Volume 3, Issue 2 -

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment-specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator’s performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression-based estimator in simulation studies.

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

Research by the Observational Medical Outcomes Partnership (OMOP) has focused on developing and evaluating strategies to exploit observational electronic data to improve post-market prescription drug surveillance. A data simulator known as OSIM2 developed by the OMOP statistical methods group has been used as a testbed for evaluating and comparing different estimation procedures for detecting adverse drug-related events from data similar to that found in electronic insurance claims data. The simulation scheme produces a longitudinal dataset with millions of observations designed to closely match marginal distributions of important covariates in a known dataset. In this paper we provide a non-parametric structural equation model for the data generating process and construct the associated directed acyclic graph (DAG) depicting the causal structure. These representations reveal key differences between simulated and real-world data, including a departure from longitudinal causal relationships, absence of (presumed) sources of bias and time ordering of covariates that conflicts with reality. The DAG also reveals the presence of unmeasured baseline confounding of the causal effect of a drug on a subsequent medical condition. Conclusions naively drawn from this simulation study could mislead an investigator trying to gain insight into estimator performance on real data. Applying causal inference tools allows us to draw more informed conclusions and suggests modifications to the simulation scheme that would more closely align simulated and real-world data.

Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.

Estimating causal exposure effects in observational studies ideally requires the analyst to have a vast knowledge of the domain of application. Investigators often bypass difficulties related to the identification and selection of confounders through the use of fully adjusted outcome regression models. However, since such models likely contain more covariates than required, the variance of the regression coefficient for exposure may be unnecessarily large. Instead of using a fully adjusted model, model selection can be attempted. Most classical statistical model selection approaches, such as Bayesian model averaging, do not readily address causal effect estimation. We present a new model averaged approach to causal inference, Bayesian causal effect estimation (BCEE), which is motivated by the graphical framework for causal inference. BCEE aims to unbiasedly estimate the causal effect of a continuous exposure on a continuous outcome while being more efficient than a fully adjusted approach.

Propensity score analysis (PSA) is a common method for estimating treatment effects, but researchers dealing with data from survey designs are generally not properly accounting for the sampling weights in their analyses. Moreover, recommendations given in the few existing methodological articles on this subject are susceptible to bias. We show in this article through derivation, simulation, and a real data example that using sampling weights in the propensity score estimation stage and the outcome model stage results in an estimator that is robust to a variety of conditions that lead to bias for estimators currently recommended in the statistical literature. We highly recommend researchers use the more robust approach described here. This article provides much needed rigorous statistical guidance for researchers working with survey designs involving sampling weights and using PSAs.

Ding and Miratrix [1] recently concluded that adjustment on a pre-treatment covariate is almost always preferable to reduce bias. I extend the examined parameter space of the models considered by Ding and Miratrix, and consider slight extensions of their models as well. Similar to the conclusion by Pearl [7], I identify constellations in which bias due to adjustment, or failing to adjust is symmetrical, but also confirm some findings of Ding and Miratrix.

This note examines one of the most crucial questions in causal inference: “How generalizable are randomized clinical trials?” The question has received a formal treatment recently, using a non-parametric setting, and has led to a simple and general solution. I will describe this solution and several of its ramifications, and compare it to the way researchers have attempted to tackle the problem using the language of ignorability. We will see that ignorability-type assumptions need to be enriched with structural assumptions in order to capture the full spectrum of conditions that permit generalizations, and in order to judge their plausibility in specific applications.