An information criterion for marginal structural models

Doubly robust estimation and sensitivity analysis for marginal structural quantile models

The marginal structure quantile model (MSQM) provides a unique lens to understand the causal effect of a time-varying treatment on the full distribution of potential outcomes. Under the semiparametric framework, we derive the efficiency influence function for the MSQM, from which a new doubly robust estimator is proposed for point estimation and inference. We show that the doubly robust estimator is consistent if either of the models associated with treatment assignment or the potential outcome distributions is correctly specified, and is semiparametric efficient if both models are correct. To implement the doubly robust MSQM estimator, we propose to solve a smoothed estimating equation to facilitate efficient computation of the point and variance estimates. In addition, we develop a confounding function approach to investigate the sensitivity of several MSQM estimators when the sequential ignorability assumption is violated. Extensive simulations are conducted to examine the finite-sample performance characteristics of the proposed methods. We apply the proposed methods to the Yale New Haven Health System Electronic Health Record data to study the effect of antihypertensive medications to patients with severe hypertension and assess the robustness of the findings to unmeasured baseline and time-varying confounding.

Association of Preeclampsia With Incident Stroke in Later Life Among Women in the Framingham Heart Study

IMPORTANCE

Contemporary research suggests an association between preeclampsia and later-life stroke among women. To our knowledge, no research to date has accounted for the time-varying nature of shared risk factors for preeclampsia and later-life stroke incidence.

OBJECTIVE

To assess the relative risk of incident stroke in later life among women with and without a history of preeclampsia after accounting for time-varying covariates.

DESIGN, SETTING, AND PARTICIPANTS

This population-based cohort study was a secondary analysis of data from the Framingham Heart Study, which was conducted from 1948 to 2016. Women were included in the analysis if they were stroke free at enrollment and had a minimum of 3 study visits and 1 pregnancy before menopause, hysterectomy, or age 45 years. Data on vascular risk factors, history of preeclampsia, and stroke incidence were collected biannually. Participants were followed up until incident stroke or censorship from the study. Marginal structural models were used to evaluate the relative risk of incident stroke among participants with and without a history of preeclampsia after accounting for time-varying covariates. Data were analyzed from May 2019 to December 2020.

EXPOSURES

Presence or absence of preeclampsia among women with 1 or more pregnancies.

MAIN OUTCOMES AND MEASURES

Incident stroke in later life.

RESULTS

A total of 1435 women (mean [SD] age, 44.4 [7.7] years at the beginning of the study; 100% White) with 41 422 person-years of follow-up were included in the analytic sample. Of those, 169 women had a history of preeclampsia, and 231 women experienced strokes during follow-up. At baseline, women with preeclampsia were more likely to be younger, to be receiving cholesterol-lowering medications, to have lower cholesterol and higher diastolic blood pressure, and to currently smoke. The association between preeclampsia and stroke in the marginal structural model was only evident when adjustment was made for all vascular risk factors over the life course, which indicated that women with a history of preeclampsia had a higher risk of stroke in later life compared with women without a history of preeclampsia (relative risk, 3.79; 95% CI, 1.24-11.60).

CONCLUSIONS AND RELEVANCE

The findings of this cohort study suggest that preeclampsia may be a risk factor for later-life stroke among women after adjustment for time-varying vascular and demographic factors. Future research is warranted to fully explore the mediation of this association by midlife vascular risk factors.

Understanding Marginal Structural Models for Time-Varying Exposures: Pitfalls and Tips

Epidemiologists are increasingly encountering complex longitudinal data, in which exposures and their confounders vary during follow-up. When a prior exposure affects the confounders of the subsequent exposures, estimating the effects of the time-varying exposures requires special statistical techniques, possibly with structural (ie, counterfactual) models for targeted effects, even if all confounders are accurately measured. Among the methods used to estimate such effects, which can be cast as a marginal structural model in a straightforward way, one popular approach is inverse probability weighting. Despite the seemingly intuitive theory and easy-to-implement software, misunderstandings (or "pitfalls") remain. For example, one may mistakenly equate marginal structural models with inverse probability weighting, failing to distinguish a marginal structural model encoding the causal parameters of interest from a nuisance model for exposure probability, and thereby failing to separate the problems of variable selection and model specification for these distinct models. Assuming the causal parameters of interest are identified given the study design and measurements, we provide a step-by-step illustration of generalized computation of standardization (called the g-formula) and inverse probability weighting, as well as the specification of marginal structural models, particularly for time-varying exposures. We use a novel hypothetical example, which allows us access to typically hidden potential outcomes. This illustration provides steppingstones (or "tips") to understand more concretely the estimation of the effects of complex time-varying exposures.

A test for the correct specification of marginal structural models

Marginal structural models (MSMs) allow estimating the causal effect of a time-varying exposure on an outcome in the presence of time-dependent confounding. The parameters of MSMs can be estimated utilizing an inverse probability of treatment weight estimator under certain assumptions. One of these assumptions is that the proposed causal model relating the outcome to exposure history is correctly specified. However, in practice, the true model is unknown. We propose a test that employs the observed data to attempt validating the assumption that the model is correctly specified. The performance of the proposed test is investigated with a simulation study. We illustrate our approach by estimating the effect of repeated exposure to psychosocial stressors at work on ambulatory blood pressure in a large cohort of white-collar workers in Québec City, Canada. Code examples in SAS and R are provided to facilitate the implementation of the test.

Empirical-likelihood-based criteria for model selection on marginal analysis of longitudinal data with dropout missingness

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equation (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate criteria for the selection of marginal mean and correlation structures, unsatisfactory selection performance in small-sample setups, and so forth. In particular, there are few studies to develop joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into the WGEE framework, we propose two innovative information criteria named a joint empirical Akaike information criterion and a joint empirical Bayesian information criterion, which can simultaneously select the variables for marginal mean regression and also correlation structure. Through extensive simulation studies, these empirical-likelihood-based criteria exhibit robustness, flexibility, and outperformance compared to the other criteria including the weighted quasi-likelihood under the independence model criterion, the missing longitudinal information criterion, and the joint longitudinal information criterion. In addition, we provide a theoretical justification of our proposed criteria, and present two real data examples in practice for further illustration.

Downstream Effects of Upstream Causes

The United States Environmental Protection Agency considers nutrient pollution in stream ecosystems one of the U.S.' most pressing environmental challenges. But limited independent replicates, lack of experimental randomization, and space- and time-varying confounding handicap causal inference on effects of nutrient pollution. In this paper the causal g-methods are extended to allow for exposures to vary in time and space in order to assess the effects of nutrient pollution on chlorophyll a - a proxy for algal production. Publicly available data from North Carolina's Cape Fear River and a simulation study are used to show how causal effects of upstream nutrient concentrations on downstream chlorophyll a levels may be estimated from typical water quality monitoring data. Estimates obtained from the parametric g-formula, a marginal structural model, and a structural nested model indicate that chlorophyll a concentrations at Lock and Dam 1 were influenced by nitrate concentrations measured 86 to 109 km upstream, an area where four major industrial and municipal point sources discharge wastewater.

An R package for model fitting, model selection and the simulation for longitudinal data with dropout missingness

Missing data arise frequently in clinical and epidemiological fields, in particular in longitudinal studies. This paper describes the core features of an R package wgeesel, which implements marginal model fitting (i.e., weighted generalized estimating equations, WGEE; doubly robust GEE) for longitudinal data with dropouts under the assumption of missing at random. More importantly, this package comprehensively provide existing information criteria for WGEE model selection on marginal mean or correlation structures. Also, it can serve as a valuable tool for simulating longitudinal data with missing outcomes. Lastly, a real data example and simulations are presented to illustrate and validate our package.

Inverse probability weighted estimation of risk under representative interventions in observational studies

Researchers are often interested in using observational data to estimate the effect on a health outcome of maintaining a continuous treatment within a pre-specified range over time; e.g. "always exercise at least 30 minutes per day". There may be many precise interventions that could achieve this range. In this paper we consider representative interventions. These are special cases of random dynamic interventions; interventions under which treatment at each time is assigned according to a random draw from a distribution that may depend on a subject's measured past. Estimators of risk under representative interventions on a time-varying treatment have previously been described based on g-estimation of structural nested cumulative failure time models. In this paper, we consider an alternative approach based on inverse probability weighting (IPW) of marginal structural models. In particular, we show that the risk under a representative intervention on a time-varying continuous treatment can be consistently estimated via computationally simple IPW methods traditionally used for deterministic static (i.e. "nonrandom" and "nondynamic") interventions for binary treatments. We present an application of IPW in this setting to estimate the 28-year risk of coronary heart disease under various representative interventions on lifestyle behaviors in the Nurses Health Study.

Longterm Effectiveness of Intraarticular Injections on Patient-reported Symptoms in Knee Osteoarthritis

OBJECTIVE

We examined the longterm effectiveness of corticosteroid or hyaluronic acid injections in relieving symptoms among persons with knee osteoarthritis (OA).

METHODS

Using Osteoarthritis Initiative data, a new-user design was applied to identify participants initiating corticosteroid or hyaluronic acid injections (n = 412). Knee symptoms (pain, stiffness, function) were measured using The Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC). We used marginal structural models adjusting for time-varying confounders to estimate the effect on symptoms of newly initiated injection use compared to nonusers over 2 years of followup.

RESULTS

Among 412 participants initiating injections, 77.2% used corticosteroid injections and 22.8% used hyaluronic acid injections. About 18.9% had additional injection use after initiation, but switching between injection types was common. Compared to nonusers, on average, participants initiating a corticosteroid injection experienced a worsening of pain (yearly worsening: 1.24 points, 95% CI 0.82-1.66), stiffness (yearly worsening: 0.30 points, 95% CI 0.10-0.49), and physical functioning (yearly worsening: 2.62 points, 95% CI 0.94-4.29) after adjusting for potential confounders with marginal structural models. Participants initiating hyaluronic acid injections did not show improvements of WOMAC subscales (pain: 0.50, 95% CI -0.11 to 1.11; stiffness: -0.07, 95% CI -0.38 to 0.24; and functioning: 0.49, 95% CI -1.34 to 2.32).

CONCLUSION

Although intraarticular injections may support the effectiveness of reducing symptoms in short-term clinical trials, the initiation of corticosteroid or hyaluronic acid injections did not appear to provide sustained symptom relief over 2 years of followup for persons with knee OA.

Application of causal inference methods in the analyses of randomised controlled trials: a systematic review

BACKGROUND

Applications of causal inference methods to randomised controlled trial (RCT) data have usually focused on adjusting for compliance with the randomised intervention rather than on using RCT data to address other, non-randomised questions. In this paper we review use of causal inference methods to assess the impact of aspects of patient management other than the randomised intervention in RCTs.

METHODS

We identified papers that used causal inference methodology in RCT data from Medline, Premedline, Embase, Cochrane Library, and Web of Science from 1986 to September 2014, using a forward citation search of five seminal papers, and a keyword search. We did not include studies where inverse probability weighting was used solely to balance baseline characteristics, adjust for loss to follow-up or adjust for non-compliance to randomised treatment. Studies where the exposure could not be assigned were also excluded.

RESULTS

There were 25 papers identified. Nearly half the papers (11/25) estimated the causal effect of concomitant medication on outcome. The remainder were concerned with post-randomisation treatment regimens (sequential treatments, n =5 ), effects of treatment timing (n = 2) and treatment dosing or duration (n = 7). Examples were found in cardiovascular disease (n = 5), HIV (n = 7), cancer (n = 6), mental health (n = 4), paediatrics (n = 2) and transfusion medicine (n = 1). The most common method implemented was a marginal structural model with inverse probability of treatment weighting.

CONCLUSIONS

Examples of studies which exploit RCT data to address non-randomised questions using causal inference methodology remain relatively limited, despite the growth in methodological development and increasing utilisation in observational studies. Further efforts may be needed to promote use of causal methods to address additional clinical questions within RCTs to maximise their value.

Estimating multiple time-fixed treatment effects using a semi-Bayes semiparametric marginal structural Cox proportional hazards regression model

Marginal structural models for time-fixed treatments fit using inverse-probability weighted estimating equations are increasingly popular. Nonetheless, the resulting effect estimates are subject to finite-sample bias when data are sparse, as is typical for large-sample procedures. Here we propose a semi-Bayes estimation approach which penalizes or shrinks the estimated model parameters to improve finite-sample performance. This approach uses simple symmetric data-augmentation priors. Limited simulation experiments indicate that the proposed approach reduces finite-sample bias and improves confidence-interval coverage when the true values lie within the central "hill" of the prior distribution. We illustrate the approach with data from a nonexperimental study of HIV treatments.

A $C_p$ criterion for semiparametric causal inference

For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator as a $C_{p}$ criterion using an ignorable treatment assignment condition. Simulation shows that the proposed criterion outperforms a conventional one by providing smaller squared errors and higher frequencies of selecting the true model in all the settings considered. Moreover, in a real-data analysis we found a clear difference between the two criteria.

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.

A Case Study of the Impact of Data-Adaptive Versus Model-Based Estimation of the Propensity Scores on Causal Inferences from Three Inverse Probability Weighting Estimators

OBJECTIVE

Consistent estimation of causal effects with inverse probability weighting estimators is known to rely on consistent estimation of propensity scores. To alleviate the bias expected from incorrect model specification for these nuisance parameters in observational studies, data-adaptive estimation and in particular an ensemble learning approach known as Super Learning has been proposed as an alternative to the common practice of estimation based on arbitrary model specification. While the theoretical arguments against the use of the latter haphazard estimation strategy are evident, the extent to which data-adaptive estimation can improve inferences in practice is not. Some practitioners may view bias concerns over arbitrary parametric assumptions as academic considerations that are inconsequential in practice. They may also be wary of data-adaptive estimation of the propensity scores for fear of greatly increasing estimation variability due to extreme weight values. With this report, we aim to contribute to the understanding of the potential practical consequences of the choice of estimation strategy for the propensity scores in real-world comparative effectiveness research.

METHOD

We implement secondary analyses of Electronic Health Record data from a large cohort of type 2 diabetes patients to evaluate the effects of four adaptive treatment intensification strategies for glucose control (dynamic treatment regimens) on subsequent development or progression of urinary albumin excretion. Three Inverse Probability Weighting estimators are implemented using both model-based and data-adaptive estimation strategies for the propensity scores. Their practical performances for proper confounding and selection bias adjustment are compared and evaluated against results from previous randomized experiments.

CONCLUSION

Results suggest both potential reduction in bias and increase in efficiency at the cost of an increase in computing time when using Super Learning to implement Inverse Probability Weighting estimators to draw causal inferences.

The Choice of Analytical Strategies in Inverse-Probability-of-Treatment-Weighted Analysis: A Simulation Study

We sought to explore the impact of intention to treat and complex treatment use assumptions made during weight construction on the validity and precision of estimates derived from inverse-probability-of-treatment-weighted analysis. We simulated data assuming a nonexperimental design that attempted to quantify the effect of statin on lowering low-density lipoprotein cholesterol. We created 324 scenarios by varying parameter values (effect size, sample size, adherence level, probability of treatment initiation, associations between low-density lipoprotein cholesterol and treatment initiation and continuation). Four analytical approaches were used: 1) assuming intention to treat; 2) assuming complex mechanisms of treatment use; 3) assuming a simple mechanism of treatment use; and 4) assuming invariant confounders. With a continuous outcome, estimates assuming intention to treat were biased toward the null when there were nonnull treatment effect and nonadherence after treatment initiation. For each 1% decrease in the proportion of patients staying on treatment after initiation, the bias in estimated average treatment effect increased by 1%. Inverse-probability-of-treatment-weighted analyses that took into account the complex mechanisms of treatment use generated approximately unbiased estimates. Studies estimating the actual effect of a time-varying treatment need to consider the complex mechanisms of treatment use during weight construction.

Effects of prescription nonsteroidal antiinflammatory drugs on symptoms and disease progression among patients with knee osteoarthritis

OBJECTIVE

The effect of short-term and long-term use of nonsteroidal antiinflammatory drugs (NSAIDs) on structural change is equivocal. The aim of this study was to estimate the extent to which short- and long-term use of prescription NSAIDs relieve symptoms and delay structural progression among patients with radiographically confirmed osteoarthritis (OA) of the knee.

METHODS

We applied a new-user design among participants with confirmed OA not reporting NSAID use at the time of enrollment in the Osteoarthritis Initiative. Participants were evaluated for changes in the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) subscales (n = 1,846) and joint space width was measured using serial radiographs and a customized software tool (n = 1,116) over 4 years. We used marginal structural modeling to estimate the effect of NSAIDs.

RESULTS

Compared to participants who never reported prescription NSAID use, those reporting use at 1 or 2 assessments had no clinically important changes, but those reporting prescription NSAID use at all 3 assessments had, on average, 0.88 point improvement over the followup period (95% confidence interval [95% CI] -0.46 to 2.22) in pain, 0.72 point improvement (95% CI -0.12 to 1.56) in stiffness, and 4.27 points improvement (95% CI -0.31 to 8.84) in function. The average change in joint space width was 0.28 mm less among those reporting NSAID use at 3 assessments relative to nonusers (95% CI -0.06 to 0.62). Recent NSAID use findings were not clinically or statistically significant.

CONCLUSION

Long-term, but not short-term, NSAID use was associated with an a priori-defined minimally important clinical change in stiffness, physical function, and joint space width, but not pain. While showing modest clinical importance, the estimates did not reach statistical significance.

Effects of glucosamine and chondroitin supplementation on knee osteoarthritis: an analysis with marginal structural models

OBJECTIVE

The purpose of this study was to estimate the effectiveness of the combination of glucosamine and chondroitin in relieving knee symptoms and slowing disease progression among patients with knee osteoarthritis (OA).

METHODS

The 4-year followup data from the Osteoarthritis Initiative data set were analyzed. We used a "new-user" design, for which only participants who were not using glucosamine/chondroitin at baseline were included in the analyses (n = 1,625). Cumulative exposure was calculated as the number of visits when participants reported use of glucosamine/chondroitin. Knee symptoms were measured with the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), and structural progression was determined by measuring the joint space width (JSW). To control for the time-varying confounders that might be influenced by previous treatments, we used marginal structural models to estimate the effects on OA of using glucosamine/chondroitin for 3 years, 2 years, and 1 year.

RESULTS

During the study period, 18% of the participants initiated treatment with glucosamine/chondroitin. After adjustment for potential confounders with marginal structural models, we found no clinically significant differences between users at all assessments and never-users of glucosamine/chondroitin in WOMAC pain (β = 0.68 [95% confidence interval (95% CI) -0.16 to 1.53]), WOMAC stiffness (β = 0.41 [95% CI 0 to 0.82]), and WOMAC function (β = 1.28 [95% CI -1.23 to 3.79]) or JSW (β = 0.11 [95% CI -0.21 to 0.44]).

CONCLUSION

Use of glucosamine/chondroitin did not appear to relieve symptoms or modify disease progression among patients with radiographically confirmed OA. Our findings are consistent with the results of meta-analyses of clinical trials and extend those results to a more general population with knee OA.

A Boosting Algorithm for Estimating Generalized Propensity Scores with Continuous Treatments

In this article, we study the causal inference problem with a continuous treatment variable using propensity score-based methods. For a continuous treatment, the generalized propensity score is defined as the conditional density of the treatment-level given covariates (confounders). The dose-response function is then estimated by inverse probability weighting, where the weights are calculated from the estimated propensity scores. When the dimension of the covariates is large, the traditional nonparametric density estimation suffers from the curse of dimensionality. Some researchers have suggested a two-step estimation procedure by first modeling the mean function. In this study, we suggest a boosting algorithm to estimate the mean function of the treatment given covariates. In boosting, an important tuning parameter is the number of trees to be generated, which essentially determines the trade-off between bias and variance of the causal estimator. We propose a criterion called average absolute correlation coefficient (AACC) to determine the optimal number of trees. Simulation results show that the proposed approach performs better than a simple linear approximation or L2 boosting. The proposed methodology is also illustrated through the Early Dieting in Girls study, which examines the influence of mothers' overall weight concern on daughters' dieting behavior.

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.

Targeted learning in real-world comparative effectiveness research with time-varying interventions

In comparative effectiveness research (CER), often the aim is to contrast survival outcomes between exposure groups defined by time-varying interventions. With observational data, standard regression analyses (e.g., Cox modeling) cannot account for time-dependent confounders on causal pathways between exposures and outcome nor for time-dependent selection bias that may arise from informative right censoring. Inverse probability weighting (IPW) estimation to fit marginal structural models (MSMs) has commonly been applied to properly adjust for these expected sources of bias in real-world observational studies. We describe the application and performance of an alternate estimation approach in such a study. The approach is based on the recently proposed targeted learning methodology and consists in targeted minimum loss-based estimation (TMLE) with super learning (SL) within a nonparametric MSM. The evaluation is based on the analysis of electronic health record data with both IPW estimation and TMLE to contrast cumulative risks under four more or less aggressive strategies for treatment intensification in adults with type 2 diabetes already on 2+ oral agents or basal insulin. Results from randomized experiments provide a surrogate gold standard to validate confounding and selection bias adjustment. Bootstrapping is used to validate analytic estimation of standard errors. This application does the following: (1) establishes the feasibility of TMLE in real-world CER based on large healthcare databases; (2) provides evidence of proper confounding and selection bias adjustment with TMLE and SL; and (3) motivates their application for improving estimation efficiency. Claims are reinforced with a simulation study that also illustrates the double-robustness property of TMLE.

Application of marginal structural models in pharmacoepidemiologic studies: a systematic review

PURPOSE

We systematically reviewed pharmacoepidemiologic studies published in 2012 that used inverse probability weighted (IPW) estimation of marginal structural models (MSM) to estimate the effect from a time-varying treatment.

METHODS

Potential studies were retrieved through a citation search within Web of Science and a keyword search within PubMed. Eligibility of retrieved studies was independently assessed by at least two reviewers. One reviewer performed data extraction, and a senior epidemiologist confirmed the extracted information for all eligible studies.

RESULTS

Twenty pharmacoepidemiologic studies were eligible for data extraction. The majority of reviewed studies did not report whether the positivity assumption was checked. Six studies performed intention-to-treat analyses, but none of them reported adherence levels after treatment initiation. Eight studies chose an as-treated analytic strategy, but only one of them reported modeling the multiphase of treatment use. Almost all studies performing as-treated analyses chose the most recent treatment status as the functional form of exposure in the outcome model. Nearly half of the studies reported that the IPW estimate was substantially different from the estimate derived from a standard regression model.

CONCLUSIONS

The use of IPW method to control for time-varying confounding is increasing in medical literature. However, reporting of the application of the technique is variable and suboptimal. It may be prudent to develop best practices in reporting complex methods in epidemiologic research.

Making valid causal inferences from observational data

The ability to make strong causal inferences, based on data derived from outside of the laboratory, is largely restricted to data arising from well-designed randomized control trials. Nonetheless, a number of methods have been developed to improve our ability to make valid causal inferences from data arising from observational studies. In this paper, I review concepts of causation as a background to counterfactual causal ideas; the latter ideas are central to much of current causal theory. Confounding greatly constrains causal inferences in all observational studies. Confounding is a biased measure of effect that results when one or more variables, that are both antecedent to the exposure and associated with the outcome, are differentially distributed between the exposed and non-exposed groups. Historically, the most common approach to control confounding has been multivariable modeling; however, the limitations of this approach are discussed. My suggestions for improving causal inferences include asking better questions (relates to counterfactual ideas and "thought" trials); improving study design through the use of forward projection; and using propensity scores to identify potential confounders and enhance exchangeability, prior to seeing the outcome data. If time-dependent confounders are present (as they are in many longitudinal studies), more-advanced methods such as marginal structural models need to be implemented. Tutorials and examples are cited where possible.