Sensitivity analysis of G-estimators to invalid instrumental variables

Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured confounders. A valid instrumental variable is a variable that is associated with the exposure, affects the outcome only through the exposure (exclusion), and is not confounded with the outcome (exogeneity). Unlike the first assumption, the other two are generally untestable and rely on subject-matter knowledge. Therefore, a sensitivity analysis is desirable to assess the impact of assumptions' violation on the estimated parameters. In this paper, we propose and demonstrate a new method of sensitivity analysis for G-estimators in causal linear and non-linear models. We introduce two novel aspects of sensitivity analysis in instrumental variables studies. The first is a single sensitivity parameter that captures violations of exclusion and exogeneity assumptions. The second is an application of the method to non-linear models. The introduced framework is theoretically justified and is illustrated via a simulation study. Finally, we illustrate the method by application to real-world data and provide guidelines on conducting sensitivity analysis.

G-estimation of structural nested mean models for interval-censored data using pseudo-observations

Two large-scale randomized clinical trials compared fenofibrate and placebo in diabetic patients with pre-existing retinopathy (FIELD study) or risk factors (ACCORD trial) on an intention-to-treat basis and reported a significant reduction in the progression of diabetic retinopathy in the fenofibrate arms. However, their analyses involved complications due to intercurrent events, that is, treatment-switching and interval-censoring. This article addresses these problems involved in estimation of causal effects of long-term use of fibrates in a cohort study that followed patients with type 2 diabetes for 8 years. We propose structural nested mean models (SNMMs) of time-varying treatment effects and pseudo-observation estimators for interval-censored data. The first estimator for SNMMs uses a nonparametric maximum likelihood estimator (MLE) as a pseudo-observation, while the second estimator is based on MLE under a parametric piecewise exponential distribution. Through numerical studies with real and simulated datasets, the pseudo-observations estimators of causal effects using the nonparametric Wellner-Zhan estimator perform well even under dependent interval-censoring. Its application to the diabetes study revealed that the use of fibrates in the first 4 years reduced the risk of diabetic retinopathy but did not support its efficacy beyond 4 years.

Estimation of average treatment effect based on a multi-index propensity score

BACKGROUND

Estimating the average effect of a treatment, exposure, or intervention on health outcomes is a primary aim of many medical studies. However, unbalanced covariates between groups can lead to confounding bias when using observational data to estimate the average treatment effect (ATE). In this study, we proposed an estimator to correct confounding bias and provide multiple protection for estimation consistency.

METHODS

With reference to the kernel function-based double-index propensity score (Ker.DiPS) estimator, we proposed the artificial neural network-based multi-index propensity score (ANN.MiPS) estimator. The ANN.MiPS estimator employed the artificial neural network to estimate the MiPS that combines the information from multiple candidate models for propensity score and outcome regression. A Monte Carlo simulation study was designed to evaluate the performance of the proposed ANN.MiPS estimator. Furthermore, we applied our estimator to real data to discuss its practicability.

RESULTS

The simulation study showed the bias of the ANN.MiPS estimators is very small and the standard error is similar if any one of the candidate models is correctly specified under all evaluated sample sizes, treatment rates, and covariate types. Compared to the kernel function-based estimator, the ANN.MiPS estimator usually yields smaller standard error when the correct model is incorporated in the estimator. The empirical study indicated the point estimation for ATE and its bootstrap standard error of the ANN.MiPS estimator is stable under different model specifications.

CONCLUSIONS

The proposed estimator extended the combination of information from two models to multiple models and achieved multiply robust estimation for ATE. Extra efficiency was gained by our estimator compared to the kernel-based estimator. The proposed estimator provided a novel approach for estimating the causal effects in observational studies.

Coherent modeling of longitudinal causal effects on binary outcomes

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Towards this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the non-causal nuisance parameters. This leads to a series of difficulties in interpretation, estimation and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparametrization of the non-causal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parametrization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parametrization, thereby justifying the restriction to multiplicative SNMMs. This article is protected by copyright. All rights reserved.

Effectiveness of the Strengthening Families Programme in the UK at preventing substance misuse in 10-14 year-olds: a pragmatic randomised controlled trial

OBJECTIVES

The Strengthening Families Programme 10-14 (SFP10-14) is a USA-developed universal group-based intervention aiming to prevent substance misuse by strengthening protective factors within the family. This study evaluated a proportionate universal implementation of the adapted UK version (SFP10-14UK) which brought together families identified as likely/not likely to experience/present challenges within a group setting.

DESIGN

Pragmatic cluster-randomised controlled effectiveness trial, with families as the unit of randomisation and embedded process and economic evaluations.

SETTING

The study took place in seven counties of Wales, UK.

PARTICIPANTS

715 families (919 parents/carers, 931 young people) were randomised.

INTERVENTIONS

Families randomised to the intervention arm received the SFP10-14 comprising seven weekly sessions. Families in intervention and control arms received existing services as normal.

OUTCOME MEASURES

Primary outcomes were the number of occasions young people reported drinking alcohol in the last 30 days; and drunkenness during the same period, dichotomised as 'never' and '1-2 times or more'. Secondary outcomes examined alcohol/tobacco/substance behaviours including: cannabis use; weekly smoking (validated by salivary cotinine measures); age of alcohol initiation; frequency of drinking >5 drinks in a row; frequency of different types of alcoholic drinks; alcohol-related problems. Retention: primary analysis included 746 young people (80.1%) (alcohol consumption) and 732 young people (78.6%) (drunkenness).

RESULTS

There was no evidence of statistically significant between-group differences 2 years after randomisation for primary outcomes (young people's alcohol consumption in the last 30 days adjusted OR=1.11, 95% CI 0.72 to 1.71, p=0.646; drunkenness in the last 30 days adjusted OR=1.46, 95% CI 0.83 to 2.55, p=0.185). There were no statistically significant between-group differences for other substance use outcomes, or those relating to well-being/stress, and emotional/behavioural problems.

CONCLUSIONS

Previous evidence of effectiveness was not replicated. Findings highlight the importance of evaluating interventions when they are adapted for new settings.

TRIAL REGISTRATION NUMBER

ISRCTN63550893.Cite Now.

Formulating causal questions and principled statistical answers

Although review papers on causal inference methods are now available, there is a lack of introductory overviews on what they can render and on the guiding criteria for choosing one particular method. This tutorial gives an overview in situations where an exposure of interest is set at a chosen baseline ("point exposure") and the target outcome arises at a later time point. We first phrase relevant causal questions and make a case for being specific about the possible exposure levels involved and the populations for which the question is relevant. Using the potential outcomes framework, we describe principled definitions of causal effects and of estimation approaches classified according to whether they invoke the no unmeasured confounding assumption (including outcome regression and propensity score-based methods) or an instrumental variable with added assumptions. We mainly focus on continuous outcomes and causal average treatment effects. We discuss interpretation, challenges, and potential pitfalls and illustrate application using a "simulation learner," that mimics the effect of various breastfeeding interventions on a child's later development. This involves a typical simulation component with generated exposure, covariate, and outcome data inspired by a randomized intervention study. The simulation learner further generates various (linked) exposure types with a set of possible values per observation unit, from which observed as well as potential outcome data are generated. It thus provides true values of several causal effects. R code for data generation and analysis is available on www.ofcaus.org, where SAS and Stata code for analysis is also provided.

G-estimation of structural nested mean models for competing risks data using pseudo-observations

This article provides methods of causal inference for competing risks data. The methods are formulated as structural nested mean models of causal effects directly related to the cumulative incidence function or subdistribution hazard, which reflect the survival experience of a subject in the presence of competing risks. The effect measures include causal risk differences, causal risk ratios, causal subdistribution hazard ratios, and causal effects of time-varying exposures. Inference is implemented by g-estimation using pseudo-observations, a technique to handle censoring. The finite-sample performance of the proposed estimators in simulated datasets and application to time-varying exposures in a cohort study of type 2 diabetes are also presented.

Boundary violations and adolescent drinking: Observational evidence that symbolic boundaries moderate social influence

Scholars of social influence can benefit from attending to symbolic boundaries. A common and influential way to understand symbolic boundaries is as widely shared understandings of what types of behaviors, tastes, and opinions are appropriate for different kinds of people. Scholars following this understanding have mostly focused on how people judge others and how symbolic boundaries align with and thus reproduce social differences. Although this work has been impressive, I argue that it might miss important ways in which symbolic boundaries become effective in everyday social life. I therefore develop an understanding of how symbolic boundaries affect people's ideas and decisions about themselves and their own behavior. Based on this, I argue that focusing on boundary violations-that is, what happens if people express opinions or enact behavior that contravenes what is considered (in)appropriate for people like them-might offer an important way to understand how symbolic boundaries initiate and shape cultural and social change. Using data from Add Health, I demonstrate the utility of this line of argument and show that boundary violations play an important role in channeling social influence. Conservative/Evangelical Protestants and to a lesser degree Catholics, but not Mainline Protestants are highly influenced by the drinking of co-religionists. I consider the implications for cultural sociology.

Using instrumental variables to estimate the attributable fraction

In order to design efficient interventions aimed to improve public health, policy makers need to be provided with reliable information of the health burden of different risk factors. For this purpose, we are interested in the proportion of cases that could be prevented had some harmful exposure been eliminated from the population, i.e. the attributable fraction. The attributable fraction is a causal measure; thus, to estimate the attributable fraction from observational data, we have to make appropriate adjustment for confounding. However, some confounders may be unobserved, or even unknown to the investigator. A possible solution to this problem is to use instrumental variable analysis. In this work, we present how the attributable fraction can be estimated with instrumental variable methods based on the two-stage estimator or the G-estimator. One situation when the problem of unmeasuredconfounding may be particularly severe is when assessing the effect of low educational qualifications on coronary heart disease. By using Mendelian randomization, a special case of instrumental variable analysis, it has been claimed that low educational qualifications is a causal risk factor for coronary heart disease. We use Mendelian randomization to estimate the causal risk ratio and causal odds ratio of low educational qualifications as a risk factor for coronary heart disease with data from the UK Biobank. We compare the two-stage and G-estimator as well as the attributable fraction based on the two estimators. The plausibility of drawing causal conclusion in this analysis is thoroughly discussed and alternative genetic instrumental variables are tested.

A SEMIPARAMETRIC MODELING APPROACH USING BAYESIAN ADDITIVE REGRESSION TREES WITH AN APPLICATION TO EVALUATE HETEROGENEOUS TREATMENT EFFECTS

Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interactions among covariates. We extend BART to a semiparametric regression framework in which the conditional expectation of an outcome is a function of treatment, its effect modifiers, and confounders. The confounders are allowed to have unspecified functional form, while treatment and effect modifiers that are directly related to the research question are given a linear form. The result is a Bayesian semiparametric linear regression model where the posterior distribution of the parameters of the linear part can be interpreted as in parametric Bayesian regression. This is useful in situations where a subset of the variables are of substantive interest and the others are nuisance variables that we would like to control for. An example of this occurs in causal modeling with the structural mean model (SMM). Under certain causal assumptions, our method can be used as a Bayesian SMM. Our methods are demonstrated with simulation studies and an application to dataset involving adults with HIV/Hepatitis C coinfection who newly initiate antiretroviral therapy. The methods are available in an R package called semibart.

A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting

In this paper we present a framework to do estimation in a structural Cox model when there may be unobserved confounding. The model is phrased in terms of a selection bias function and a baseline model that describes how covariates affect the survival time in a scenario without exposure. In this way model congeniality is ensured. The method uses an instrumental variable. Interestingly, the formulated model turns out to have similarities to the so-called Cox-Aalen survival model for the observed data. We exploit this to enhance estimation of the unknown parameters. This also allows us to derive large sample properties of the proposed estimator.

Survivor bias in Mendelian randomization analysis

Mendelian randomization studies employ genotypes as experimental handles to infer the effect of genetically modified exposures (e.g. vitamin D exposure) on disease outcomes (e.g. mortality). The statistical analysis of these studies makes use of the standard instrumental variables framework. Many of these studies focus on elderly populations, thereby ignoring the problem of left truncation, which arises due to the selection of study participants being conditional upon surviving up to the time of study onset. Such selection, in general, invalidates the assumptions on which the instrumental variables analysis rests. We show that Mendelian randomization studies of adult or elderly populations will therefore, in general, return biased estimates of the exposure effect when the considered genotype affects mortality; in contrast, standard tests of the causal null hypothesis that the exposure does not affect the mortality rate remain unbiased, even when they ignore this problem of left truncation. To eliminate "survivor bias" or "truncation bias" from the effect of exposure on mortality, we next propose various simple strategies under a semi-parametric additive hazard model. We examine the performance of the proposed methods in simulation studies and use them to infer the effect of vitamin D on all-cause mortality based on the Monica10 study with the genetic variant filaggrin as instrumental variable.

Protocol for a double-blind placebo-controlled trial to evaluate the efficacy of probiotics in reducing antibiotics for infection in care home residents: the Probiotics to Reduce Infections iN CarE home reSidentS (PRINCESS) trial

INTRODUCTION

Care home residents are at increased risk of infections and antibiotic prescription. Reduced antibiotic use from fewer infections would improve quality of life. The Probiotics to Reduce Infections iN CarE home reSidentS (PRINCESS) trial aims to determine the efficacy and investigate mechanisms of daily probiotics on antibiotic use and incidence of infections in care home residents.

METHODS AND ANALYSIS

PRINCESS is a double-blind, individually randomised, placebo-controlled trial that will assess the effect of a daily oral probiotic combination of Lactobacillus rhamnosus, GG (LGG) and Bifidobacterium animalis subsp. lactis, BB-12 (BB-12) on cumulative antibiotic administration days (CAADs) (primary outcome) for infection in up to 330 care home residents aged ≥65 years over up to 12 months. Secondary outcomes include: Infection: Total number of days of antibiotic administration for each infection type (respiratory tract infection, urinary tract infection, gastrointestinal infection, unexplained fever and other); number, site, duration of infection; estimation of incidence and duration of diarrhoea and antibiotic-associated diarrhoea; Stool microbiology: Clostridium difficile infection; Gram-negative Enterobacteriaceae and vancomycin-resistant enterococci; LGG and BB-12. Oral microbiology: Candida spp. Health and well-being: Self and/or proxy health-related quality of life EQ5D (5 L); self-and/or proxy-reported ICEpop CAPability measure for older people. Hospitalisations: number and duration of all-cause hospital stays. Mortality: deaths. Mechanistic immunology outcomes: influenza vaccine efficacy (haemagglutination inhibition assay and antibody titres); full blood count and immune cell phenotypes, plasma cytokines and chemokines; cytokine and chemokine response in whole blood stimulated ex vivo by toll-like receptor 2 and 4 agonists; monocyte and neutrophil phagocytosis of Escherichia coli; serum vitamin D.

ETHICS AND DISSEMINATION

Ethics approval is from the Wales Research Ethics Committee 3. Findings will be disseminated through peer-reviewed journals and conferences; results will be of interest to patient and policy stakeholders.

TRIAL REGISTRATION NUMBER

ISRCTN16392920; Pre-results.

Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail

In the current era, with increasing availability of results from genetic association studies, finding genetic instruments for inferring causality in observational epidemiology has become apparently simple. Mendelian randomisation (MR) analyses are hence growing in popularity and, in particular, methods that can incorporate multiple instruments are being rapidly developed for these applications. Such analyses have enormous potential, but they all rely on strong, different, and inherently untestable assumptions. These have to be clearly stated and carefully justified for every application in order to avoid conclusions that cannot be replicated. In this article, we review the instrumental variable assumptions and discuss the popular linear additive structural model. We advocate the use of tests for the null hypothesis of ‘no causal effect’ and calculation of the bounds for a causal effect, whenever possible, as these do not rely on parametric modelling assumptions. We clarify the difference between a randomised trial and an MR study and we comment on the importance of validating instruments, especially when considering them for joint use in an analysis. We urge researchers to stand by their convictions, if satisfied that the relevant assumptions hold, and to interpret their results causally since that is the only reason for performing an MR analysis in the first place.

Adjustment for treatment changes in epilepsy trials: A comparison of causal methods for time-to-event outcomes

BACKGROUND

When trials are subject to departures from randomised treatment, simple statistical methods that aim to estimate treatment efficacy, such as per protocol or as treated analyses, typically introduce selection bias. More appropriate methods to adjust for departure from randomised treatment are rarely employed, primarily due to their complexity and unfamiliarity. We demonstrate the use of causal methodologies for the production of estimands with valid causal interpretation for time-to-event outcomes in the analysis of a complex epilepsy trial, as an example to guide non-specialist analysts undertaking similar analyses.

METHODS

Two causal methods, the structural failure time model and inverse probability of censoring weighting, are adapted to allow for skewed time-varying confounders, competing reasons for treatment changes and a complicated time to remission outcome. We demonstrate the impact of various factors: choice of method (structural failure time model versus inverse probability of censoring weighting), model for inverse probability of censoring weighting (pooled logistic regression versus Cox models), time interval (for creating panel data for time-varying confounders and outcome), choice of confounders and (in pooled logistic regression) use of splines to estimate underlying risk.

RESULTS

The structural failure time model could adjust for switches between trial treatments but had limited ability to adjust for the other treatment changes that occurred in this epilepsy trial. Inverse probability of censoring weighting was able to adjust for all treatment changes and demonstrated very similar results with Cox and pooled logistic regression models. Accounting for increasing numbers of time-varying confounders and reasons for treatment change suggested a more pronounced advantage of the control treatment than that obtained using intention to treat.

CONCLUSIONS

In a complex trial featuring a remission outcome, underlying assumptions of the structural failure time model are likely to be violated, and inverse probability of censoring weighting may provide the most useful option, assuming availability of appropriate data and sufficient sample sizes. Recommendations are provided for analysts when considering which of these methods should be applied in a given trial setting.

Diagnostics for Pleiotropy in Mendelian Randomization Studies: Global and Individual Tests for Direct Effects

Diagnosing pleiotropy is critical for assessing the validity of Mendelian randomization (MR) analyses. The popular MR-Egger method evaluates whether there is evidence of bias-generating pleiotropy among a set of candidate genetic instrumental variables. In this article, we propose a statistical method-global and individual tests for direct effects (GLIDE)-for systematically evaluating pleiotropy among the set of genetic variants (e.g., single nucleotide polymorphisms (SNPs)) used for MR. As a global test, simulation experiments suggest that GLIDE is nearly uniformly more powerful than the MR-Egger method. As a sensitivity analysis, GLIDE is capable of detecting outliers in individual variant-level pleiotropy, in order to obtain a refined set of genetic instrumental variables. We used GLIDE to analyze both body mass index and height for associations with colorectal cancer risk in data from the Genetics and Epidemiology of Colorectal Cancer Consortium and the Colon Cancer Family Registry (multiple studies). Among the body mass index-associated SNPs and the height-associated SNPs, several individual variants showed evidence of pleiotropy. Removal of these potentially pleiotropic SNPs resulted in attenuation of respective estimates of the causal effects. In summary, the proposed GLIDE method is useful for sensitivity analyses and improves the validity of MR.

A Literature Survey and Experimental Evaluation of the State-of-the-Art in Uplift Modeling: A Stepping Stone Toward the Development of Prescriptive Analytics

Prescriptive analytics extends on predictive analytics by allowing to estimate an outcome in function of control variables, allowing as such to establish the required level of control variables for realizing a desired outcome. Uplift modeling is at the heart of prescriptive analytics and aims at estimating the net difference in an outcome resulting from a specific action or treatment that is applied. In this article, a structured and detailed literature survey on uplift modeling is provided by identifying and contrasting various groups of approaches. In addition, evaluation metrics for assessing the performance of uplift models are reviewed. An experimental evaluation on four real-world data sets provides further insight into their use. Uplift random forests are found to be consistently among the best performing techniques in terms of the Qini and Gini measures, although considerable variability in performance across the various data sets of the experiments is observed. In addition, uplift models are frequently observed to be unstable and display a strong variability in terms of performance across different folds in the cross-validation experimental setup. This potentially threatens their actual use for business applications. Moreover, it is found that the available evaluation metrics do not provide an intuitively understandable indication of the actual use and performance of a model. Specifically, existing evaluation metrics do not facilitate a comparison of uplift models and predictive models and evaluate performance either at an arbitrary cutoff or over the full spectrum of potential cutoffs. In conclusion, we highlight the instability of uplift models and the need for an application-oriented approach to assess uplift models as prime topics for further research.

Estimating the Effect of School Water, Sanitation, and Hygiene Improvements on Pupil Health Outcomes

Supplemental Digital Content is available in the text.

We conducted a cluster-randomized water, sanitation, and hygiene trial in 185 schools in Nyanza province, Kenya. The trial, however, had imperfect school-level adherence at many schools. The primary goal of this study was to estimate the causal effects of school-level adherence to interventions on pupil diarrhea and soil-transmitted helminth infection.

Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies

Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors.

Estimating Moderated Causal Effects with Time-varying Treatments and Time-varying Moderators: Structural Nested Mean Models and Regression with Residuals

Individuals differ in how they respond to a particular treatment or exposure, and social scientists are often interested in understanding how treatment effects are moderated by observed characteristics of individuals. Effect moderation occurs when individual covariates dampen or amplify the effect of some exposure. This article focuses on estimating moderated causal effects in longitudinal settings where both the treatment and effect moderator vary over time. Effect moderation is typically examined using covariate by treatment interactions in regression analyses, but in the longitudinal setting, this approach may be problematic because time-varying moderators of future treatment may be affected by prior treatment-for example, moderators may also be mediators-and naively conditioning on an outcome of treatment in a conventional regression model can lead to bias. This article introduces to sociology moderated intermediate causal effects and the structural nested mean model for analyzing effect moderation in the longitudinal setting. It discusses problems with conventional regression and presents a new approach to estimation that avoids these problems (regression-with-residuals). The method is illustrated using longitudinal data from the PSID to examine whether the effects of time-varying exposures to poor neighborhoods on the risk of adolescent childbearing are moderated by time-varying family income.

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.

The use of randomisation-based efficacy estimators in non-inferiority trials

BACKGROUND

In a non-inferiority (NI) trial, analysis based on the intention-to-treat (ITT) principle is anti-conservative, so current guidelines recommend analysing on a per-protocol (PP) population in addition. However, PP analysis relies on the often implausible assumption of no confounders. Randomisation-based efficacy estimators (RBEEs) allow for treatment non-adherence while maintaining a comparison of randomised groups. Fischer et al. have developed an approach for estimating RBEEs in randomised trials with two active treatments, a common feature of NI trials. The aim of this paper was to demonstrate the use of RBEEs in NI trials using this approach, and to appraise the feasibility of these estimators as the primary analysis in NI trials.

METHODS

Two NI trials were used. One comparing two different dosing regimens for the maintenance of remission in people with ulcerative colitis (CODA), and the other comparing an orally administered treatment to an intravenously administered treatment in preventing skeletal-related events in patients with bone metastases from breast cancer (ZICE). Variables that predicted adherence in each of the trial arms, and were also independent of outcome, were sought in each of the studies. Structural mean models (SMMs) were fitted that conditioned on these variables, and the point estimates and confidence intervals compared to that found in the corresponding ITT and PP analyses.

RESULTS

In the CODA study, no variables were found that differentially predicted treatment adherence while remaining independent of outcome. The SMM, using standard methodology, moved the point estimate closer to 0 (no difference between arms) compared to the ITT and PP analyses, but the confidence interval was still within the NI margin, indicating that the conclusions drawn would remain the same. In the ZICE study, cognitive functioning as measured by the corresponding domain of the QLQ-C30, and use of chemotherapy at baseline were both differentially associated with adherence while remaining independent of outcome. However, while the SMM again moved the point estimate closer to 0, the confidence interval was wide, overlapping with any NI margin that could be justified.

CONCLUSION

Deriving RBEEs in NI trials with two active treatments can provide a randomisation-respecting estimate of treatment efficacy that accounts for treatment adherence, is straightforward to implement, but requires thorough planning during the design stage of the study to ensure that strong baseline predictors of treatment are captured. Extension of the approach to handle nonlinear outcome variables is also required.

TRIAL REGISTRATION

The CODA study: ClinicalTrials.gov, identifier: NCT00708656 . Registered on 8 April 2008. The ZICE study trial: ClinicalTrials.gov, identifier: NCT00326820 . Registered on 16 May 2006.

Instrumental variable analysis of multiplicative models with potentially invalid instruments

Instrumental variable (IV) methods have potential to consistently estimate the causal effect of an exposure on an outcome in the presence of unmeasured confounding. However, validity of IV methods relies on strong assumptions, some of which cannot be conclusively verified from observational data. One such assumption is that the effect of the proposed instrument on the outcome is completely mediated by the exposure. We consider the situation where this assumption is violated, but the remaining IV assumptions hold; that is, the proposed IV (1) is associated with the exposure and (2) has no unmeasured causes in common with the outcome. We propose a method to estimate multiplicative structural mean models of binary outcomes in this scenario in the presence of unmeasured confounding. We also extend the method to address multiple scenarios, including mediation analysis. The method adapts the asymptotically efficient G-estimation approach that was previously proposed for additive structural mean models, and it can be carried out using off-the-shelf software for generalized method of moments. Monte Carlo simulation studies show that the method has low bias and accurate coverage. We applied the method to a case study of circulating vitamin D and depressive symptoms using season of blood collection as a (potentially invalid) instrumental variable. Potential applications of the proposed method include randomized intervention studies as well as Mendelian randomization studies with genetic variants that affect multiple phenotypes, possibly including the outcome. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Estimating treatment effects from randomized clinical trials with noncompliance and loss to follow-up: the role of instrumental variable methods

Perfectly implemented randomized clinical trials, particularly of complex interventions, are extremely rare. Almost always they are characterized by imperfect adherence to the randomly allocated treatment and variable amounts of missing outcome data. Here we start by describing a wide variety of examples and then introduce instrumental variable methods for the analysis of such trials. We concentrate mainly on situations in which compliance is all or nothing (either the patient receives the allocated treatment or they do not - in the latter case they may receive no treatment or a treatment other than the one allocated). The main purpose of the review is to illustrate the use of latent class (finite mixture) models, using maximum likelihood, for complier-average causal effect estimation under varying assumptions concerning the mechanism of the missing outcome data.

Statistical Reasoning and Methods in Epidemiology to Promote Individualized Health: In Celebration of the 100th Anniversary of the Johns Hopkins Bloomberg School of Public Health

Epidemiology is concerned with determining the distribution and causes of disease. Throughout its history, epidemiology has drawn upon statistical ideas and methods to achieve its aims. Because of the exponential growth in our capacity to measure and analyze data on the underlying processes that define each person's state of health, there is an emerging opportunity for population-based epidemiologic studies to influence health decisions made by individuals in ways that take into account the individuals' characteristics, circumstances, and preferences. We refer to this endeavor as "individualized health." The present article comprises 2 sections. In the first, we describe how graphical, longitudinal, and hierarchical models can inform the project of individualized health. We propose a simple graphical model for informing individual health decisions using population-based data. In the second, we review selected topics in causal inference that we believe to be particularly useful for individualized health. Epidemiology and biostatistics were 2 of the 4 founding departments in the world's first graduate school of public health at Johns Hopkins University, the centennial of which we honor. This survey of a small part of the literature is intended to demonstrate that the 2 fields remain just as inextricably linked today as they were 100 years ago.

Comparing treatment policies with assistance from the structural nested mean model

Treatment policies, also known as dynamic treatment regimes, are sequences of decision rules that link the observed patient history with treatment recommendations. Multiple, plausible, treatment policies are frequently constructed by researchers using expert opinion, theories, and reviews of the literature. Often these different policies represent competing approaches to managing an illness. Here, we develop an "assisted estimator" that can be used to compare the mean outcome of competing treatment policies. The term "assisted" refers to the fact estimators from the Structural Nested Mean Model, a parametric model for the causal effect of treatment at each time point, are used in the process of estimating the mean outcome. This work is motivated by our work on comparing the mean outcome of two competing treatment policies using data from the ExTENd study in alcohol dependence.

New methods for treatment effect calibration, with applications to non-inferiority trials

In comparative effectiveness research, it is often of interest to calibrate treatment effect estimates from a clinical trial to a target population that differs from the study population. One important application is an indirect comparison of a new treatment with a placebo control on the basis of two separate randomized clinical trials: a non-inferiority trial comparing the new treatment with an active control and a historical trial comparing the active control with placebo. The available methods for treatment effect calibration include an outcome regression (OR) method based on a regression model for the outcome and a weighting method based on a propensity score (PS) model. This article proposes new methods for treatment effect calibration: one based on a conditional effect (CE) model and two doubly robust (DR) methods. The first DR method involves a PS model and an OR model, is asymptotically valid if either model is correct, and attains the semiparametric information bound if both models are correct. The second DR method involves a PS model, a CE model, and possibly an OR model, is asymptotically valid under the union of the PS and CE models, and attains the semiparametric information bound if all three models are correct. The various methods are compared in a simulation study and applied to recent clinical trials for treating human immunodeficiency virus infection.

A review of instrumental variable estimators for Mendelian randomization

Instrumental variable analysis is an approach for obtaining causal inferences on the effect of an exposure (risk factor) on an outcome from observational data. It has gained in popularity over the past decade with the use of genetic variants as instrumental variables, known as Mendelian randomization. An instrumental variable is associated with the exposure, but not associated with any confounder of the exposure–outcome association, nor is there any causal pathway from the instrumental variable to the outcome other than via the exposure. Under the assumption that a single instrumental variable or a set of instrumental variables for the exposure is available, the causal effect of the exposure on the outcome can be estimated. There are several methods available for instrumental variable estimation; we consider the ratio method, two-stage methods, likelihood-based methods, and semi-parametric methods. Techniques for obtaining statistical inferences and confidence intervals are presented. The statistical properties of estimates from these methods are compared, and practical advice is given about choosing a suitable analysis method. In particular, bias and coverage properties of estimators are considered, especially with weak instruments. Settings particularly relevant to Mendelian randomization are prioritized in the paper, notably the scenario of a continuous exposure and a continuous or binary outcome.

Structural Nested Mean Models to Estimate the Effects of Time-Varying Treatments on Clustered Outcomes

In assessing the efficacy of a time-varying treatment structural nested models (SNMs) are useful in dealing with confounding by variables affected by earlier treatments. These models often consider treatment allocation and repeated measures at the individual level. We extend SNMMs to clustered observations with time-varying confounding and treatments. We demonstrate how to formulate models with both cluster- and unit-level treatments and show how to derive semiparametric estimators of parameters in such models. For unit-level treatments, we consider interference, namely the effect of treatment on outcomes in other units of the same cluster. The properties of estimators are evaluated through simulations and compared with the conventional GEE regression method for clustered outcomes. To illustrate our method, we use data from the treatment arm of a glaucoma clinical trial to compare the effectiveness of two commonly used ocular hypertension medications.

Mendelian randomization studies for a continuous exposure under case-control sampling

In this article, we assess the impact of case-control sampling on mendelian randomization analyses with a dichotomous disease outcome and a continuous exposure. The 2-stage instrumental variables (2SIV) method uses the prediction of the exposure given genotypes in the logistic regression for the outcome and provides a valid test and an approximation of the causal effect. Under case-control sampling, however, the first stage of the 2SIV procedure becomes a secondary trait association, which requires proper adjustment for the biased sampling. Through theoretical development and simulations, we compare the naïve estimator, the inverse probability weighted estimator, and the maximum likelihood estimator for the first-stage association and, more importantly, the resulting 2SIV estimates of the causal effect. We also include in our comparison the causal odds ratio estimate derived from structural mean models by double-logistic regression. Our results suggest that the naïve estimator is substantially biased under the alternative, yet it remains unbiased under the null hypothesis of no causal effect; the maximum likelihood estimator yields smaller variance and mean squared error than other estimators; and the structural mean models estimator delivers the smallest bias, though generally incurring a larger variance and sometimes having issues in algorithm stability and convergence.

Adherence-adjusted estimates of benefits and harms from treatment with amoxicillin for LRTI: secondary analysis of a 12-country randomised placebo-controlled trial using randomisation-based efficacy estimators

OBJECTIVES

Estimate the efficacy of amoxicillin for acute uncomplicated lower-respiratory-tract infection (LRTI) in primary care and demonstrate the use of randomisation-based efficacy estimators.

DESIGN

Secondary analysis of a two-arm individually-randomised placebo-controlled trial.

SETTING

Primary care practices in 12 European countries.

PARTICIPANTS

Patients aged 18 or older consulting with an acute LRTI in whom pneumonia was not suspected by the clinician.

INTERVENTIONS

Amoxicillin (two 500 mg tablets three times a day for 7 days) or matched placebo.

MAIN OUTCOME MEASURES

Clinician-rated symptom severity between days 2-4; new/worsening symptoms and presence of side effects at 4-weeks. Adherence was captured using self-report and tablet counts.

RESULTS

2061 participants were randomised to the amoxicillin or placebo group. On average, 88% of the prescribed amoxicillin was taken. The original analysis demonstrated small increases in both benefits and harms from amoxicillin. Minor improvements in the benefits of amoxicillin were observed when an adjustments for adherence were made (mean difference in symptom severity -0.08, 95% CI -0.17 to 0.01, OR for new/worsening symptoms 0.81, 95% CI 0.66 to 0.98) as well as minor increases in harms (OR for side effects 1.32, 95% CI 1.12 to 1.57).

CONCLUSIONS

Adherence to amoxicillin was high, and the findings from the original analysis were robust to non-adherence. Participants consulting to primary care with an acute uncomplicated LRTI can on average expect minor improvements in outcome from taking amoxicillin. However, they are also at an increased risk of experiencing side effects.

TRIAL REGISTRATION NUMBERS

Eudract-CT 2007-001586-15 and ISRCTN52261229. The trial was registered at EudraCT in 2007 due to an administrative misunderstanding that EudraCT was a suitable registry--which it was not in 2007, but has become since. On discovery of this error, the trial was also registered at ISRCTN (January 2009). Trial procedures did not change between the two registrations.

Testing concordance of instrumental variable effects in generalized linear models with application to Mendelian randomization

Instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies. Built on structural mean models, there has been considerable work recently developed for consistent estimation of causal relative risk and causal odds ratio. Such models can sometimes suffer from identification issues for weak instruments. This hampered the applicability of Mendelian randomization analysis in genetic epidemiology. When there are multiple genetic variants available as instrumental variables, and causal effect is defined in a generalized linear model in the presence of unmeasured confounders, we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome, as a means to test the causal effect. We show that a class of generalized least squares estimators provide valid and consistent tests of causality. For causal effect of a continuous exposure on a dichotomous outcome in logistic models, the proposed estimators are shown to be asymptotically conservative. When the disease outcome is rare, such estimators are consistent because of the log-linear approximation of the logistic function. Optimality of such estimators relative to the well-known two-stage least squares estimator and the double-logistic structural mean model is further discussed.

Allowing for non-adherence to treatment in a randomized controlled trial of two antidepressants (citalopram versus reboxetine): an example from the GENPOD trial

BACKGROUND

Meta-analyses suggest that reboxetine may be less effective than other antidepressants. Such comparisons may be biased by lower adherence to reboxetine and subsequent handling of missing outcome data. This study illustrates how to adjust for differential non-adherence and hence derive an unbiased estimate of the efficacy of reboxetine compared with citalopram in primary care patients with depression.

METHOD

A structural mean modelling (SMM) approach was used to generate adherence-adjusted estimates of the efficacy of reboxetine compared with citalopram using GENetic and clinical Predictors Of treatment response in Depression (GENPOD) trial data. Intention-to-treat (ITT) analyses were performed to compare estimates of effectiveness with results from previous meta-analyses.

RESULTS

At 6 weeks, 92% of those randomized to citalopram were still taking their medication, compared with 72% of those randomized to reboxetine. In ITT analysis, there was only weak evidence that those on reboxetine had a slightly worse outcome than those on citalopram [adjusted difference in mean Beck Depression Inventory (BDI) scores: 1.19, 95% confidence interval (CI) -0.52 to 2.90, p = 0.17]. There was no evidence of a difference in efficacy when differential non-adherence was accounted for using the SMM approach for mean BDI (-0.29, 95% CI -3.04 to 2.46, p = 0.84) or the other mental health outcomes.

CONCLUSIONS

There was no evidence of a difference in the efficacy of reboxetine and citalopram when these drugs are taken and tolerated by depressed patients. The SMM approach can be implemented in standard statistical software to adjust for differential non-adherence and generate unbiased estimates of treatment efficacy for comparisons of two (or more) active interventions.

Time-varying effect moderation using the structural nested mean model: estimation using inverse-weighted regression with residuals

This article considers the problem of examining time-varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time-varying causal effects of interest in a conditional mean model for a continuous response given time-varying treatments and moderators. We present an easy-to-use estimator of the SNMM that combines an existing regression-with-residuals (RR) approach with an inverse-probability-of-treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time-varying causal effects if the time-varying moderators are also the sole time-varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time-varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time-varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time-varying moderators and time-varying confounders. We illustrate the methodology in a case study to assess if time-varying substance use moderates treatment effects on future substance use.

Estimating the efficacy of an interstitial cystitis/painful bladder syndrome medication in a randomized trial with both non-adherence and loss to follow-up

We are motivated by a randomized clinical trial evaluating the efficacy of amitriptyline for the treatment of interstitial cystitis and painful bladder syndrome in treatment-naïve patients. In the trial, both the non-adherence rate and the rate of loss to follow-up are fairly high. To estimate the effect of the treatment received on the outcome, we use the generalized structural mean model (GSMM), originally proposed to deal with non-adherence, to adjust for both non-adherence and loss to follow-up. In the model, loss to follow-up is handled by weighting the estimation equations for GSMM with one over the probability of not being lost to follow-up, estimated using a logistic regression model. We re-analyzed the data from the trial and found a possible benefit of amitriptyline when administered at a high-dose level.

A Semiparametric Bivariate Probit Model for Joint Modeling of Outcomes in STEMI Patients

In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient's condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.

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.

Causal inference in paired two-arm experimental studies under noncompliance with application to prognosis of myocardial infarction

Motivated by a study about prompt coronary angiography in myocardial infarction, we propose a method to estimate the causal effect of a treatment in two-arm experimental studies with possible noncompliance in both treatment and control arms. We base the method on a causal model for repeated binary outcomes (before and after the treatment), which includes individual covariates and latent variables for the unobserved heterogeneity between subjects. Moreover, given the type of noncompliance, the model assumes the existence of three subpopulations of subjects: compliers, never-takers, and always-takers. We estimate the model using a two-step estimator: at the first step, we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates; at the second step, we estimate the causal effects through a conditional logistic method, the implementation of which depends on the results from the first step. The estimator is approximately consistent and, under certain circumstances, exactly consistent. We provide evidence that the bias is negligible in relevant situations. We compute standard errors on the basis of a sandwich formula. The application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years, with a log-odds of about  - 2. Given that noncompliance is significant for patients being given the treatment because of high-risk conditions, classical estimators fail to detect, or at least underestimate, this effect.