Impact of mis-specification of the treatment model on estimates from a marginal structural model

Within-Person Variability Score-Based Causal Inference: A Two-Step Estimation for Joint Effects of Time-Varying Treatments

Behavioral science researchers have shown strong interest in disaggregating within-person relations from between-person differences (stable traits) using longitudinal data. In this paper, we propose a method of within-person variability score-based causal inference for estimating joint effects of time-varying continuous treatments by controlling for stable traits of persons. After explaining the assumed data-generating process and providing formal definitions of stable trait factors, within-person variability scores, and joint effects of time-varying treatments at the within-person level, we introduce the proposed method, which consists of a two-step analysis. Within-person variability scores for each person, which are disaggregated from stable traits of that person, are first calculated using weights based on a best linear correlation preserving predictor through structural equation modeling (SEM). Causal parameters are then estimated via a potential outcome approach, either marginal structural models (MSMs) or structural nested mean models (SNMMs), using calculated within-person variability scores. Unlike the approach that relies entirely on SEM, the present method does not assume linearity for observed time-varying confounders at the within-person level. We emphasize the use of SNMMs with G-estimation because of its property of being doubly robust to model misspecifications in how observed time-varying confounders are functionally related to treatments/predictors and outcomes at the within-person level. Through simulation, we show that the proposed method can recover causal parameters well and that causal estimates might be severely biased if one does not properly account for stable traits. An empirical application using data regarding sleep habits and mental health status from the Tokyo Teen Cohort study is also provided.

Application of Inverse-Probability-of-Treatment Weighting to Estimate the Effect of Daytime Sleepiness in Patients with Obstructive Sleep Apnea

Rationale: Continuous positive airway pressure (CPAP), the first line therapy for obstructive sleep apnea (OSA), is considered effective in reducing daytime sleepiness. Its efficacy relies on adequate adherence, often defined as >4 hours per night. However, this binary threshold may limit our understanding of the causal effect of CPAP adherence and daytime sleepiness, and a multilevel approach for CPAP adherence can be more appropriate. Objectives: In this study, we show how two causal inference methods can be applied on observational data for the estimation of the effect of different ranges of CPAP adherence on daytime sleepiness as measured by the Epworth Sleepiness Scale (ESS). Methods: Data were collected from a large prospective observational French cohort for patients with OSA. Four groups of CPAP adherence were considered (0-4, 4-6, 6-7, and 7-10 h per night). Multivariable regression, inverse-probability-of-treatment weighting (IPTW), and inverse propensity weighting with regression adjustment (IPW-RA) were used to assess the impact of CPAP adherence level on daytime sleepiness. Results: In this study, 9,244 patients with OSA treated by CPAP were included. The mean initial ESS score was 11 (±5.2), with a mean reduction of 4 points (±5.1). Overall, there was evidence of the causal effect of CPAP adherence on daytime sleepiness which was mainly observed between the lower CPAP adherence group (0-4 h) compared with the higher CPAP adherence group (7-10 h). There are no differences by considering higher level of CPAP adherence (>4 h). Conclusions: We showed that IPTW and IPW-RA can be easily implemented to answer questions regarding causal effects using observational data when randomized trials cannot be conducted. Both methods give a direct causal interpretation at the population level and allow the assessment of the appropriate consideration of measured confounders.

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.

Challenges in interpreting results from 'multiple regression' when there is interaction between covariates

Properly interpreting research results is the foundation of evidence-based medicine. Most observational studies use multiple regression and report adjusted effects. In randomised trials, adjusted effects are often provided when there are chance baseline imbalances. The estimates for the exposure of interest (eg, treatment) from these adjusted analyses are usually interpreted as population average causal effects (PACEs); for example, what would be the difference in the mean outcome if everyone in the population was treated versus untreated? In this paper, we show this interpretation is incorrect when there is an interaction between treatment and other variables with respect to the outcome. We provide the appropriate methods to calculate the PACE from regression analyses and also introduce alternative methods that have gained popularity over the last 20 years. Finally, we explain why researchers should be cautious when excluding interaction terms based on p values.

The impact of adjusting for pure predictors of exposure, mediator, and outcome on the variance of natural direct and indirect effect estimators

It is now well established that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the total exposure effect on an outcome with generally reduced standard errors (SEs). However, no analogous results have been derived for mediation analysis. Considering the simplest linear regression setting and the ordinary least square estimator, we obtained theoretical results showing that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the natural indirect effect (NIE) and the natural direct effect (NDE) on the difference scale with reduced SEs. Adjusting for pure predictors of the mediator increases the SE of the NDE's estimator, but may increase or decrease the variance of the NIE's estimator. Adjusting for pure predictors of the exposure increases the variance of estimators of the NIE and NDE. Simulation studies were used to confirm and extend these results to the case where the mediator or the outcome is binary. Additional simulations were conducted to explore scenarios featuring an exposure-mediator interaction as well as the relative risk and odds ratio scales for the case of binary mediator and outcome. Both a regression approach and an inverse probability weighting approach were considered in the simulation study. A real-data illustration employing data from the Canadian Study of Health and Aging is provided. This analysis is concerned with the mediating effect of vitamin D in the effect of physical activity on dementia and its results are overall consistent with the theoretical and empirical findings.

G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

In clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes.

Joint calibrated estimation of inverse probability of treatment and censoring weights for marginal structural models

Marginal structural models (MSMs) with inverse probability weighted estimators (IPWEs) are widely used to estimate causal effects of treatment sequences on longitudinal outcomes in the presence of time‐varying confounding and dependent censoring. However, IPWEs for MSMs can be inefficient and unstable if weights are estimated by maximum likelihood. To improve the performance of IPWEs, covariate balancing weight (CBW) methods have been proposed and recently extended to MSMs. However, existing CBW methods for MSMs are inflexible for practical use because they often do not handle dependent censoring, nonbinary treatments, and longitudinal outcomes (instead of eventual outcomes at a study end). In this paper, we propose a joint calibration approach to CBW estimation for MSMs that can accommodate (1) both time‐varying confounding and dependent censoring, (2) binary and nonbinary treatments, (3) eventual outcomes and longitudinal outcomes. We develop novel calibration restrictions by jointly eliminating covariate associations with both treatment assignment and censoring processes after weighting the observed data sample (i.e., to optimize covariate balance in finite samples). Two different methods are proposed to implement the calibration. Simulations show that IPWEs with calibrated weights perform better than IPWEs with weights from maximum likelihood and the “Covariate Balancing Propensity Score” method. We apply our method to a natural history study of HIV for estimating the effects of highly active antiretroviral therapy on CD4 cell counts over time.

G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study

Controlling for confounding bias is crucial in causal inference. Distinct methods are currently employed to mitigate the effects of confounding bias. Each requires the introduction of a set of covariates, which remains difficult to choose, especially regarding the different methods. We conduct a simulation study to compare the relative performance results obtained by using four different sets of covariates (those causing the outcome, those causing the treatment allocation, those causing both the outcome and the treatment allocation, and all the covariates) and four methods: g-computation, inverse probability of treatment weighting, full matching and targeted maximum likelihood estimator. Our simulations are in the context of a binary treatment, a binary outcome and baseline confounders. The simulations suggest that considering all the covariates causing the outcome led to the lowest bias and variance, particularly for g-computation. The consideration of all the covariates did not decrease the bias but significantly reduced the power. We apply these methods to two real-world examples that have clinical relevance, thereby illustrating the real-world importance of using these methods. We propose an R package RISCA to encourage the use of g-computation in causal inference.

Missing Data in Marginal Structural Models: A Plasmode Simulation Study Comparing Multiple Imputation and Inverse Probability Weighting

BACKGROUND

The use of marginal structural models (MSMs) to adjust for time-varying confounding has increased in epidemiologic studies. However, in the setting of MSMs, recommendations for how best to handle missing data are contradictory. We present a plasmode simulation study to compare the validity and precision of MSMs estimates using complete case analysis (CC), multiple imputation (MI), and inverse probability weighting (IPW) in the presence of missing data on time-independent and time-varying confounders.

MATERIALS AND METHODS

Simulations were based on a cohort substudy using data from the Osteoarthritis Initiative which estimated the marginal causal effect of intra-articular injection use on yearly changes in knee pain. We simulated 81 scenarios with parameter values varied on missing mechanisms (MCAR, MAR, and MNAR), percentages of missing (10%, 20%, and 30%), type of confounders (time-independent, time-varying, either or both), and analytical approaches (CC, IPW, and MI). The performance of CC, IPW, and MI methods was compared using relative bias, mean squared error of the estimates of interest, and empirical power.

RESULTS

Across scenarios defined by missing data mechanism, extent of missing data, and confounder type, MI generally produced less biased estimates (range: 1.2%-6.7%) with better precision (range: 0.17-0.18) compared with IPW (relative bias: -5.3% to 8.0%; precision: 0.19-0.53). Empirical power was constant across the scenarios using MI.

CONCLUSIONS

Under simple yet realistically constructed scenarios, MI seems to confer an advantage over IPW in MSMs applications.

Evaluating Flexible Modeling of Continuous Covariates in Inverse-Weighted Estimators

Correct specification of the exposure model is essential for unbiased estimation in marginal structural models with inverse-probability-of-treatment weights. However, although flexible modeling is commonplace when estimating effects of continuous covariates in outcome models, its use is less frequent in estimation of inverse probability weights. Using simulations, we assess the accuracy of the treatment effect estimates and covariate balance obtained with different exposure model specifications when the true relationship between a continuous, possibly time-varying covariate Lt and the logit of the probability of exposure is nonlinear. Specifically, we compare 4 approaches to modeling the effect of Lt when estimating inverse probability weights: a linear function, the covariate-balancing propensity score, and 2 easy-to-implement flexible methods that relax the assumption of linearity: cubic regression splines and fractional polynomials. Using data from 2 empirical studies, we compare linear exposure models with flexible exposure models to estimate the effect of sustained virological response to hepatitis C virus treatment on the progression of liver fibrosis. Our simulation results demonstrate that ignoring important nonlinear relationships when fitting the exposure model may provide poorer covariate balance and induce substantial bias in the estimated exposure-outcome associations. Analysts should routinely consider flexible modeling of continuous covariates when estimating inverse-probability-of-treatment weights.

Comparative Effectiveness of Mycophenolate Mofetil for the Treatment of Juvenile-Onset Proliferative Lupus Nephritis

OBJECTIVE

Although juvenile-onset proliferative lupus nephritis (PLN) leads to significant morbidity and mortality, there is no clinical trials-based evidence to support the treatment effectiveness of any therapy for juvenile-onset PLN. Marginal structural models enable us to estimate treatment effectiveness using observational data while accounting for confounding by indication.

METHODS

We used prospectively collected data to examine the effect of mycophenolate mofetil (MMF), compared to the use of other therapies, on the long-term outcome of a juvenile-onset PLN cohort (age at PLN onset <18 years). The major outcome variable was the estimated glomerular filtration rate (GFR) using the revised Schwartz formula. Confounding by indication was corrected for marginal structural model.

RESULTS

A total of 172 subjects with juvenile-onset PLN, with a mean followup duration of approximately 4 years, were included. Overall, MMF was superior to other therapies, with a relative effect estimate for MMF of 1.06, i.e., 6% better estimated GFR on average (95% confidence interval 0.7, 11.3), corrected for potential confounding by indication. We found that beginning in year 4 there was a significant improvement in estimated GFR in the patients who were treated with MMF versus other therapies. This improvement was maintained until the end of the study.

CONCLUSION

MMF was more beneficial than other therapies in improving/maintaining long-term renal function in patients with juvenile-onset PLN up to a maximum followup of 7 years. This finding is consistent with evidence from adult PLN clinical trials.

simcausal R Package: Conducting Transparent and Reproducible Simulation Studies of Causal Effect Estimation with Complex Longitudinal Data

The simcausal R package is a tool for specification and simulation of complex longitudinal data structures that are based on non-parametric structural equation models. The package aims to provide a flexible tool for simplifying the conduct of transparent and reproducible simulation studies, with a particular emphasis on the types of data and interventions frequently encountered in real-world causal inference problems, such as, observational data with time-dependent confounding, selection bias, and random monitoring processes. The package interface allows for concise expression of complex functional dependencies between a large number of nodes, where each node may represent a measurement at a specific time point. The package allows for specification and simulation of counterfactual data under various user-specified interventions (e.g., static, dynamic, deterministic, or stochastic). In particular, the interventions may represent exposures to treatment regimens, the occurrence or non-occurrence of right-censoring events, or of clinical monitoring events. Finally, the package enables the computation of a selected set of user-specified features of the distribution of the counterfactual data that represent common causal quantities of interest, such as, treatment-specific means, the average treatment effects and coefficients from working marginal structural models. The applicability of simcausal is demonstrated by replicating the results of two published simulation studies.

Contours of a causal feedback mechanism between adaptive personality and psychosocial function in patients with personality disorders: a secondary analysis from a randomized clinical trial

BACKGROUND

Patients with personality disorders commonly exhibit impairment in psychosocial function that persists over time even with diagnostic remission. Further causal knowledge may help to identify and assess factors with a potential to alleviate this impairment. Psychosocial function is associated with personality functioning which describes personality disorder severity in DSM-5 (section III) and which can reportedly be improved by therapy.

METHODS

The reciprocal association between personality functioning and psychosocial function was assessed, in 113 patients with different personality disorders, in a secondary longitudinal analysis of data from a randomized clinical trial, over six years. Personality functioning was represented by three domains of the Severity Indices of Personality Problems: Relational Capacity, Identity Integration, and Self-control. Psychosocial function was measured by Global Assessment of Functioning. The marginal structural model was used for estimation of causal effects of the three personality functioning domains on psychosocial function, and vice versa. The attractiveness of this model lies in the ability to assess an effect of a time - varying exposure on an outcome, while adjusting for time - varying confounding.

RESULTS

Strong causal effects were found. A hypothetical intervention to increase Relational Capacity by one standard deviation, both at one and two time-points prior to assessment of psychosocial function, would increase psychosocial function by 3.5 standard deviations (95% CI: 2.0, 4.96). Significant effects of Identity Integration and Self-control on psychosocial function, and from psychosocial function on all three domains of personality functioning, although weaker, were also found.

CONCLUSION

This study indicates that persistent impairment in psychosocial function can be addressed through a causal pathway of personality functioning, with interventions of at least 18 months duration.

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.

The Balance Super Learner: A robust adaptation of the Super Learner to improve estimation of the average treatment effect in the treated based on propensity score matching

Consistency of the propensity score estimators rely on correct specification of the propensity score model. The propensity score is frequently estimated using a main effect logistic regression. It has recently been shown that the use of ensemble machine learning algorithms, such as the Super Learner, could improve covariate balance and reduce bias in a meaningful manner in the case of serious model misspecification for treatment assignment. However, the loss functions normally used by the Super Learner may not be appropriate for propensity score estimation since the goal in this problem is not to optimize propensity score prediction but rather to achieve the best possible balance in the covariate distribution between treatment groups. In a simulation study, we evaluated the benefit of a modification of the Super Learner by propensity score estimation geared toward achieving covariate balance between the treated and untreated after matching on the propensity score. Our simulation study included six different scenarios characterized by various degrees of deviation from the usual main term logistic model for the true propensity score and outcome as well as the presence (or not) of instrumental variables. Our results suggest that the use of this adapted Super Learner to estimate the propensity score can further improve the robustness of propensity score matching estimators.

Effect Estimation in Point-Exposure Studies with Binary Outcomes and High-Dimensional Covariate Data - A Comparison of Targeted Maximum Likelihood Estimation and Inverse Probability of Treatment Weighting

Inverse probability of treatment weighting (IPW) and targeted maximum likelihood estimation (TMLE) are relatively new methods proposed for estimating marginal causal effects. TMLE is doubly robust, yielding consistent estimators even under misspecification of either the treatment or the outcome model. While IPW methods are known to be sensitive to near violations of the practical positivity assumption (e. g., in the case of data sparsity), the consequences of this violation in the TMLE framework for binary outcomes have been less widely investigated. As near practical positivity violations are particularly likely in high-dimensional covariate settings, a better understanding of the performance of TMLE is of particular interest for pharmcoepidemiological studies using large databases. Using plasmode and Monte-Carlo simulation studies, we evaluated the performance of TMLE compared to that of IPW estimators based on a point-exposure cohort study of the marginal causal effect of post-myocardial infarction statin use on the 1-year risk of all-cause mortality from the Clinical Practice Research Datalink. A variety of treatment model specifications were considered, inducing different degrees of near practical non-positivity. Our simulation study showed that the performance of the TMLE and IPW estimators were comparable when the dimension of the fitted treatment model was small to moderate; however, they differed when a large number of covariates was considered. When a rich outcome model was included in the TMLE, estimators were unbiased. In some cases, we found irregular bias and large standard errors with both methods even with a correctly specified high-dimensional treatment model. The IPW estimator showed a slightly better root MSE with high-dimensional treatment model specifications in our simulation setting. In conclusion, for estimation of the marginal expectation of the outcome under a fixed treatment, TMLE and IPW estimators employing the same treatment model specification may perform differently due to differential sensitivity to practical positivity violations; however, TMLE, being doubly robust, shows improved performance with richer specifications of the outcome model. Although TMLE is appealing for its double robustness property, such violations in a high-dimensional covariate setting are problematic for both methods.

Statin adherence and risk of acute cardiovascular events among women: a cohort study accounting for time-dependent confounding affected by previous adherence

OBJECTIVES

Previous studies on the effect of statin adherence on cardiovascular events in the primary prevention of cardiovascular disease have adjusted for time-dependent confounding, but potentially introduced bias into their estimates as adherence and confounders were measured simultaneously. We aimed to evaluate the effect when accounting for time-dependent confounding affected by previous adherence as well as time sequence between factors.

DESIGN

Retrospective cohort study.

SETTING

Finnish healthcare registers.

PARTICIPANTS

Women aged 45-64 years initiating statin use for primary prevention of cardiovascular disease in 2001-2004 (n=42 807).

OUTCOMES

Acute cardiovascular event defined as a composite of acute coronary syndrome and acute ischaemic stroke was our primary outcome. Low-energy fractures were used as a negative control outcome to evaluate the healthy-adherer effect.

RESULTS

During the 3-year follow-up, 474 women experienced the primary outcome event and 557 suffered a low-energy fracture. The causal HR estimated with marginal structural model for acute cardiovascular events for all the women who remained adherent (proportion of days covered ≥80%) to statin therapy during the previous adherence assessment year was 0.78 (95% CI: 0.65 to 0.94) when compared with everybody remaining non-adherent (proportion of days covered <80%). The result was robust against alternative model specifications. Statin adherers had a potentially reduced risk of experiencing low-energy fractures compared with non-adherers (HR 0.90, 95% CI 0.76 to 1.07).

CONCLUSIONS

Our study, which took into account the time dependence of adherence and confounders, as well as temporal order between these factors, is support for the concept that adherence to statins in women in primary prevention decreases the risk of acute cardiovascular events by about one-fifth in comparison to non-adherence. However, part of the observed effect of statin adherence on acute cardiovascular events may be due to the healthy-adherer effect.

Variable Selection for Confounder Control, Flexible Modeling and Collaborative Targeted Minimum Loss-Based Estimation in Causal Inference

This paper investigates the appropriateness of the integration of flexible propensity score modeling (nonparametric or machine learning approaches) in semiparametric models for the estimation of a causal quantity, such as the mean outcome under treatment. We begin with an overview of some of the issues involved in knowledge-based and statistical variable selection in causal inference and the potential pitfalls of automated selection based on the fit of the propensity score. Using a simple example, we directly show the consequences of adjusting for pure causes of the exposure when using inverse probability of treatment weighting (IPTW). Such variables are likely to be selected when using a naive approach to model selection for the propensity score. We describe how the method of Collaborative Targeted minimum loss-based estimation (C-TMLE; van der Laan and Gruber, 2010 [27]) capitalizes on the collaborative double robustness property of semiparametric efficient estimators to select covariates for the propensity score based on the error in the conditional outcome model. Finally, we compare several approaches to automated variable selection in low- and high-dimensional settings through a simulation study. From this simulation study, we conclude that using IPTW with flexible prediction for the propensity score can result in inferior estimation, while Targeted minimum loss-based estimation and C-TMLE may benefit from flexible prediction and remain robust to the presence of variables that are highly correlated with treatment. However, in our study, standard influence function-based methods for the variance underestimated the standard errors, resulting in poor coverage under certain data-generating scenarios.

Evaluating the treatment effects model for estimation of cross-sectional associations between risk factors and cardiovascular biomarkers influenced by medication use

PURPOSE

In cross-sectional observational data, evaluation of biomarker-to-exposure associations is often complicated by nonrandom medication use. Traditional approaches often lead to biased estimates, consistent with known results involving confounding by indication. More sophisticated, yet easy to implement approaches such as inverse probability weighting and censored normal regression can address medication use in certain settings but have poor performance when medication use depends on off-medication biomarker values. More sophisticated approaches are necessary.

METHODS

Heckman's treatment effects model resembles the process that gives rise to cross-sectional data. In this study, we conduct a variety of simulation studies to illustrate why traditional approaches are inappropriate when medication use depends on underlying biomarker values. We illustrate how Heckman's model can accommodate this feature. We also apply the models to data from the Multi-Ethnic Study of Atherosclerosis.

RESULTS

Inverse probability weighting and censored normal regression are sensitive to how strongly medication use is associated with untreated biomarker values (the untreated value acts as an unmeasured predictor of medication use in this context). Heckman's model can often adequately remove bias and is robust to certain forms of model misspecification but relies on knowing important predictors of medication use, even when they are independent of the biomarker. The advantages of Heckman's model can be negated if the effect of medication on biomarker values is proportionate to the underlying biomarker.

CONCLUSIONS

If predictors of medication use are measured, data are cross-sectional, and effects are approximately additive, then Heckman's model is more accurate relative to alternative approaches.

Statistical power in parallel group point exposure studies with time-to-event outcomes: an empirical comparison of the performance of randomized controlled trials and the inverse probability of treatment weighting (IPTW) approach

Background

Estimating statistical power is an important component of the design of both randomized controlled trials (RCTs) and observational studies. Methods for estimating statistical power in RCTs have been well described and can be implemented simply. In observational studies, statistical methods must be used to remove the effects of confounding that can occur due to non-random treatment assignment. Inverse probability of treatment weighting (IPTW) using the propensity score is an attractive method for estimating the effects of treatment using observational data. However, sample size and power calculations have not been adequately described for these methods.

Methods

We used an extensive series of Monte Carlo simulations to compare the statistical power of an IPTW analysis of an observational study with time-to-event outcomes with that of an analysis of a similarly-structured RCT. We examined the impact of four factors on the statistical power function: number of observed events, prevalence of treatment, the marginal hazard ratio, and the strength of the treatment-selection process.

Results

We found that, on average, an IPTW analysis had lower statistical power compared to an analysis of a similarly-structured RCT. The difference in statistical power increased as the magnitude of the treatment-selection model increased.

Conclusions

The statistical power of an IPTW analysis tended to be lower than the statistical power of a similarly-structured RCT.

The Impact of Different CD4 Cell-Count Monitoring and Switching Strategies on Mortality in HIV-Infected African Adults on Antiretroviral Therapy: An Application of Dynamic Marginal Structural Models

In Africa, antiretroviral therapy (ART) is delivered with limited laboratory monitoring, often none. In 2003–2004, investigators in the Development of Antiretroviral Therapy in Africa (DART) Trial randomized persons initiating ART in Uganda and Zimbabwe to either laboratory and clinical monitoring (LCM) or clinically driven monitoring (CDM). CD4 cell counts were measured every 12 weeks in both groups but were only returned to treating clinicians for management in the LCM group. Follow-up continued through 2008. In observational analyses, dynamic marginal structural models on pooled randomized groups were used to estimate survival under different monitoring-frequency and clinical/immunological switching strategies. Assumptions included no direct effect of randomized group on mortality or confounders and no unmeasured confounders which influenced treatment switch and mortality or treatment switch and time-dependent covariates. After 48 weeks of first-line ART, 2,946 individuals contributed 11,351 person-years of follow-up, 625 switches, and 179 deaths. The estimated survival probability after a further 240 weeks for post-48-week switch at the first CD4 cell count less than 100 cells/mm³ or non-Candida World Health Organization stage 4 event (with CD4 count <250) was 0.96 (95% confidence interval (CI): 0.94, 0.97) with 12-weekly CD4 testing, 0.96 (95% CI: 0.95, 0.97) with 24-weekly CD4 testing, 0.95 (95% CI: 0.93, 0.96) with a single CD4 test at 48 weeks (baseline), and 0.92 (95% CI: 0.91, 0.94) with no CD4 testing. Comparing randomized groups by 48-week CD4 count, the mortality risk associated with CDM versus LCM was greater in persons with CD4 counts of <100 (hazard ratio = 2.4, 95% CI: 1.3, 4.3) than in those with CD4 counts of ≥100 (hazard ratio = 1.1, 95% CI: 0.8, 1.7; interaction P = 0.04). These findings support a benefit from identifying patients immunologically failing first-line ART at 48 weeks.

Improving propensity score estimators' robustness to model misspecification using super learner

The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed better for highly unbalanced variables. The SL-based estimators were associated with the smallest bias in cases of severe model misspecification. Our results suggest that use of SL to estimate the PS can improve covariate balance and reduce bias in a meaningful manner in cases of serious model misspecification for treatment assignment.

The effect of error-in-confounders on the estimation of the causal parameter when using marginal structural models and inverse probability-of-treatment weights: a simulation study

We performed an empirical study to evaluate the effect of mismeasured continuous confounders on the estimation of the causal parameter when using marginal structural models and inverse probability-of-treatment weighting. By executing an extensive simulation using 500 randomly generated parameter value combinations within a defined space, we observed the well-understood effects of attenuation and augmentation, and two unanticipated effects: null effects and sign reversals. We implemented a secondary empirical study to further investigate the sign reversal effect. We use the results of our study to identify conceptual similarities between the analytic and empirical results for multivariable linear and logistic regression, and our empirical results. Through this synthesis, we have been able to suggest feasible directions of research as well as outline the form of expected results.

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.

Intensity of factor VIII treatment and inhibitor development in children with severe hemophilia A: the RODIN study

High-dose intensive factor VIII treatment increases the risk for inhibitor development in patients with severe hemophilia A. In patients with severe hemophilia A, factor VIII prophylaxis decreases inhibitor risk, especially in patients with low-risk F8 mutations.

An information criterion for marginal structural models

Marginal structural models were developed as a semiparametric alternative to the G-computation formula to estimate causal effects of exposures. In practice, these models are often specified using parametric regression models. As such, the usual conventions regarding regression model specification apply. This paper outlines strategies for marginal structural model specification and considerations for the functional form of the exposure metric in the final structural model. We propose a quasi-likelihood information criterion adapted from use in generalized estimating equations. We evaluate the properties of our proposed information criterion using a limited simulation study. We illustrate our approach using two empirical examples. In the first example, we use data from a randomized breastfeeding promotion trial to estimate the effect of breastfeeding duration on infant weight at 1 year. In the second example, we use data from two prospective cohorts studies to estimate the effect of highly active antiretroviral therapy on CD4 count in an observational cohort of HIV-infected men and women. The marginal structural model specified should reflect the scientific question being addressed but can also assist in exploration of other plausible and closely related questions. In marginal structural models, as in any regression setting, correct inference depends on correct model specification. Our proposed information criterion provides a formal method for comparing model fit for different specifications.

The positivity assumption and marginal structural models: the example of warfarin use and risk of bleeding

Estimates of the average causal effect (ACE) of warfarin on the risk of bleeding may be confounded by indication as patients at high risk of bleeding are unlikely to be prescribed warfarin. One approach to estimating the ACE is inverse probability of treatment weighting (IPTW). This study was designed to examine the use of IPTW in this setting, and to demonstrate problems with the violation of the positivity assumption. We analyzed a case-control study on 4,028 cases of gastro-intestinal bleeding and 79,239 controls set in the United Kingdom's General Practice Research Database. Warfarin exposure was defined as a prescription issued in the 90 days before the index date. Secondary analyses were conducted restricted to patients more likely to receive warfarin and with a truncated weight distribution, to exclude subjects highly unlikely to be treated. The estimated association between warfarin use and bleeding was stronger with IPTW [odds ratio (OR): 17.2; 95% confidence interval (CI): 6.5-37.7] than with a standard logistic regression model (OR: 2.1; 95% CI: 1.7-2.5). The presence of large weights (five subjects with stabilized weight >500) indicated a potential violation of the positivity assumption. In the restricted analysis, both IPTW (OR: 2.0; 95% CI: 0.4-9.6) and standard regression (OR: 1.6; 95% CI: 1.3-2.0) were compatible with a meta-analysis of randomized trials inverse probability of treatment weighting is sensitive to the positivity assumption; however, such sensitivity may assist in diagnosing off-support inference.

Estimation of dynamic treatment strategies for maintenance therapy of children with acute lymphoblastic leukaemia: an application of history-adjusted marginal structural models

Childhood acute lymphoblastic leukaemia is treated with long-term intensive chemotherapy. During the latter part of the treatment, the maintenance therapy, the patients receive oral doses of two cytostatics. The doses are tailored to blood counts measured on a weekly basis, and the treatment is therefore highly dynamic. In 1992-1996, the Nordic Society of Paediatric Haematology and Oncology (NOPHO) conducted a randomised study (NOPHO-ALL-92) to investigate the effect of a new and more sophisticated dynamic treatment strategy. Unexpectedly, the new strategy worsened the outcome for the girls, whereas there were no treatment differences for the boys. There are as yet no general guidelines for optimising the treatment. On basis of the data from this study, our goal is to formulate an alternative dosing strategy. We use recently developed methods proposed by van der Laan et al. to obtain statistical models that may be used in the guidance of how the physicians should assign the doses to the patients to obtain the target of the treatment. We present a possible strategy and discuss the reliability of this strategy. The implementation is complicated, and we touch upon the limitations of the methods in relation to the formulation of alternative dosing strategies for the maintenance therapy.

Colon cancer survival with herbal medicine and vitamins combined with standard therapy in a whole-systems approach: ten-year follow-up data analyzed with marginal structural models and propensity score methods

Although localized colon cancer is often successfully treated with surgery, advanced disease requires aggressive systemic therapy that has lower effectiveness. Approximately 30% to 75% of patients with colon cancer use complementary and alternative medicine (CAM), but there is limited formal evidence of survival efficacy. In a consecutive case series with 10-year follow-up of all colon cancer patients (n = 193) presenting at a San Francisco Bay-Area center for Chinese medicine (Pine Street Clinic, San Anselmo, CA), the authors compared survival in patients choosing short-term treatment lasting the duration of chemotherapy/radiotherapy with those continuing long-term. To put these data into the context of treatment responses seen in conventional medical practice, they also compared survival with Pan-Asian medicine + vitamins (PAM+V) with that of concurrent external controls from Kaiser Permanente Northern California and California Cancer Registries. Kaplan-Meier, traditional Cox regression, and more modern methods were used for causal inference-namely, propensity score and marginal structural models (MSMs), which have not been used before in studies of cancer survival and Chinese herbal medicine. PAM+V combined with conventional therapy, compared with conventional therapy alone, reduced the risk of death in stage I by 95%, stage II by 64%, stage III by 29%, and stage IV by 75%. There was no significant difference between short-term and long-term PAM+V. Combining PAM+V with conventional therapy improved survival, compared with conventional therapy alone, suggesting that prospective trials combining PAM+V with conventional therapy are justified.

Lung Cancer Survival With Herbal Medicine and Vitamins in a Whole-Systems Approach

Complementary and alternative medicines are used by up to 48% of lung cancer patients but have seen little formal assessment of survival efficacy. In this 10-year retrospective survival study, the authors investigated Pan-Asian medicine + vitamins (PAM+V) therapy in a consecutive case series of all non-small-cell lung cancer patients (n = 239) presenting at a San Francisco Bay Area Chinese medicine center (Pine Street Clinic). They compared short-term treatment lasting the duration of chemotherapy/radiotherapy with long-term therapy continuing beyond conventional therapy. They also compared PAM+V plus conventional therapy with conventional therapy alone, using concurrent controls from the Kaiser Permanente Northern California and California Cancer Registries. They adjusted for confounding with Kaplan-Meier, Cox regression, and newer methods – propensity score and marginal structural models (MSMs), which when analyzing data from observational studies or clinical practice records can provide results comparable with randomized trials. Long-term use of PAM+V beyond completion of chemotherapy reduced stage IIIB deaths by 83% and stage IV by 72% compared with short-term use only for the duration of chemotherapy. Long-term PAM+V combined with conventional therapy reduced stage IIIA deaths by 46%, stage IIIB by 62%, and stage IV by 69% compared with conventional therapy alone. Survival rates for stage IV patients treated with PAM+V were 82% at 1 year, 68% at 2 years, and 14% at 5 years. PAM+V combined with conventional therapy improved survival in stages IIIA, IIIB, and IV, compared with conventional therapy alone. Prospective trials using PAM+V with conventional therapy for lung cancer patients are justified.

Marginal Structural Models: unbiased estimation for longitudinal studies

INTRODUCTION

In this article, we introduce Marginal Structural Models, which yield unbiased estimates of causal effects of exposures in the presence of time-varying confounding variables that also act as mediators.

OBJECTIVES

We describe estimation via inverse probability weighting; estimation may also be accomplished by g-computation (Robins in Latent Variable Modeling and Applications to Causality, Springer, New York, pp 69-117, 1997; van der Wal et al. in Stat Med 28:2325-2337, 2009) or targeted maximum likelihood (Rosenblum and van der Laan in Int J Biostat 6, 2010).

CONCLUSIONS

When both time-varying confounding and mediation are present in a longitudinal setting data, Marginal Structural Models are a useful tool that provides unbiased estimates.

Estimating ethnic differences in self-reported new use of antidepressant medications: results from the Multi-Ethnic Study of Atherosclerosis

INTRODUCTION

There is evidence that the utilization of antidepressant medications (ADM) may vary between different ethnic groups in the United States population.

METHODS

The Multi-Ethnic Study of Atherosclerosis (MESA) is a population-based prospective cohort study of 6814 US adults from 4 different ethnic groups. After excluding baseline users of ADM, we examined the relation between baseline depression and new use of ADM for 4 different ethnicities: African-Americans (n = 1822), Asians (n = 784) Caucasians (n = 2300), and Hispanics (n = 1405). Estimates of the association of ethnicity and ADM use were adjusted for age, study site, gender, Center for Epidemiologic Studies Depression Scale (CES-D), alcohol use, smoking, blood pressure, diabetes, education, and exercise. Non-random loss to follow-up was present and estimates were adjusted using inverse probability of censoring weighting (IPCW).

RESULTS

Of the four ethnicities, Caucasian participants had the highest rate of ADM use (12%) compared with African-American (4%), Asian (2%), and Hispanic (6%) participants. After adjustment, non-Caucasian ethnicity was associated with reduced ADM use: African-American (HR: 0.42; 95% Confidence Interval (CI): 0.31-0.58), Asian (HR: 0.14; 95%CI: 0.08-0.26), and Hispanic (HR: 0.47; 95%CI: 0.31-0.65). Applying IPCW to correct for non-random loss to follow-up among the study participants weakened but did not eliminate these associations: African-American (HR: 0.48; 95%CI: 0.30-0.57), Asian (HR: 0.23; 95%CI: 0.13-0.37), and Hispanic (HR: 0.58; 95%CI: 0.47-0.67).

CONCLUSION

Non-Caucasian ethnicity is associated with lower rates of new ADM use. After IPCW adjustment, the observed ethnicity differences in ADM use are smaller although still statistically significant.

Risk factor adjustment in marginal structural model estimation of optimal treatment regimes

Marginal structural models (MSMs) are an increasingly popular tool, particularly in epidemiological applications, to handle the problem of time-varying confounding by intermediate variables when studying the effect of sequences of exposures. Considerable attention has been devoted to the optimal choice of treatment model for propensity score-based methods and, more recently, to variable selection in the treatment model for inverse weighting in MSMs. However, little attention has been paid to the modeling of the outcome of interest, particularly with respect to the best use of purely predictive, non-confounding variables in MSMs. Four modeling approaches are investigated in the context of both static treatment sequences and optimal dynamic treatment rules with the goal of estimating a marginal effect with the least error, both in terms of bias and variability.

High-dimensional propensity score adjustment in studies of treatment effects using health care claims data

BACKGROUND

Adjusting for large numbers of covariates ascertained from patients' health care claims data may improve control of confounding, as these variables may collectively be proxies for unobserved factors. Here, we develop and test an algorithm that empirically identifies candidate covariates, prioritizes covariates, and integrates them into a propensity-score-based confounder adjustment model.

METHODS

We developed a multistep algorithm to implement high-dimensional proxy adjustment in claims data. Steps include (1) identifying data dimensions, eg, diagnoses, procedures, and medications; (2) empirically identifying candidate covariates; (3) assessing recurrence of codes; (4) prioritizing covariates; (5) selecting covariates for adjustment; (6) estimating the exposure propensity score; and (7) estimating an outcome model. This algorithm was tested in Medicare claims data, including a study on the effect of Cox-2 inhibitors on reduced gastric toxicity compared with nonselective nonsteroidal anti-inflammatory drugs (NSAIDs).

RESULTS

In a population of 49,653 new users of Cox-2 inhibitors or nonselective NSAIDs, a crude relative risk (RR) for upper GI toxicity (RR = 1.09 [95% confidence interval = 0.91-1.30]) was initially observed. Adjusting for 15 predefined covariates resulted in a possible gastroprotective effect (0.94 [0.78-1.12]). A gastroprotective effect became stronger when adjusting for an additional 500 algorithm-derived covariates (0.88 [0.73-1.06]). Results of a study on the effect of statin on reduced mortality were similar. Using the algorithm adjustment confirmed a null finding between influenza vaccination and hip fracture (1.02 [0.85-1.21]).

CONCLUSIONS

In typical pharmacoepidemiologic studies, the proposed high-dimensional propensity score resulted in improved effect estimates compared with adjustment limited to predefined covariates, when benchmarked against results expected from randomized trials.

Time-modified confounding

According to the authors, time-modified confounding occurs when the causal relation between a time-fixed or time-varying confounder and the treatment or outcome changes over time. A key difference between previously described time-varying confounding and the proposed time-modified confounding is that, in the former, the values of the confounding variable change over time while, in the latter, the effects of the confounder change over time. Using marginal structural models, the authors propose an approach to account for time-modified confounding when the relation between the confounder and treatment is modified over time. An illustrative example and simulation show that, when time-modified confounding is present, a marginal structural model with inverse probability-of-treatment weights specified to account for time-modified confounding remains approximately unbiased with appropriate confidence limit coverage, while models that do not account for time-modified confounding are biased. Correct specification of the treatment model, including accounting for potential variation over time in confounding, is an important assumption of marginal structural models. When the effect of confounders on either the treatment or outcome changes over time, time-modified confounding should be considered.

Traditional versus marginal structural models to estimate the effectiveness of beta-blocker use on mortality after myocardial infarction

BACKGROUND

Observational studies of the effect of beta-blockers on all-cause mortality after an acute myocardial infarction (AMI) have tended to overestimate the effectiveness of this treatment.

OBJECTIVE

To compare the estimates of the effect of beta-blocker use on mortality post-AMI derived from a traditional adjusted regression model with those from a marginal structural model.

METHODS

A population-based cohort spanning the period of 2002-2004 was formed from the United Kingdom General Practice Research Database (GPRD). The cohort included all subjects who survived 90 days after their first AMI, who were then followed for 9 months. beta-Blocker use and blood pressure were identified in both the 90-day period before and the 90-day period after the AMI. Rate ratios (RR) were estimated using pooled logistic regression.

RESULTS

The cohort included 9939 participants who survived 90 days after their AMI, of whom 633 died during the 9-month follow-up. Over 23% were taking beta-blockers pre-AMI, compared with 71% post-AMI. Using the traditional adjusted regression analysis, the RR of death with post-AMI beta-blocker use was 0.54 (95% confidence interval (CI): 0.45-0.67), while using the inverse probability of treatment weighting (IPTW) model it was 0.72 (95%CI: 0.61-0.84). The IPTW estimate is compatible with the estimate derived from a meta-analysis of randomized controlled trials (RCTs) while the adjusted regression estimate exaggerates the effectiveness.

CONCLUSIONS

Observational studies of the association of anti-hypertensive medications with all-cause mortality should consider adding a marginal structural model to their armamentarium of data analysis.