleming (1991) was the more efficient of the two semiparametric methods.     

幽门螺杆菌疫苗诱导的免疫保护反应及临床试验研究进展

幽门螺杆菌(Helicobacter pylori,Hp)是一种微需氧、寄生于胃黏膜表面的革兰阴性致病菌,可导致各种不同的疾病,如慢性活动性胃炎、胃和十二指肠溃疡,甚至包括胃黏膜相关淋巴样组织(mucosa-associated lymphoid tissue,MALT)淋巴瘤和胃腺癌等恶性疾病。目前根除Hp主要依靠包括2种抗生素、铋剂和质子泵抑制剂(proton pumpinhibitors,PPI)在内的四联疗法。随着Hp耐药性的增强,研发Hp疫苗成为防治Hp感染的新途径。Hp疫苗能够诱导机体产生抗原特异性血清IgG和黏膜sIgA体液免疫反应以及抗原特异性CD4+T细胞免疫反应等的有效免疫保护反应。     

On estimation of the survivor average causal effect in observational studies when important confounders are missing due to death

Summary .  We focus on estimation of the causal effect of treatment on the functional status of individuals at a fixed point in time t * after they have experienced a catastrophic event, from observational data with the following features: (i) treatment is imposed shortly after the event and is nonrandomized, (ii) individuals who survive to t * are scheduled to be interviewed, (iii) there is interview nonresponse, (iv) individuals who die prior to t * are missing information on preevent confounders, and (v) medical records are abstracted on all individuals to obtain information on postevent, pretreatment confounding factors. To address the issue of survivor bias, we seek to estimate the survivor average causal effect (SACE), the effect of treatment on functional status among the cohort of individuals who would survive to t * regardless of whether or not assigned to treatment. To estimate this effect from observational data, we need to impose untestable assumptions, which depend on the collection of all confounding factors. Because preevent information is missing on those who die prior to t *, it is unlikely that these data are missing at random. We introduce a sensitivity analysis methodology to evaluate the robustness of SACE inferences to deviations from the missing at random assumption. We apply our methodology to the evaluation of the effect of trauma center care on vitality outcomes using data from the National Study on Costs and Outcomes of Trauma Care.     

A Bayesian analysis of colonic crypt structure and coordinated response to carcinogen exposure incorporating missing crypts

This paper is concerned with modeling the architecture of colonic crypts and the implications of this modeling for understanding possible coordinated response of carcinogen-induced DNA damage between various regions of the colon. The methods we develop to address these two issues are applied to a particular important example in colon carcinogenesis. We cast the problem as an unusual and not previously studied hierarchical mixed-effects model characterized by completely missing covariates in units at a structurally base level, except for some randomly selected units. Information concerning the missing covariates is available through certain known ordering constraints and surrogate measures. Our methods use Bayesian machinery. We exploit the biological structure of this problem to generate the missing covariates simultaneously and efficiently at the base levels, as opposed to the naive practice of generating units at the base levels one-at-a-time with Metropolis-Hastings steps. We apply our methods to show that different regions of the colon have different architectures, and to estimate an important but non-standard function that measures the interrelationship of DNA damage mechanisms in different regions of the colon.     

Impact of Time to Start Treatment Following Infection with Application to Initiating HAART in HIV-Positive Patients

Summary We estimate how the effect of antiretroviral treatment depends on the time from HIV-infection to initiation of treatment, using observational data. A major challenge in making inferences from such observational data arises from biases associated with the nonrandom assignment of treatment, for example bias induced by dependence of time of initiation on disease status. To address this concern, we develop a new class of Structural Nested Mean Models (SNMMs) to estimate the impact of time of initiation of treatment after infection on an outcome measured a fixed duration after initiation, compared to the effect of not initiating treatment. This leads to a SNMM that models the effect of multiple dosages of treatment on a time-dependent outcome, in contrast to most existing SNNMs, which focus on the effect of one dosage of treatment on an outcome measured at the end of the study. Our identifying assumption is that there are no unmeasured confounders. We illustrate our methods using the observational Acute Infection and Early Disease Research Program (AIEDRP) Core01 database on HIV. The current standard of care in HIV-infected patients is Highly Active Anti-Retroviral Treatment (HAART); however, the optimal time to start HAART has not yet been identified. The new class of SNNMs allows estimation of the dependence of the effect of 1 year of HAART on the time between estimated date of infection and treatment initiation, and on patient characteristics. Results of fitting this model imply that early use of HAART substantially improves immune reconstitution in the early and acute phase of HIV-infection.