Identifiability and Estimation of Causal Effects by Principal Stratification With Outcomes Truncated by Death

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

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

Identification and estimation of causal effects in the presence of confounded principal strata

Principal stratification has become a popular tool to address a broad class of causal inference questions, particularly in dealing with non-compliance and truncation by death problems. The causal effects within principal strata, which are determined by joint potential values of the intermediate variable, also known as the principal causal effects, are often of interest in these studies. The analysis of principal causal effects from observational studies mostly relies on the ignorability assumption of treatment assignment, which requires practitioners to accurately measure as many covariates as possible so that all potential sources of confounders are captured. However, in practice, collecting all potential confounding factors can be challenging and costly, rendering the ignorability assumption questionable. In this paper, we consider the identification and estimation of causal effects when treatment and principal stratification are confounded by unmeasured confounding. Specifically, we establish the nonparametric identification of principal causal effects using a pair of negative controls to mitigate unmeasured confounding, requiring they have no direct effect on the outcome variable. We also provide an estimation method for principal causal effects. Extensive simulations and a leukemia study are employed for illustration.

A BAYESIAN MACHINE LEARNING APPROACH FOR ESTIMATING HETEROGENEOUS SURVIVOR CAUSAL EFFECTS: APPLICATIONS TO A CRITICAL CARE TRIAL

Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development in tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for many participants in which case principal stratification is an appealing framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate mean models for the potential outcomes and latent stratum membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by biologic sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and degree of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field.

A mixed model approach to estimate the survivor average causal effect in cluster-randomized trials

In many medical studies, the outcome measure (such as quality of life, QOL) for some study participants becomes informatively truncated (censored, missing, or unobserved) due to death or other forms of dropout, creating a nonignorable missing data problem. In such cases, the use of a composite outcome or imputation methods that fill in unmeasurable QOL values for those who died rely on strong and untestable assumptions and may be conceptually unappealing to certain stakeholders when estimating a treatment effect. The survivor average causal effect (SACE) is an alternative causal estimand that surmounts some of these issues. While principal stratification has been applied to estimate the SACE in individually randomized trials, methods for estimating the SACE in cluster-randomized trials are currently limited. To address this gap, we develop a mixed model approach along with an expectation-maximization algorithm to estimate the SACE in cluster-randomized trials. We model the continuous outcome measure with a random intercept to account for intracluster correlations due to cluster-level randomization, and model the principal strata membership both with and without a random intercept. In simulations, we compare the performance of our approaches with an existing fixed-effects approach to illustrate the importance of accounting for clustering in cluster-randomized trials. The methodology is then illustrated using a cluster-randomized trial of telecare and assistive technology on health-related QOL in the elderly.

The survival-incorporated median vs the median in the survivors or in the always-survivors: What are we measuring? and Why?

Many clinical studies evaluate the benefit of a treatment based on both survival and other continuous/ordinal clinical outcomes, such as quality of life scores. In these studies, when subjects die before the follow-up assessment, the clinical outcomes become undefined and are truncated by death. Treating outcomes as "missing" or "censored" due to death can be misleading for treatment effect evaluation. We show that if we use the median in the survivors or in the always-survivors as estimands to summarize clinical outcomes, we may conclude that a trade-off exists between the probability of survival and good clinical outcomes, even in settings where both the probability of survival and the probability of any good clinical outcome are better for one treatment. Therefore, we advocate not always treating death as a mechanism through which clinical outcomes are missing, but rather as part of the outcome measure. To account for the survival status, we describe the survival-incorporated median as an alternative summary measure for outcomes in the presence of death. The survival-incorporated median is the threshold such that 50% of the population is alive with an outcome above that threshold. Through conceptual examples and an application to a prostate cancer treatment study, we show that the survival-incorporated median provides a simple and useful summary measure to inform clinical practice.

A multistate approach for the study of interventions on an intermediate time-to-event in health disparities research

We propose a novel methodology to quantify the effect of stochastic interventions for a non-terminal intermediate time-to-event on a terminal time-to-event outcome. Investigating these effects is particularly important in health disparities research when we seek to quantify inequities in the timely delivery of treatment and its impact on patients' survival time. Current approaches fail to account for time-to-event intermediates and semi-competing risks arising in this setting. Under the potential outcome framework, we define causal contrasts relevant in health disparities research and provide identifiability conditions when stochastic interventions on an intermediate non-terminal time-to-event are of interest. Causal contrasts are estimated in continuous time within a multistate modeling framework and analytic formulae for the estimators of the causal contrasts are developed. We show via simulations that ignoring censoring in intermediate and/or terminal time-to-event processes or ignoring semi-competing risks may give misleading results. This work demonstrates that a rigorous definition of the causal effects and joint estimation of the terminal outcome and intermediate non-terminal time-to-event distributions are crucial for valid investigation of interventions and mechanisms in continuous time. We employ this novel methodology to investigate the role of delaying treatment uptake in explaining racial disparities in cancer survival in a cohort study of colon cancer patients.

Defining estimands in clinical trials: A unified procedure

The ICH E9 (R1) addendum proposes five strategies to define estimands by addressing intercurrent events. However, mathematical forms of these targeted quantities are lacking, which might lead to discordance between statisticians who estimate these quantities and clinicians, drug sponsors, and regulators who interpret them. To improve the concordance, we provide a unified four-step procedure for constructing the mathematical estimands. We apply the procedure for each strategy to derive the mathematical estimands and compare the five strategies in practical interpretations, data collection, and analytical methods. Finally, we show that the procedure can help ease tasks of defining estimands in settings with multiple types of intercurrent events using two real clinical trials.

Causal inference with outcomes truncated by death in multiarm studies

It is challenging to evaluate causal effects when the outcomes of interest suffer from truncation-by-death in many clinical studies; that is, outcomes cannot be observed if patients die before the time of measurement. To address this problem, it is common to consider average treatment effects by principal stratification, for which, the identifiability results and estimation methods with a binary treatment have been established in previous literature. However, in multiarm studies with more than two treatment options, estimation of causal effects becomes more complicated and requires additional techniques. In this article, we consider identification, estimation, and bounds of causal effects with multivalued ordinal treatments and the outcomes subject to truncation-by-death. We define causal parameters of interest in this setting and show that they are identifiable either using some auxiliary variable or based on linear model assumption. We then propose a semiparametric method for estimating the causal parameters and derive their asymptotic results. When the identification conditions are invalid, we derive sharp bounds of the causal effects by use of covariates adjustment. Simulation studies show good performance of the proposed estimator. We use the estimator to analyze the effects of a four-level chronic toxin on fetal developmental outcomes such as birth weight in rats and mice, with data from a developmental toxicity trial conducted by the National Toxicology Program. Data analyses demonstrate that a high dose of the toxin significantly reduces the weights of pups.

Doubly robust estimation of the hazard difference for competing risks data

We consider the conditional treatment effect for competing risks data in observational studies. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to (1) the assumed propensity score for treatment and the censoring model, and (2) the outcome models for the competing risks. An important property regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-n $$ n $$ asymptotic normality of the estimated treatment effect for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes. The approaches developed in this article are implemented in the R package "HazardDiff".

Using principal stratification in analysis of clinical trials

The ICH E9(R1) addendum (2019) proposed principal stratification (PS) as one of five strategies for dealing with intercurrent events. Therefore, understanding the strengths, limitations, and assumptions of PS is important for the broad community of clinical trialists. Many approaches have been developed under the general framework of PS in different areas of research, including experimental and observational studies. These diverse applications have utilized a diverse set of tools and assumptions. Thus, need exists to present these approaches in a unifying manner. The goal of this tutorial is threefold. First, we provide a coherent and unifying description of PS. Second, we emphasize that estimation of effects within PS relies on strong assumptions and we thoroughly examine the consequences of these assumptions to understand in which situations certain assumptions are reasonable. Finally, we provide an overview of a variety of key methods for PS analysis and use a real clinical trial example to illustrate them. Examples of code for implementation of some of these approaches are given in Supplemental Materials.

Estimating the treatment effect for adherers using multiple imputation

Randomized controlled trials are considered the gold standard to evaluate the treatment effect (estimand) for efficacy and safety. According to the recent International Council on Harmonization (ICH)-E9 addendum (R1), intercurrent events (ICEs) need to be considered when defining an estimand, and principal stratum is one of the five strategies to handle ICEs. Qu et al. (2020, Statistics in Biopharmaceutical Research 12:1-18) proposed estimators for the adherer average causal effect (AdACE) for estimating the treatment difference for those who adhere to one or both treatments based on the causal-inference framework, and demonstrated the consistency of those estimators; however, this method requires complex custom programming related to high-dimensional numeric integrations. In this article, we implemented the AdACE estimators using multiple imputation (MI) and constructed confidence intervals (CIs) through bootstrapping. A simulation study showed that the MI-based estimators provided consistent estimators with the nominal coverage probabilities of CIs for the treatment difference for the adherent populations of interest. As an illustrative example, the new method was applied to data from a real clinical trial comparing two types of basal insulin for patients with type 1 diabetes.

Causal Inference in Studying the Long-Term Health Effects of Disasters: Challenges and Potential Solutions

Two frequently encountered but underrecognized challenges for causal inference in studying the long-term health effects of disasters among survivors include 1) time-varying effects of disasters on a time-to-event outcome and 2) selection bias due to selective attrition. In this paper, we review approaches for overcoming these challenges and demonstrate application of the approaches to a real-world longitudinal data set of older adults who were directly affected by the 2011 Great East Japan Earthquake and Tsunami (n = 4,857). To illustrate the problem of time-varying effects of disasters, we examined the association between degree of damage due to the tsunami and all-cause mortality. We compared results from Cox regression analysis assuming proportional hazards with those derived using adjusted parametric survival curves allowing for time-varying hazard ratios. To illustrate the problem of selection bias, we examined the association between proximity to the coast (a proxy for housing damage from the tsunami) and depressive symptoms. We corrected for selection bias due to attrition in the 2 postdisaster follow-up surveys (conducted in 2013 and 2016) using multivariable adjustment, inverse probability of censoring weighting, and survivor average causal effect estimation. Our results demonstrate that analytical approaches which ignore time-varying effects on mortality and selection bias due to selective attrition may underestimate the long-term health effects of disasters.

Survival mediation analysis with the death-truncated mediator: The completeness of the survival mediation parameter

In medical research, the development of mediation analysis with a survival outcome has facilitated investigation into causal mechanisms. However, studies have not discussed the death-truncation problem for mediators, the problem being that conventional mediation parameters cannot be well defined in the presence of a truncated mediator. In the present study, we systematically defined the completeness of causal effects to uncover the gap, in conventional causal definitions, between the survival and nonsurvival settings. We propose a novel approach to redefining natural direct and indirect effects, which are generalized forms of conventional causal effects for survival outcomes. Furthermore, we developed three statistical methods for the binary outcome of survival status and formulated a Cox model for survival time. We performed simulations to demonstrate that the proposed methods are unbiased and robust. We also applied the proposed method to explore the effect of hepatitis C virus infection on mortality, as mediated through hepatitis B viral load.

Implementation of tripartite estimands using adherence causal estimators under the causal inference framework

Intercurrent events (ICEs) and missing values are inevitable in clinical trials of any size and duration, making it difficult to assess the treatment effect for all patients in randomized clinical trials. Defining the appropriate estimand that is relevant to the clinical research question is the first step in analyzing data. The tripartite estimands, which evaluate the treatment differences in the proportion of patients with ICEs due to adverse events, the proportion of patients with ICEs due to lack of efficacy, and the primary efficacy outcome for those who can adhere to study treatment under the causal inference framework, are of interest to many stakeholders in understanding the totality of treatment effects. In this manuscript, we discuss the details of how to estimate tripartite estimands based on a causal inference framework and how to interpret tripartite estimates through a phase 3 clinical study evaluating a basal insulin treatment for patients with type 1 diabetes.

A causal framework for classical statistical estimands in failure-time settings with competing events

In failure-time settings, a competing event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest or a direct effect of the treatment on the event of interest not mediated by the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams, in which competing events are depicted as time-varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

A comparison of methods to estimate the survivor average causal effect in the presence of missing data: a simulation study

BACKGROUND

Attrition due to death and non-attendance are common sources of bias in studies of age-related diseases. A simulation study is presented to compare two methods for estimating the survivor average causal effect (SACE) of a binary exposure (sex-specific dietary iron intake) on a binary outcome (age-related macular degeneration, AMD) in this setting.

METHODS

A dataset of 10,000 participants was simulated 1200 times under each scenario with outcome data missing dependent on measured and unmeasured covariates and survival. Scenarios differed by the magnitude and direction of effect of an unmeasured confounder on both survival and the outcome, and whether participants who died following a protective exposure would also die if they had not received the exposure (validity of the monotonicity assumption). The performance of a marginal structural model (MSM, weighting for exposure, survival and missing data) was compared to a sensitivity approach for estimating the SACE. As an illustrative example, the SACE of iron intake on AMD was estimated using data from 39,918 participants of the Melbourne Collaborative Cohort Study.

RESULTS

The MSM approach tended to underestimate the true magnitude of effect when the unmeasured confounder had opposing directions of effect on survival and the outcome. Overestimation was observed when the unmeasured confounder had the same direction of effect on survival and the outcome. Violation of the monotonicity assumption did not increase bias. The estimates were similar between the MSM approach and the sensitivity approach assessed at the sensitivity parameter of 1 (assuming no survival bias). In the illustrative example, high iron intake was found to be protective of AMD (adjusted OR 0.57, 95% CI 0.40-0.82) using complete case analysis via traditional logistic regression. The adjusted SACE odds ratio did not differ substantially from the complete case estimate, ranging from 0.54 to 0.58 for each of the SACE methods.

CONCLUSIONS

On average, MSMs with weighting for exposure, missing data and survival produced biased estimates of the SACE in the presence of an unmeasured survival-outcome confounder. The direction and magnitude of effect of unmeasured survival-outcome confounders should be considered when assessing exposure-outcome associations in the presence of attrition due to death.

Analyzing patient-reported outcome data when completion differs between arms in open-label trials: an application of principal stratification

PURPOSE

Cancer trials are often open-label and include patient-reported outcomes (PROs). Previous work has demonstrated that patients may complete PRO assessments less frequently in the control arm compared with the experimental arm in open-label trials. Such differential completion may affect PRO results. This paper sought to explore principal stratification methodology to address potential bias caused by the posttreatment intermediate variable of questionnaire completion.

METHODS

We evaluated six randomized trials (five open-label and one double-blind) of anticancer therapies with varying levels of PRO completion submitted to the Food and Drug Administration (FDA). We applied complete case analysis (CCA), multiple imputation (MI), and principal stratification to evaluate PRO results for quality of life (QOL) and the domains of physical, role, and emotional function (PF, RF, and EF). Assignment to potential principal strata was by the expectation maximization algorithm using patient baseline characteristics.

RESULTS

Completion rates in the experimental arm ranged from 66% to 94% and 51% to 95% in the control arm. Four trials had negligible completion differences between arms (1%-2%), and two had large differences favoring the experimental arm (15%-17%). For trials with negligible completion differences, principal stratification results were similar to CCA and MI results for all domains. Notable differences in point estimates may be observed in trials with large differences in completion rates. However, in the examined trials, the confidence intervals for the principal stratification estimates overlapped with the ones obtained using CCA.

CONCLUSIONS

The principal stratification estimand may be a useful additional analysis, especially if PRO completion differs between arms.

Estimating causal effects of treatment in RCTs with provider and subject noncompliance

Subject noncompliance is a common problem in the analysis of randomized clinical trials (RCTs). With cognitive behavioral interventions, the addition of provider noncompliance further complicates making causal inference. As a motivating example, we consider an RCT of a motivational interviewing (MI)-based behavioral intervention for treating problem drug use. Treatment receipt depends on compliance of both a therapist (provider) and a patient (subject), where MI is received when the therapist adheres to the MI protocol and the patient actively participates in the intervention. However, therapists cannot be forced to follow protocol and patients cannot be forced to cooperate in an intervention. In this article, we (1) define a causal estimand of interest based on a principal stratification framework, the average causal effect of treatment among provider-subject pairs that comply with assignment or ACE(cc); (2) explore possible assumptions that identify ACE(cc); (3) develop novel estimators of ACE(cc); (4) evaluate estimators' statistical properties via simulation; and (5) apply our proposed methods for estimating ACE(cc) to data from our motivating example.

A sensitivity analysis for missing outcomes due to truncation by death under the matched-pairs design

The matched-pairs design enables researchers to efficiently infer causal effects from randomized experiments. In this paper, we exploit the key feature of the matched-pairs design and develop a sensitivity analysis for missing outcomes due to truncation by death, in which the outcomes of interest (e.g., quality of life measures) are not even well defined for some units (e.g., deceased patients). Our key idea is that if 2 nearly identical observations are paired prior to the randomization of the treatment, the missingness of one unit's outcome is informative about the potential missingness of the other unit's outcome under an alternative treatment condition. We consider the average treatment effect among always-observed pairs (ATOP) whose units exhibit no missing outcome regardless of their treatment status. The naive estimator based on available pairs is unbiased for the ATOP if 2 units of the same pair are identical in terms of their missingness patterns. The proposed sensitivity analysis characterizes how the bounds of the ATOP widen as the degree of the within-pair similarity decreases. We further extend the methodology to the matched-pairs design in observational studies. Our simulation studies show that informative bounds can be obtained under some scenarios when the proportion of missing data is not too large. The proposed methodology is also applied to the randomized evaluation of the Mexican universal health insurance program. An open-source software package is available for implementing the proposed research.

Using survival information in truncation by death problems without the monotonicity assumption

In some randomized clinical trials, patients may die before the measurement time point of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the potential outcomes framework, the only well-defined causal effect on the outcome is within the subgroup of patients who would always survive under both treatment and control. Because the definition of the subgroup depends on the potential values of the survival status that could not be observed jointly, without making strong parametric assumptions, we cannot identify the causal effect of interest and consequently can only obtain bounds of it. Unfortunately, however, many bounds are too wide to be useful. We propose to use detailed survival information before and after the measurement time point of the outcomes to sharpen the bounds of the subgroup causal effect. Because survival times contain useful information about the final outcome, carefully utilizing them could improve statistical inference without imposing strong parametric assumptions. Moreover, we propose to use a copula model to relax the commonly-invoked but often doubtful monotonicity assumption that the treatment extends the survival time for all patients.

Identification and estimation of causal effects with outcomes truncated by death

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.

Causal analysis of ordinal treatments and binary outcomes under truncation by death

It is common that in multi-arm randomized trials, the outcome of interest is "truncated by death," meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts.

Design and inference for the intent-to-treat principle using adaptive treatment

Nonadherence to assigned treatment jeopardizes the power and interpretability of intent-to-treat comparisons from clinical trial data and continues to be an issue for effectiveness studies, despite their pragmatic emphasis. We posit that new approaches to design need to complement developments in methods for causal inference to address nonadherence, in both experimental and practice settings. This paper considers the conventional study design for psychiatric research and other medical contexts, in which subjects are randomized to treatments that are fixed throughout the trial and presents an alternative that converts the fixed treatments into an adaptive intervention that reflects best practice. The key element is the introduction of an adaptive decision point midway into the study to address a patient's reluctance to remain on treatment before completing a full-length trial of medication. The clinical uncertainty about the appropriate adaptation prompts a second randomization at the new decision point to evaluate relevant options. Additionally, the standard 'all-or-none' principal stratification (PS) framework is applied to the first stage of the design to address treatment discontinuation that occurs too early for a midtrial adaptation. Drawing upon the adaptive intervention features, we develop assumptions to identify the PS causal estimand and to introduce restrictions on outcome distributions to simplify expectation-maximization calculations. We evaluate the performance of the PS setup, with particular attention to the role played by a binary covariate. The results emphasize the importance of collecting covariate data for use in design and analysis. We consider the generality of our approach beyond the setting of psychiatric research.

Identification and estimation of survivor average causal effects

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

Identifiability of subgroup causal effects in randomized experiments with nonignorable missing covariates

Although randomized experiments are widely regarded as the gold standard for estimating causal effects, missing data of the pretreatment covariates makes it challenging to estimate the subgroup causal effects. When the missing data mechanism of the covariates is nonignorable, the parameters of interest are generally not pointly identifiable, and we can only get bounds for the parameters of interest, which may be too wide for practical use. In some real cases, we have prior knowledge that some restrictions may be plausible. We show the identifiability of the causal effects and joint distributions for four interpretable missing data mechanisms and evaluate the performance of the statistical inference via simulation studies. One application of our methods to a real data set from a randomized clinical trial shows that one of the nonignorable missing data mechanisms fits better than the ignorable missing data mechanism, and the results conform to the study's original expert opinions. We also illustrate the potential applications of our methods to observational studies using a data set from a job-training program.

Sharpening bounds on principal effects with covariates

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