Structural Mean Models Research Articles

Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models

We consider estimation of the received treatment effect on a dichotomous outcome in randomised trials with non-compliance. We explore inference about the parameters of the structural mean models of Robins (1994, 1997) and Robins et al. (1999). We show that, in contrast to the additive and multiplicative structural mean models for continuous and count outcomes, unbiased estimating functions for a nonzero (structural) treatment effect parameter do not exist in the presence of many continuous and discrete baseline covariates, even when the randomisation probabilities are known. The best that can be hoped for are estimators, such as those proposed in this paper, that are guaranteed both to estimate consistently the (null) treatment effect when the null hypothesis of no treatment effect is true and to have small bias when the true treatment effect is close to but not equal to zero.

Structural Mean Effects of Noncompliance

A randomized, placebo-controlled blood pressure (BP) reduction trial has recorded compliance measures by electronic monitoring. Causal questions regarding dose effects are of interest, but one often wants to avoid the assumption that compliance quantiles on both randomized arms are comparable. Structural mean models (SMMs) do avoid this assumption; however, they do not allow for interaction effects between variables observed on different randomized arms. Such an interaction between observed exposure on the treatment arm and latent treatmentfree response (i. e., placebo response) was suggested by the data. Building on structural models, we propose an approach that makes this possible. To allow for a structural interaction effect with potential placebo response, we invoke a compliance selection model. It turns out that SMMs imply identifiable selection models; hence the secondary model is testable. Next, to assess the amount of variation explained by the structural model, we identify separate variance components for different error types. This yields a measure of the variation in treatment effects over individuals. In addition, it allows us to compare the fit of different plausible structural models. On the BP data, we find a significant interaction effect: Higher exposure levels are estimated to have more effect in subgroups with poorer placebo response. Finite-sample properties of the proposed estimators are verified through simulation.

Causal Models for Randomized Physician Encouragement Trials in Treating Primary Care Depression

This article addresses unique causal issues in the context of a randomized study on improving adherence to best practice guidelines by primary care physicians (PCP's) in treating their depressed patients. The study assessed an encouragement strategy to improve PCP guideline adherence. In this context, we compare two causal approaches: the conditional-compliance (CC) Bayesian latent class and the conditional-observable (CO) structural mean model methods. The CC methods estimate contrasts between randomized encouragement and no-encouragement arms [intent-to-treat (ITT) estimand] given latent PCP guideline complier classes. The CO methods estimate contrasts between PCP guideline adherence and nonadherence conditions (as-treated estimand) given observed PCP adherence status. The CC ITT estimand for patients with PCP compliers equals the CO as-treated estimand depending on assumptions. One such assumption pertains to the absence of physician defiers, who do the opposite of what they are encouraged to do in treating patients for depression. We relate these two estimands to each other in our clinical context when the no-defier assumption is not plausible. In other contexts, previous statistical literature has appropriately assumed the absence of defiers. However, indications in the behavioral literature, anecdotal evidence in the study, and results from the data analysis and simulations suggest that defiers do exist in the context of physician-based interventions in primary care. Both simulation and empirical results show that even with a small estimated proportion of defiers under Bayesian model assumptions, inference is sensitive to different assumptions about this class of PCP noncompliers.

Causal Inference with Generalized Structural Mean Models

SummaryWe estimate cause–effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to overcome these limitations. This is a semiparametric two-stage model which extends the structural mean model to handle non-linear average exposure effects. The first-stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure-free outcomes in exposed subsets of the population. For identification of the structural parameters, a second stage ‘nuisance’ model is introduced. This takes the form of a classical association model for expected outcomes given observed exposure. Under the model, we derive estimating equations which yield consistent, asymptotically normal and efficient estimators of the structural effects. We examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect. The double-logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self-selected non-compliance.

Practical Properties of Some Structural Mean Analyses of the Effect of Compliance in Randomized Trials

We can use the structural mean model (SMM) to estimate the mean effect of dose-timing patterns of active treatment actually taken by patients in a randomized placebo-controlled trial. An SMM therefore models the expected difference between a patient's potential response on the treatment arm and potential response on the placebo arm as a function of observed compliance on the treatment arm and baseline predictors. It accounts for the possibly selective nature of noncompliance without needing to model that aspect directly. It nevertheless enjoys the intention-to-treat property of protecting the α level when we are testing the hypothesis of no treatment effect. In the presence of selective compliance, classical regression methods lead to inconsistent and seriously biased estimates of the effects of treatment actually taken. The SMM is designed to reduce these problems. This paper studies selectivity and addresses some practical properties of the SMM estimator. Specifically, we use a blood pressure trial to explore the precision of the estimates in practical cases. We also compare mean squared errors (MSEs) of an SMM and the ordinary least-squares (OLS) estimator. We study the effect of baseline covariates on the precision of the SMM estimator and describe the potential role of a run-in period in this regard. Control Clin Trials 1999;20:531–546