Sense and sensitivity when correcting for observed exposures in randomized clinical trials

Instrumental variable estimation of causal odds ratios using structural nested mean models

We consider estimating causal odds ratios using an instrumental variable under a logistic structural nested mean model (LSNMM). Current methods for LSNMMs either rely heavily on possible "uncongenial" modeling assumptions or involve intricate numerical challenges, which have impeded their use. In this article, we present an alternative method that ensures a congenial parametrization, circumvents computational complexity of existing methods, and is easy to implement. We illustrate the proposed method to (1) estimate the causal effect of years of education on earnings using data from the NLSYM and (2) assess the impact of moving families from high to low-poverty neighborhoods had on lifetime major depressive disorder among adolescents in the "Moving to Opportunity (MTO) for Fair Housing Demonstration Project" from the Department of Housing and Urban Development.

Noncompliance in cancer screening trials

Background Randomized trials evaluating new cancer screening technologies may underestimate the efficacy of screening to reduce cancer mortality if study participants are noncompliant. Participants may fail to comply with the screening itself or fail to obtain appropriate diagnostic follow-up and treatment. Noncompliance with screening has drawn wide attention, but little attention has been paid to noncompliance with diagnostic follow-up and treatment.

Purpose To examine the importance of noncompliance with screening, follow-up, and treatment in cancer screening trials.

Methods The unique problems associated with noncompliance in screening trials are described and provide an example illustrating the potential impact of noncompliance in a screening trial. I discuss issues that arise with measurement of follow-up and therapeutic noncompliance, and the benefit of collecting information on health system and participant characteristics associated with noncompliance.

Results The estimate of the efficacy of a screening program on cancer mortality can be adjusted for screening, follow-up, and treatment noncompliance. Noncompliance needs to be measured in a rigorous, systematic manner across all arms of the trial. Information on health system and participant characteristics associated with compliance may also be incorporated into statistical models to estimate screening effects with full compliance, plan interventions to increase compliance, and extrapolate results of screening trials from one population to another.

Limitations Measuring compliance with follow-up and treatment can be difficult when these occur outside the trial, and when there is variation among providers in follow-up and treatment practices.

Conclusions Noncompliance may alter the estimate of a screening effect on cancer mortality in clinical trials. It is possible to adjust screening efficacy estimates for noncompliance using existing statistical techniques. It is important that data describing compliance with screening, follow-up, and treatment are collected as part of standard data collection in cancer screening trials. Clinical Trials 2007; 4: 341—349. http://ctj.sagepub.com

Model selection criterion for causal parameters in structural mean models based on a quasi-likelihood

Structural mean models (SMMs) have been proposed for estimating causal parameters in the presence of non-ignorable non-compliance in clinical trials. To obtain a valid causal estimate, we must impose several assumptions. One of these is the correct specification of the structural model. Building on Pan's work (2001, Biometrics 57, 120-125) on developing a model selection criterion for generalized estimating equations, we propose a new approach for model selection of SMMs based on a quasi-likelihood. We provide a formal model selection criterion that is an extension of Akaike's information criterion. Using subset selection of baseline covariates, our method allows us to understand whether the treatment effect varies across the available baseline covariate levels, and/or to quantify the treatment effect on a specific covariates level to target specific individuals to maximize treatment benefit. We present simulation results in which our method performs reasonably well compared to other testing methods in terms of both the probability of selecting the correct model and the predictive performances of the individual treatment effects. We use a large randomized clinical trial of pravastatin as a motivation.

Using structural-nested models to estimate the effect of cluster-level adherence on individual-level outcomes with a three-armed cluster-randomized trial

Much attention has been paid to estimating the causal effect of adherence to a randomized protocol using instrumental variables to adjust for unmeasured confounding. Researchers tend to use the instrumental variable within one of the three main frameworks: regression with an endogenous variable, principal stratification, or structural-nested modeling. We found in our literature review that even in simple settings, causal interpretations of analyses with endogenous regressors can be ambiguous or rely on a strong assumption that can be difficult to interpret. Principal stratification and structural-nested modeling are alternative frameworks that render unambiguous causal interpretations based on assumptions that are, arguably, easier to interpret. Our interest stems from a wish to estimate the effect of cluster-level adherence on individual-level binary outcomes with a three-armed cluster-randomized trial and polytomous adherence. Principal stratification approaches to this problem are quite challenging because of the sheer number of principal strata involved. Therefore, we developed a structural-nested modeling approach and, in the process, extended the methodology to accommodate cluster-randomized trials with unequal probability of selecting individuals. Furthermore, we developed a method to implement the approach with relatively simple programming. The approach works quite well, but when the structural-nested model does not fit the data, there is no solution to the estimating equation. We investigate the performance of the approach using simulated data, and we also use the approach to estimate the effect on pupil absence of school-level adherence to a randomized water, sanitation, and hygiene intervention in western Kenya.

Estimating causal effects using prior information on nontrial treatments

Background Departures from randomized treatments complicate the analysis of many randomized controlled trials. Intention-to-treat analysis estimates the effect of being allocated to treatment. It is now possible to estimate the effect of receiving treatment without assuming comparability of groups defined by actual treatment. However, the methodology is largely confined to trials where the only treatment changes were switches to other trial treatments.

Purpose To propose a method for comparing the effects of receiving trial treatments in an active-controlled clinical trial where some participants received nontrial treatments and others received no treatment at all, and to illustrate the method in the PENTA 5 trial in HIV-infected children.

Methods We combine the instrumental variables approach, which forms unbiased estimating equations based on the randomization but does not fully identify the contrasts of trial treatment effects, with prior information about the distribution of possible effects of nontrial treatments and of one trial treatment; we do not need to use prior information about the comparisons of trial treatments. Prior information in PENTA 5 was elicited from the investigators.

Results In PENTA 5, the prior information suggested that all treatments were beneficial, but there was uncertainty about the degree of benefit. Allowing for this prior information changed point estimates and increased standard errors compared with ignoring nontrial treatments.

Limitations The method depends on the correct specification of the causal effect of treatment: in PENTA 5, this assumed a linear effect of dose and no interactions between treatments. This specification is hard to check from the data but can be explored in sensitivity analyses. Prior information would be better derived from the literature whenever possible.

Conclusions The use of partial prior information gives a way to adjust for complex patterns of departures from randomized treatments. It should be useful in all trials where nontrial treatments are used and in active-controlled trials where trial treatments are not universally used.

Linear and loglinear structural mean models to evaluate the benefits of an on-demand dosing regimen

Background Structural mean models can be used to estimate treatment efficacy when drug exposure varies. We applied stuctural mean model to evaluate the clinical benefits of a proton pump inhibitor prescribed to be taken as needed to alleviate epigastric pain. We also investigated a new diagnostic approach to evaluate model assumptions.

Methods All patients were suffering from nonerosive reflux disease or functional ulcer-like dyspepsia and were prescribed a proton pump inhibitor to be taken as needed for relief of epigastric pain. The primary endpoint was a score variable that expresses the magnitude of gastro-intestinal symptoms at 8 weeks after randomization. We developed linear and loglinear versions of the structural mean models to derive an unbiased estimator of the reduction in symptom score as a function of exposure to the test drug. Semi-parametric models based on splines and corresponding simultaneous confidence bands identified the presence of potential interactions between drug exposure and baseline covariates.

Results The on-demand dosing regimen generated a wide range of drug exposure. Application of SMM showed that the potential treatment-induced reduction in symptom score was much greater than the average treatment reduction observed in this population of patients. Our diagnostic tool was useful for detecting the interaction between drug exposure and baseline covariates. Limitations Analysis could only be performed over the first 2 months after randomization because, afterwards, many patients dropped out from the placebo group. Conclusions The structural mean model approach allows one to estimate treatment efficacy in the presence of variable drug exposure. Similar results were obtained using linear and loglinear structural mean model. Clinical Trials 2009; 6: 403—415. http://ctj.sagepub.com

Sensitivity analysis for principal stratum direct effects, with an application to a study of physical activity and coronary heart disease

SUMMARY

In many studies, the aim is to learn about the direct exposure effect, that is, the effect not mediated through an intermediate variable. For example, in circulation disease studies it may be of interest to assess whether a suitable level of physical activity can prevent disease, even if it fails to prevent obesity. It is well known that stratification on the intermediate may introduce a so-called posttreatment selection bias. To handle this problem, we use the framework of principal stratification (Frangakis and Rubin, 2002, Biometrics 58, 21-29) to define a causally relevant estimand--the principal stratum direct effect (PSDE). The PSDE is not identified in our setting. We propose a method of sensitivity analysis that yields a range of plausible values for the causal estimand. We compare our work to similar methods proposed in the literature for handling the related problem of "truncation by death."

Effect of highly active antiretroviral therapy on incident AIDS using calendar period as an instrumental variable

Human immunodeficiency virus (HIV) researchers often use calendar periods as an imperfect proxy for highly active antiretroviral therapy (HAART) when estimating the effect of HAART on HIV disease progression. The authors report on 614 HIV-positive homosexual men followed from 1984 to 2007 in 4 US cities. During 5,321 person-years, 268 of 614 men incurred acquired immunodeficiency syndrome, 49 died, and 90 were lost to follow-up. Comparing the pre-HAART calendar period (<1996) with the HAART calendar period (>or=1996) resulted in a naive rate ratio of 3.62 (95% confidence limits: 2.67, 4.92). However, this estimate is likely biased because of misclassification of HAART use by calendar period. Simple calendar period approaches may circumvent confounding by indication at the cost of inducing exposure misclassification. To correct this misclassification, the authors propose an instrumental-variable estimator analogous to ones previously used for noncompliance corrections in randomized clinical trials. When the pre-HAART calendar period was compared with the HAART calendar period, the instrumental-variable rate ratio was 5.02 (95% confidence limits: 3.45, 7.31), 39% higher than the naive result. Weighting by the inverse probability of calendar period given age at seroconversion, race/ethnicity, and time since seroconversion did not appreciably alter the results. These methods may help resolve discrepancies between observational and randomized evidence.

Identifiability and estimation of causal effects in randomized trials with noncompliance and completely nonignorable missing data

In this article, we first study parameter identifiability in randomized clinical trials with noncompliance and missing outcomes. We show that under certain conditions the parameters of interest are identifiable even under different types of completely nonignorable missing data: that is, the missing mechanism depends on the outcome. We then derive their maximum likelihood and moment estimators and evaluate their finite-sample properties in simulation studies in terms of bias, efficiency, and robustness. Our sensitivity analysis shows that the assumed nonignorable missing-data model has an important impact on the estimated complier average causal effect (CACE) parameter. Our new method provides some new and useful alternative nonignorable missing-data models over the existing latent ignorable model, which guarantees parameter identifiability, for estimating the CACE in a randomized clinical trial with noncompliance and missing data.

An introduction to causal modeling in clinical trials

PURPOSE

We review and compare two causal modeling approaches that correspond to two major and distinct classes of inference - efficacy and intervention-based inference - in the context of randomized trials with subject noncompliance.

METHODS

We review the definitions of efficacy and intervention-based effects in the clinical trials literature and relate these to two separate and distinct causal modeling approaches: the structural mean modeling (SMM) approach and the principal stratification, instrumental variable approach.

RESULTS

The SMM-based efficacy approach focuses on the effect of actually receiving treatment. In contrast, the principal stratification method addresses the effect of treatment assignment within partially unobserved latent subgroups defined by compliance behavior. While these approaches differ in terms of philosophy, model definitions, and estimation, they estimate the same causal effect under certain assumptions, but estimate very different causal effects when those assumptions are relaxed. We illustrate these results using a randomized psychiatry trial where the focus is physician compliance to the designated protocol and the other examines patient compliance to the designated protocol, both from the same trial.

LIMITATIONS

The validity of the models under the instrumental variable, SMM and principal stratification approaches depends on modeling assumptions, some of which may not be verifiable from the observed data and potentially less realistic than the no-confounding assumption made by non-causal approaches.

CONCLUSIONS

This comparison in terms of efficacy versus intervention-based effects in causal modeling parallels the explanatory versus pragmatic approaches in clinical trials research; therefore researchers should weigh carefully when choosing causal modeling methodology based on whether efficacy or intervention-based effects are of interest.

Structural mean models for compliance analysis in randomized clinical trials and the impact of errors on measures of exposure

Partial compliance with assigned treatment regimes is common in drug trials and calls for a causal analysis of the effect of treatment actually received. As such observed exposure is no longer randomized, selection bias must be carefully accounted for. The framework of potential outcomes allows this by defining a subject-specific treatment-free reference outcome, which may be latent and is modelled in relation to the observed (treated) data. Causal parameters enter these structural models explicitly. In this paper we review recent progress in randomization-based inference for structural mean modelling, from the additive linear model to the structural generalized linear models. An arsenal of tools currently available for standard association regression has steadily been developed in the structural setting, providing many parallel features to help randomization-based inference. We argue that measurement error on exposure is an important practical complication that has, however, not yet been addressed. We show how standard additive linear structural mean models are robust against unbiased measurement error and how efficient, asymptotically unbiased inference can be drawn when the degree of measurement error bias is known. The impact of measurement error is illustrated in a blood pressure example and finite sample properties are verified by simulation. We end with a plea for more and careful use of this methodology and point to directions for further development.