Dealing with time-dependent exposures and confounding when defining and estimating attributable fractions-Revisiting estimands and estimators.

The population-attributable fraction (PAF) is commonly interpreted as the proportion of events that can be ascribed to a certain exposure in a certain population. Its estimation is sensitive to common forms of time-dependent bias in the face of a time-dependent exposure. Predominant estimation approaches based on multistate modeling fail to fully eliminate such bias and, as a result, do not permit a causal interpretation, even in the absence of confounding. While recently proposed multistate modeling approaches can successfully eliminate residual time-dependent bias, and moreover succeed to adjust for time-dependent confounding by means of inverse probability of censoring weighting, inadequate application, and misinterpretation prevails in the medical literature. In this paper, we therefore revisit recent work on previously proposed PAF estimands and estimators in settings with time-dependent exposures and competing events and extend this work in several ways. First, we critically revisit the interpretation and applied terminology of these estimands. Second, we further formalize the assumptions under which a causally interpretable PAF estimand can be identified and provide analogous weighting-based representations of the identifying functionals of other proposed estimands. This representation aims to enhance the applied statistician's understanding of different sources of bias that may arise when the aim is to obtain a valid estimate of a causally interpretable PAF. To illustrate and compare these representations, we present a real-life application to observational data from the Ghent University Hospital ICUs to estimate the fraction of ICU deaths attributable to hospital-acquired infections.

Evaluation and comparison of covariate balance metrics in studies with time-dependent confounding.

Marginal structural models have been increasingly used by analysts in recent years to account for confounding bias in studies with time-varying treatments. The parameters of these models are often estimated using inverse probability of treatment weighting. To ensure that the estimated weights adequately control confounding, it is possible to check for residual imbalance between treatment groups in the weighted data. Several balance metrics have been developed and compared in the cross-sectional case but have not yet been evaluated and compared in longitudinal studies with time-varying treatment. We have first extended the definition of several balance metrics to the case of a time-varying treatment, with or without censoring. We then compared the performance of these balance metrics in a simulation study by assessing the strength of the association between their estimated level of imbalance and bias. We found that the Mahalanobis balance performed best. Finally, the method was illustrated for estimating the cumulative effect of statins exposure over one year on the risk of cardiovascular disease or death in people aged 65 and over in population-wide administrative data. This illustration confirms the feasibility of employing our proposed metrics in large databases with multiple time-points.

Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models.

Longitudinal observational data on patients can be used to investigate causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights (IPTW) (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, and involves creating a sequence of "trials" from new time origins and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment assignment at the start of each "trial" (initiator or noninitiator), which is accounted for using inverse probability of censoring weights. The analysis uses data combined across trials. We show that the sequential trials approach can estimate the parameters of a particular MSM. The causal estimand that we focus on is the marginal risk difference between the sustained treatment strategies of "always treat" vs "never treat." We compare how the sequential trials approach and MSM-IPTW estimate this estimand, and discuss their assumptions and how data are used differently. The performance of the two approaches is compared in a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at later time points and relies on modelling assumptions. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

Metformin Treatment Among Men With Diabetes and the Risk of Prostate Cancer: A Population-Based Historical Cohort Study.

There is conflicting evidence regarding the association between metformin treatment and prostate cancer risk in diabetic men. We investigated this association in a population-based Israeli cohort of 145,617 men aged 21-89 years with incident diabetes who were followed over the period 2002-2012. We implemented a time-dependent covariate Cox model, using weighted cumulative exposure to relate metformin history to prostate cancer risk, adjusting for use of other glucose-lowering medications, age, ethnicity, and socioeconomic status. To adjust for time-varying glucose control variables, we used inverse probability weighting of a marginal structural model. With 666,553 person-years of follow-up, 1,592 men were diagnosed with prostate cancer. Metformin exposure in the previous year was positively associated with prostate cancer risk (per defined daily dose; without adjustment for glucose control, hazard ratio (HR) = 1.53 (95% confidence interval (CI): 1.19, 1.96); with adjustment, HR = 1.42 (95% CI: 1.04, 1.94)). However, exposure during the previous 2-7 years was negatively associated with risk (without adjustment for glucose control, HR = 0.58 (95% CI: 0.37, 0.93); with adjustment, HR = 0.60 (95% CI: 0.33, 1.09)). These positive and negative associations with previous-year and earlier metformin exposure, respectively, need to be confirmed and better understood.

Bias and Type I error Control in Correcting Treatment Effect for Treatment Switching Using Marginal Structural Models in Phase III Oncology Trials.

This research focuses on the bias and type I error control issues when the marginal structural models (MSMs) are applied to evaluate the causal survival benefits of active intervention versus control in randomized clinical trials (RCTs) with treatment switching after disease progression. When MSMs are applied in the RCT setting, the question of interest, model specifications, strategies for type I error control, bias reduction, etc. differ somewhat from those for observational studies. This manuscript discusses the approaches used to accommodate these differences. Through Monte Carlo simulations and a case study, our research demonstrates that, with sufficient attention paid to issues applicable to RCTs in particular, MSMs may perform better than the inverse probability of censoring weighting (IPCW) method in analyzing the survival endpoint in RCTs with treatment switching because more information is used by the MSM.

A treatment-specific marginal structural Cox model for the effect of treatment discontinuation.

Patients taking a prescribed medication often discontinue their treatment; however, this may negatively impact their health outcomes. If doctors had statistical evidence that discontinuing some prescribed medication shortened, on average, the time to a clinical event (e.g., death), they could use that knowledge to encourage their patients to stay on the prescribed treatment. We describe a treatment-specific marginal structural Cox model for estimation of the causal effect of treatment discontinuation on a survival endpoint. The effect of treatment discontinuation is quantified by the hazard ratio of the event hazard rate had the population followed the regime "take treatment a until it is discontinued at some time ν ," versus the event hazard rate had the population never discontinued treatment a . Valid causal analysis requires control for treatment confounding, regime confounding, and censoring due to regime violation. We propose new inverse probability of regime compliance weights to address the three issues simultaneously. We apply the framework to data from the Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) study. Patients from this study are treated with one of two types of oral anticoagulants (OACs). We test whether the causal effect of treatment discontinuation differs by type of OAC, and we also estimate the size and direction of the effect. We find evidence that OAC discontinuation increases the hazard for certain events, but we do not find evidence that this effect differs by treatment.

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.

Exploiting nonsystematic covariate monitoring to broaden the scope of evidence about the causal effects of adaptive treatment strategies.

In studies based on electronic health records (EHR), the frequency of covariate monitoring can vary by covariate type, across patients, and over time, which can limit the generalizability of inferences about the effects of adaptive treatment strategies. In addition, monitoring is a health intervention in itself with costs and benefits, and stakeholders may be interested in the effect of monitoring when adopting adaptive treatment strategies. This paper demonstrates how to exploit nonsystematic covariate monitoring in EHR-based studies to both improve the generalizability of causal inferences and to evaluate the health impact of monitoring when evaluating adaptive treatment strategies. Using a real world, EHR-based, comparative effectiveness research (CER) study of patients with type II diabetes mellitus, we illustrate how the evaluation of joint dynamic treatment and static monitoring interventions can improve CER evidence and describe two alternate estimation approaches based on inverse probability weighting (IPW). First, we demonstrate the poor performance of the standard estimator of the effects of joint treatment-monitoring interventions, due to a large decrease in data support and concerns over finite-sample bias from near-violations of the positivity assumption (PA) for the monitoring process. Second, we detail an alternate IPW estimator using a no direct effect assumption. We demonstrate that this estimator can improve efficiency but at the potential cost of increase in bias from violations of the PA for the treatment process.

Accounting for selection bias due to death in estimating the effect of wealth shock on cognition for the Health and Retirement Study.

The Health and Retirement Study (HRS) is a longitudinal study of U.S. adults enrolled at age 50 and older. We were interested in investigating the effect of a sudden large decline in wealth on the cognitive ability of subjects measured using a dataset provided composite score. However, our analysis was complicated by the lack of randomization, time-dependent confounding, and a substantial fraction of the sample and population will die during follow-up leading to some of our outcomes being censored. The common method to handle this type of problem is marginal structural models (MSM). Although MSM produces valid estimates, this may not be the most appropriate method to reflect a useful real-world situation because MSM upweights subjects who are more likely to die to obtain a hypothetical population that over time, resembles that would have been obtained in the absence of death. A more refined and practical framework, principal stratification (PS), would be to restrict analysis to the strata of the population that would survive regardless of negative wealth shock experience. In this work, we propose a new algorithm for the estimation of the treatment effect under PS by imputing the counterfactual survival status and outcomes. Simulation studies suggest that our algorithm works well in various scenarios. We found no evidence that a negative wealth shock experience would affect the cognitive score of HRS subjects.

Simulating longitudinal data from marginal structural models using the additive hazard model.

Observational longitudinal data on treatments and covariates are increasingly used to investigate treatment effects, but are often subject to time-dependent confounding. Marginal structural models (MSMs), estimated using inverse probability of treatment weighting or the g-formula, are popular for handling this problem. With increasing development of advanced causal inference methods, it is important to be able to assess their performance in different scenarios to guide their application. Simulation studies are a key tool for this, but their use to evaluate causal inference methods has been limited. This paper focuses on the use of simulations for evaluations involving MSMs in studies with a time-to-event outcome. In a simulation, it is important to be able to generate the data in such a way that the correct forms of any models to be fitted to those data are known. However, this is not straightforward in the longitudinal setting because it is natural for data to be generated in a sequential conditional manner, whereas MSMs involve fitting marginal rather than conditional hazard models. We provide general results that enable the form of the correctly specified MSM to be derived based on a conditional data generating procedure, and show how the results can be applied when the conditional hazard model is an Aalen additive hazard or Cox model. Using conditional additive hazard models is advantageous because they imply additive MSMs that can be fitted using standard software. We describe and illustrate a simulation algorithm. Our results will help researchers to effectively evaluate causal inference methods via simulation.

Matching with time-dependent treatments: A review and look forward.

Observational studies of treatment effects attempt to mimic a randomized experiment by balancing the covariate distribution in treated and control groups, thus removing biases related to measured confounders. Methods such as weighting, matching, and stratification, with or without a propensity score, are common in cross-sectional data. When treatments are initiated over longitudinal follow-up, a target pragmatic trial can be emulated using appropriate matching methods. The ideal experiment of interest is simple; patients would be enrolled sequentially, randomized to one or more treatments and followed subsequently. This tutorial defines a class of longitudinal matching methods that emulate this experiment and provides a review of existing variations, with guidance regarding study design, execution, and analysis. These principles are illustrated in application to the study of statins on cardiovascular outcomes in the Framingham Offspring cohort. We identify avenues for future research and highlight the relevance of this methodology to high-quality comparative effectiveness studies in the era of big data.

Mediation analysis of time-to-event endpoints accounting for repeatedly measured mediators subject to time-varying confounding.

In this article, we will present statistical methods to assess to what extent the effect of a randomised treatment (versus control) on a time-to-event endpoint might be explained by the effect of treatment on a mediator of interest, a variable that is measured longitudinally at planned visits throughout the trial. In particular, we will show how to identify and infer the path-specific effect of treatment on the event time via the repeatedly measured mediator levels. The considered proposal addresses complications due to patients dying before the mediator is assessed, due to the mediator being repeatedly measured, and due to posttreatment confounding of the effect of the mediator by other mediators. We illustrate the method by an application to data from the LEADER cardiovascular outcomes trial.

Inverse-probability-of-treatment weighted estimation of causal parameters in the presence of error-contaminated and time-dependent confounders.

Inverse-probability-of-treatment weighted (IPTW) estimation has been widely used to consistently estimate the causal parameters in marginal structural models, with time-dependent confounding effects adjusted for. Just like other causal inference methods, the validity of IPTW estimation typically requires the crucial condition that all variables are precisely measured. However, this condition, is often violated in practice due to various reasons. It has been well documented that ignoring measurement error often leads to biased inference results. In this paper, we consider the IPTW estimation of the causal parameters in marginal structural models in the presence of error-contaminated and time-dependent confounders. We explore several methods to correct for the effects of measurement error on the estimation of causal parameters. Numerical studies are reported to assess the finite sample performance of the proposed methods.

Estimating long-term treatment effects in observational data: A comparison of the performance of different methods under real-world uncertainty.

In the presence of time-dependent confounding, there are several methods available to estimate treatment effects. With correctly specified models and appropriate structural assumptions, any of these methods could provide consistent effect estimates, but with real-world data, all models will be misspecified and it is difficult to know if assumptions are violated. In this paper, we investigate five methods: inverse probability weighting of marginal structural models, history-adjusted marginal structural models, sequential conditional mean models, g-computation formula, and g-estimation of structural nested models. This work is motivated by an investigation of the effects of treatments in cystic fibrosis using the UK Cystic Fibrosis Registry data focussing on two outcomes: lung function (continuous outcome) and annual number of days receiving intravenous antibiotics (count outcome). We identified five features of this data that may affect the performance of the methods: misspecification of the causal null, long-term treatment effects, effect modification by time-varying covariates, misspecification of the direction of causal pathways, and censoring. In simulation studies, under ideal settings, all five methods provide consistent estimates of the treatment effect with little difference between methods. However, all methods performed poorly under some settings, highlighting the importance of using appropriate methods based on the data available. Furthermore, with the count outcome, the issue of non-collapsibility makes comparison between methods delivering marginal and conditional effects difficult. In many situations, we would recommend using more than one of the available methods for analysis, as if the effect estimates are very different, this would indicate potential issues with the analyses.

Joint mixed-effects models for causal inference with longitudinal data.

Causal inference with observational longitudinal data and time-varying exposures is complicated due to the potential for time-dependent confounding and unmeasured confounding. Most causal inference methods that handle time-dependent confounding rely on either the assumption of no unmeasured confounders or the availability of an unconfounded variable that is associated with the exposure (eg, an instrumental variable). Furthermore, when data are incomplete, validity of many methods often depends on the assumption of missing at random. We propose an approach that combines a parametric joint mixed-effects model for the study outcome and the exposure with g-computation to identify and estimate causal effects in the presence of time-dependent confounding and unmeasured confounding. G-computation can estimate participant-specific or population-average causal effects using parameters of the joint model. The joint model is a type of shared parameter model where the outcome and exposure-selection models share common random effect(s). We also extend the joint model to handle missing data and truncation by death when missingness is possibly not at random. We evaluate the performance of the proposed method using simulation studies and compare the method to both linear mixed- and fixed-effects models combined with g-computation as well as to targeted maximum likelihood estimation. We apply the method to an epidemiologic study of vitamin D and depressive symptoms in older adults and include code using SAS PROC NLMIXED software to enhance the accessibility of the method to applied researchers.

Estimating the Comparative Effectiveness of Feeding Interventions in the Pediatric Intensive Care Unit: A Demonstration of Longitudinal Targeted Maximum Likelihood Estimation.

Longitudinal data sources offer new opportunities for the evaluation of sequential interventions. To adjust for time-dependent confounding in these settings, longitudinal targeted maximum likelihood based estimation (TMLE), a doubly robust method that can be coupled with machine learning, has been proposed. This paper provides a tutorial in applying longitudinal TMLE, in contrast to inverse probability of treatment weighting and g-computation based on iterative conditional expectations. We apply these methods to estimate the causal effect of nutritional interventions on clinical outcomes among critically ill children in a United Kingdom study (Control of Hyperglycemia in Paediatric Intensive Care, 2008-2011). We estimate the probability of a child's being discharged alive from the pediatric intensive care unit by a given day, under a range of static and dynamic feeding regimes. We find that before adjustment, patients who follow the static regime "never feed" are discharged by the end of the fifth day with a probability of 0.88 (95% confidence interval: 0.87, 0.90), while for the patients who follow the regime "feed from day 3," the probability of discharge is 0.64 (95% confidence interval: 0.62, 0.66). After adjustment for time-dependent confounding, most of this difference disappears, and the statistical methods produce similar results. TMLE offers a flexible estimation approach; hence, we provide practical guidance on implementation to encourage its wider use.

Estimating inverse probability weights using super learner when weight-model specification is unknown in a marginal structural Cox model context.

Correct specification of the inverse probability weighting (IPW) model is necessary for consistent inference from a marginal structural Cox model (MSCM). In practical applications, researchers are typically unaware of the true specification of the weight model. Nonetheless, IPWs are commonly estimated using parametric models, such as the main-effects logistic regression model. In practice, assumptions underlying such models may not hold and data-adaptive statistical learning methods may provide an alternative. Many candidate statistical learning approaches are available in the literature. However, the optimal approach for a given dataset is impossible to predict. Super learner (SL) has been proposed as a tool for selecting an optimal learner from a set of candidates using cross-validation. In this study, we evaluate the usefulness of a SL in estimating IPW in four different MSCM simulation scenarios, in which we varied the specification of the true weight model specification (linear and/or additive). Our simulations show that, in the presence of weight model misspecification, with a rich and diverse set of candidate algorithms, SL can generally offer a better alternative to the commonly used statistical learning approaches in terms of MSE as well as the coverage probabilities of the estimated effect in an MSCM. The findings from the simulation studies guided the application of the MSCM in a multiple sclerosis cohort from British Columbia, Canada (1995-2008), to estimate the impact of beta-interferon treatment in delaying disability progression. Copyright © 2017 John Wiley & Sons, Ltd.

Performance of the marginal structural cox model for estimating individual and joined effects of treatments given in combination.

BACKGROUND: The Marginal Structural Cox Model (Cox-MSM), an alternative approach to handle time-dependent confounder, was introduced for survival analysis and applied to estimate the joint causal effect of two time-dependent nonrandomized treatments on survival among HIV-positive subjects. Nevertheless, Cox-MSM performance in the case of multiple treatments has not been fully explored under different degree of time-dependent confounding for treatments or in case of interaction between treatments. We aimed to evaluate and compare the performance of the marginal structural Cox model (Cox-MSM) to the standard Cox model in estimating the treatment effect in the case of multiple treatments under different scenarios of time-dependent confounding and when an interaction between treatment effects is present. METHODS: We specified a Cox-MSM with two treatments including an interaction term for situations where an adverse event might be caused by two treatments taken simultaneously but not by each treatment taken alone. We simulated longitudinal data with two treatments and a time-dependent confounder affected by one or the two treatments. To fit the Cox-MSM, we used the inverse probability weighting method. We illustrated the method to evaluate the specific effect of protease inhibitors combined (or not) to other antiretroviral medications on the anal cancer risk in HIV-infected individuals, with CD4 cell count as time-dependent confounder. RESULTS: Overall, Cox-MSM performed better than the standard Cox model. Furthermore, we showed that estimates were unbiased when an interaction term was included in the model. CONCLUSION: Cox-MSM may be used for accurately estimating causal individual and joined treatment effects from a combination therapy in presence of time-dependent confounding provided that an interaction term is estimated.

Accounting for Life-Course Exposures in Epigenetic Biomarker Association Studies: Early Life Socioeconomic Position, Candidate Gene DNA Methylation, and Adult Cardiometabolic Risk.

Recent studies suggest that epigenetic programming may mediate the relationship between early life environment, including parental socioeconomic position, and adult cardiometabolic health. However, interpreting associations between early environment and adult DNA methylation may be difficult because of time-dependent confounding by life-course exposures. Among 613 adult women (mean age = 32 years) of the Jerusalem Perinatal Study Family Follow-up (2007-2009), we investigated associations between early life socioeconomic position (paternal occupation and parental education) and mean adult DNA methylation at 5 frequently studied cardiometabolic and stress-response genes (ABCA1, INS-IGF2, LEP, HSD11B2, and NR3C1). We used multivariable linear regression and marginal structural models to estimate associations under 2 causal structures for life-course exposures and timing of methylation measurement. We also examined whether methylation was associated with adult cardiometabolic phenotype. Higher maternal education was consistently associated with higher HSD11B2 methylation (e.g., 0.5%-point higher in 9-12 years vs. ≤8 years, 95% confidence interval: 0.1, 0.8). Higher HSD11B2 methylation was also associated with lower adult weight and total and low-density lipoprotein cholesterol. We found that associations with early life socioeconomic position measures were insensitive to different causal assumption; however, exploratory analysis did not find evidence for a mediating role of methylation in socioeconomic position-cardiometabolic risk associations.

A cautionary note concerning the use of stabilized weights in marginal structural models.

Marginal structural models are commonly used to estimate the causal effect of a time-varying treatment in presence of time-dependent confounding. When fitting an MSM to data, the analyst must specify both the structural model for the outcome and the treatment models for the inverse-probability-of-treatment weights. The use of stabilized weights is recommended because they are generally less variable than the standard weights. In this paper, we are concerned with the use of the common stabilized weights when the structural model is specified to only consider partial treatment history, such as the current or most recent treatments. We present various examples of settings where these stabilized weights yield biased inferences while the standard weights do not. These issues are first investigated on the basis of simulated data and subsequently exemplified using data from the Honolulu Heart Program. Unlike common stabilized weights, we find that basic stabilized weights offer some protection against bias in structural models designed to estimate current or most recent treatment effects.