Volume 4, Issue 2 -

In randomized controlled trials, the evaluation of an overall treatment effect is often followed by effect modification or subgroup analyses, where the possibility of a different magnitude or direction of effect for varying values of a covariate is explored. While studies of effect modification are typically restricted to pretreatment covariates, longitudinal experimental designs permit the examination of treatment effect modification by intermediate outcomes, where intermediates are measured after treatment but before the final outcome. We present a novel application of generalized structural mean models (GSMMs) for simultaneously assessing effect modification by post-treatment covariates and accounting for noncompliance to assigned treatment status. The proposed approach may also be used to identify post-treatment effect modifiers in the absence of noncompliance. The methods are evaluated using a simulation study that demonstrates that our approach retains consistent estimation of effect modification by intermediate variables that are affected by treatment and also predict outcomes. We illustrate the method using a randomized trial designed to promote re-employment through teaching skills to enhance self-esteem and inoculate job seekers against setbacks in the job search process. Our analysis provides some evidence that the intervention was much less successful among subjects that displayed higher levels of depression at intermediate post-treatment waves of the study. We also compare the assumptions of our approach and principal stratification as alternatives to account for differences in effects by intermediate variables.

Recent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can potentially be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root-n$n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect.

Causal inference with observational data frequently requires researchers to estimate treatment effects conditional on a set of observed covariates, hoping that they remove or at least reduce the confounding bias. Using a simple linear (regression) setting with two confounders – one observed ( X ), the other unobserved ( U ) – we demonstrate that conditioning on the observed confounder X does not necessarily imply that the confounding bias decreases, even if X is highly correlated with U . That is, adjusting for X may increase instead of reduce the omitted variable bias (OVB). Two phenomena can cause an increasing OVB: (i) bias amplification and (ii) cancellation of offsetting biases. Bias amplification occurs because conditioning on X amplifies any remaining bias due to the omitted confounder U . Cancellation of offsetting biases is an issue whenever X and U induce biases in opposite directions such that they perfectly or partially offset each other, in which case adjusting for X inadvertently cancels the bias-offsetting effect. In this article we discuss the conditions under which adjusting for X increases OVB, and demonstrate that conditioning on X increases the imbalance in U , which turns U into an even stronger confounder. We also show that conditioning on an unreliably measured confounder can remove more bias than the corresponding reliable measure. Practical implications for causal inference will be discussed.

Abstract: While standard meta-analysis pools the results from randomized trials that compare two treatments, network meta-analysis aggregates the results of randomized trials comparing a wider variety of treatment options. However, it is unclear whether the aggregation of effect estimates across heterogeneous populations will be consistent for a meaningful parameter when not all treatments are evaluated on each population. Drawing from counterfactual theory and the causal inference framework, we define the population of interest in a network meta-analysis and define the target parameter under a series of nonparametric structural assumptions. This allows us to determine the requirements for identifiability of this parameter, enabling a description of the conditions under which network meta-analysis is appropriate and when it might mislead decision making. We then adapt several modeling strategies from the causal inference literature to obtain consistent estimation of the intervention-specific mean outcome and model-independent contrasts between treatments. Finally, we perform a reanalysis of a systematic review to compare the efficacy of antibiotics on suspected or confirmed methicillin-resistant Staphylococcus aureus in hospitalized patients.

Among the many peculiarities that were dubbed “paradoxes” by well meaning statisticians, the one reported by Frederic M. Lord in 1967 has earned a special status. Although it can be viewed, formally, as a version of Simpson’s paradox, its reputation has gone much worse. Unlike Simpson’s reversal, Lord’s is easier to state, harder to disentangle and, for some reason, it has been lingering for almost four decades, under several interpretations and re-interpretations, and it keeps coming up in new situations and under new lights. Most peculiar yet, while some of its variants have received a satisfactory resolution, the original version presented by Lord, to the best of my knowledge, has not been given a proper treatment, not to mention a resolution. The purpose of this paper is to trace back Lord’s paradox from its original formulation, resolve it using modern tools of causal analysis, explain why it resisted prior attempts at resolution and, finally, address the general methodological issue of whether adjustments for preexisting conditions is justified in group comparison applications.