Principal stratification--uses and limitations

Surrogate measures and consistent surrogates

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

Applying optimal model selection in principal stratification for causal inference

Noncompliance to treatment allocation is a key source of complication for causal inference. Efficacy estimation is likely to be compounded by the presence of noncompliance in both treatment arms of clinical trials where the intention-to-treat estimate provides a biased estimator for the true causal estimate even under homogeneous treatment effects assumption. Principal stratification method has been developed to address such posttreatment complications. The present work extends a principal stratification method that adjusts for noncompliance in two-treatment arms trials by developing model selection for covariates predicting compliance to treatment in each arm. We apply the method to analyse data from the Esprit study, which was conducted to ascertain whether unopposed oestrogen (hormone replacement therapy) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We adjust for noncompliance in both treatment arms under a Bayesian framework to produce causal risk ratio estimates for each principal stratum. For mild values of a sensitivity parameter and using separate predictors of compliance in each arm, principal stratification results suggested that compliance with hormone replacement therapy only would reduce the risk for death and myocardial reinfarction by about 47% and 25%, respectively, whereas compliance with either treatment would reduce the risk for death by 13% and reinfarction by 60% among the most compliant. However, the results were sensitive to the user-defined sensitivity parameter.

Accommodating missingness when assessing surrogacy via principal stratification

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 (CE) 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 the 0-1 range. Furthermore, 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 problems are of key importance. Methods Frangakis and Rubin suggested assessing the CE within prerandomization 'principal strata' defined by the counterfactual joint distribution of the surrogate marker under the different treatment arms, with the proportion of the overall outcome CE attributable to subjects for whom the treatment affects the proposed surrogate as the key measure of interest. Li et al. developed this 'principal surrogacy' approach for dichotomous markers and outcomes, utilizing Bayesian methods that accommodated nonidentifiability in the model parameters. Because the surrogate marker is typically observed early, outcome data are often missing. Here, we extend Li et al. to accommodate missing data in the observable final outcome under ignorable and nonignorable 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 nonignorability, as well as sensitivity to priors and the ability of the decision information criterion (DIC) 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 nontrivial bias in moderate sample size settings, while more noninformative priors can yield wide credible intervals.

CONCLUSIONS

Assessing the linkage between CEs of treatment on a surrogate marker and CEs of a treatment on an outcome is important to understanding the value of a marker. These CEs 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.

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

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

Mediation analysis with multiple versions of the mediator

The causal inference literature has provided definitions of direct and indirect effects based on counterfactuals that generalize the approach found in the social science literature. However, these definitions presuppose well-defined hypothetical interventions on the mediator. In many settings, there may be multiple ways to fix the mediator to a particular value, and these various hypothetical interventions may have very different implications for the outcome of interest. In this paper, we consider mediation analysis when multiple versions of the mediator are present. Specifically, we consider the problem of attempting to decompose a total effect of an exposure on an outcome into the portion through the intermediate and the portion through other pathways. We consider the setting in which there are multiple versions of the mediator but the investigator has access only to data on the particular measurement, not information on which version of the mediator may have brought that value about. We show that the quantity that is estimated as a natural indirect effect using only the available data does indeed have an interpretation as a particular type of mediated effect; however, the quantity estimated as a natural direct effect, in fact, captures both a true direct effect and an effect of the exposure on the outcome mediated through the effect of the version of the mediator that is not captured by the mediator measurement. The results are illustrated using 2 examples from the literature, one in which the versions of the mediator are unknown and another in which the mediator itself has been dichotomized.

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

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

Principal stratification 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.