Comparing dynamic treatment regimes using repeated-measures outcomes: modeling considerations in SMART studies

A dynamic treatment regime (DTR) is a sequence of decision rules, each of which recommends a treatment based on a patient's past and current health status. Sequential, multiple assignment, randomized trials (SMARTs) are multi-stage trial designs that yield data specifically for building effective DTRs. Modeling the marginal mean trajectories of a repeated-measures outcome arising from a SMART presents challenges, because traditional longitudinal models used for randomized clinical trials do not take into account the unique design features of SMART. We discuss modeling considerations for various forms of SMART designs, emphasizing the importance of considering the timing of repeated measures in relation to the treatment stages in a SMART. For illustration, we use data from three SMART case studies with increasing level of complexity, in autism, child attention deficit hyperactivity disorder, and adult alcoholism. In all three SMARTs, we illustrate how to accommodate the design features along with the timing of the repeated measures when comparing DTRs based on mean trajectories of the repeated-measures outcome.

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.

Estimating the Time-Varying Joint Effects of Obesity and Smoking on All-Cause Mortality Using Marginal Structural Models

Obesity and smoking are independently associated with a higher mortality risk, but previous studies have reported conflicting results about the relationship between these 2 time-varying exposures. Using prospective longitudinal data (1987-2007) from the Atherosclerosis Risk in Communities Study, our objective in the present study was to estimate the joint effects of obesity and smoking on all-cause mortality and investigate whether there were additive or multiplicative interactions. We fit a joint marginal structural Poisson model to account for time-varying confounding affected by prior exposure to obesity and smoking. The incidence rate ratios from the joint model were 2.00 (95% confidence interval (CI): 1.79, 2.24) for the effect of smoking on mortality among nonobese persons, 1.31 (95% CI: 1.13, 1.51) for the effect of obesity on mortality among nonsmokers, and 1.97 (95% CI: 1.73, 2.22) for the joint effect of smoking and obesity on mortality. The negative product term from the exponential model revealed a submultiplicative interaction between obesity and smoking (β = -0.28, 95% CI: -0.45, -0.11; P < 0.001). The relative excess risk of interaction was -0.34 (95% CI: -0.60, -0.07), indicating the presence of subadditive interaction. These results provide important information for epidemiologists, clinicians, and public health practitioners about the harmful impact of smoking and obesity.

An Empirical Method of Detecting Time-Dependent Confounding: An Observational Study of Next Day Delirium in a Medical ICU

Longitudinal research on older persons in the medical intensive care unit (MICU) is often complicated by the time-dependent confounding of concurrently administered interventions such as medications and intubation. Such temporal confounding can bias the respective longitudinal associations between concurrently administered treatments and a longitudinal outcome such as delirium. Although marginal structural models address time-dependent confounding, their application is non-trivial and preferably justified by empirical evidence. Using data from a longitudinal study of older persons in the MICU, we constructed a plausibility score from 0 – 10 where higher values indicate higher plausibility of time-dependent confounding of the association between a time-varying explanatory variable and an outcome. Based on longitudinal plots, measures of correlation, and longitudinal regression, the plausibility scores were compared to the differences in estimates obtained with non-weighted and marginal structural models of next day delirium. The plausibility scores of the three possible pairings of daily doses of fentanyl, haloperidol, and intubation indicated the following: low plausibility for haloperidol and intubation, moderate plausibility for fentanyl and haloperidol, and high plausibility for fentanyl and intubation. Comparing multivariable models of next day delirium with and without adjustment for time-dependent confounding, only intubation’s association changed substantively. In our observational study of older persons in the MICU, the plausibility scores were generally reflective of the observed differences between coefficients estimated from non-weighted and marginal structural models.

Effect of Long-Term Periodontal Care on Hemoglobin A1c in Type 2 Diabetes

This was a prospective cohort study evaluating 126,805 individuals with diabetes and periodontal disease receiving care at all Veterans Administration medical centers and clinics in the United States from 2005 through 2012. The exposures were periodontal treatment at baseline (PT0) and at follow-up (PT2). The outcomes were change in HbA1c following initial treatment (ΔHbA1c1) and follow-up treatment (ΔHbA1c2), and diabetes control was defined as HbA1c at <7% and <9% following initial and follow-up treatment, respectively. Marginal structural models were used to account for potential confounding and selection bias. The objective was to evaluate the impact of long-term treatment of periodontal disease on glycemic control among individuals with type 2 diabetes. Participants were 64 y old on average, 97% were men, and 71% were white. At baseline, the average diabetes duration was 4 y, 12% of participants were receiving insulin, and 60% had HbA1c <7%. After an average 1.7 y of follow-up, the mean HbA1c increased from 7.03% to 7.21%. About 29.4% of participants attended their periodontal maintenance visit following baseline. Periodontal treatment at baseline and follow-up reduced HbA1c by -0.02% and -0.074%, respectively. Treatment at follow-up increased the likelihood of individuals achieving diabetes control by 5% and 3% at the HbA1c <7% and HbA1c <9% thresholds, respectively, and was observed even among never smokers. HbA1c reduction after periodontal treatment at follow-up was greater (ΔHbA1c2 = -0.25%) among individuals with higher baseline HbA1c. Long-term periodontal care provided in a clinical setting improved long-term glycemic control among individuals with type 2 diabetes and periodontal disease.

Variation in attrition at subnational level: review of the Botswana National HIV/AIDS Treatment (Masa) programme data (2002-2013)

OBJECTIVE

To evaluate the variation in all-cause attrition [mortality and loss to follow-up (LTFU)] among HIV-infected individuals in Botswana by health district during the rapid and massive scale-up of the National Treatment Program.

METHODS

Analysis of routinely collected longitudinal data from 226 030 patients who received ART through the Botswana National HIV/AIDS Treatment Program across all 24 health districts from 2002 to 2013. A time-to-event analysis was used to measure crude mortality and loss to follow-up rates (LTFU). A marginal structural model was used to evaluate mortality and LTFU rates by district over time, adjusted for individual-level risk factors (e.g. age, gender, baseline CD4, year of treatment initiation and antiretroviral regimen).

RESULTS

Mortality rates in the districts ranged from the lowest 1.0 (95% CI 0.9-1.1) in Selibe-Phikwe, to the highest 5.0 (95% CI 4.0-6.1), in Mabutsane. There was a wide range of overall LTFU across districts, including rates as low as 4.6 (95% CI 4.4-4.9) losses per 100 person-years in Ngamiland, and 5.9 (95% CI 5.6-6.2) losses per 100 person-years in South East district, to rates as high as 25.4 (95% CI 23.08-27.89) losses per 100 person-years in Mabutsane and 46.3 (95% CI 43.48-49.23) losses per 100 person-years in Okavango. Even when known risk factors for mortality and LTFU were adjusted for, district was a significant predictor of both mortality and LTFU rates.

CONCLUSION

We found statistically significant variation in attrition (mortality and LTFU) and data quality among districts. These findings suggest that district-level contextual factors affect retention in treatment. Further research needs to investigate factors that can potentially cause this variation.

Adaptive truncated weighting for improving marginal structural model estimation of treatment effects informally censored by subsequent therapy

Randomized clinical trials are designed to estimate the direct effect of a treatment by randomly assigning patients to receive either treatment or control. However, in some trials, patients who discontinued their initial randomized treatment are allowed to switch to another treatment. Therefore, the direct treatment effect of interest may be confounded by subsequent treatment. Moreover, the decision on whether to initiate a second-line treatment is typically made based on time-dependent factors that may be affected by prior treatment history. Due to these time-dependent confounders, traditional time-dependent Cox models may produce biased estimators of the direct treatment effect. Marginal structural models (MSMs) have been applied to estimate causal treatment effects even in the presence of time-dependent confounders. However, the occurrence of extremely large weights can inflate the variance of the MSM estimators. In this article, we proposed a new method for estimating weights in MSMs by adaptively truncating the longitudinal inverse probabilities. This method provides balance in the bias variance trade-off when large weights are inevitable, without the ad hoc removal of selected observations. We conducted simulation studies to explore the performance of different methods by comparing bias, standard deviation, confidence interval coverage rates, and mean square error under various scenarios. We also applied these methods to a randomized, open-label, phase III study of patients with nonsquamous non-small cell lung cancer.

Clustering and Residual Confounding in the Application of Marginal Structural Models: Dialysis Modality, Vascular Access, and Mortality

In the application of marginal structural models to compare time-varying treatments, it is rare that the hierarchical structure of a data set is accounted for or that the impact of unmeasured confounding on estimates is assessed. These issues often arise when analyzing data sets drawn from clinical registries, where patients may be clustered within health-care providers, and the amount of data collected from each patient may be limited by design (e.g., to reduce costs or encourage provider participation). We compared the survival of patients undergoing treatment with various dialysis types, where some patients switched dialysis modality during the course of their treatment, by estimating a marginal structural model using data from the Australia and New Zealand Dialysis and Transplant Registry, 2003-2011. The number of variables recorded by the registry is limited, and patients are clustered within the dialysis centers responsible for their treatment, so we assessed the impact of accounting for unmeasured confounding or clustering on estimated treatment effects. Accounting for clustering had limited impact, and only unreasonable levels of unmeasured confounding would have changed conclusions about treatment comparisons. Our analysis serves as a case study in assessing the impact of unmeasured confounding and clustering in the application of marginal structural models.

Failure of empirical systemic antifungal therapy in mechanically ventilated critically ill patients

RATIONALE

Systemic antifungal treatments are empirically administered to the sickest critically ill patients, often without documented invasive fungal infection.

OBJECTIVES

To estimate the impact of systemic antifungal treatment on 30-day survival of patients suspected to have invasive candidiasis.

METHODS

All nonneutropenic, nontransplant recipients managed in five intensive care units intubated for at least 5 days, and free of invasive candidiasis, were included. To account for differences in patients' characteristics recorded daily before study end point, a causal model for longitudinal data was used to assess benefits from antifungal treatment. The composite primary end point was hospital mortality or occurrence of invasive candidiasis.

MEASUREMENTS AND MAIN RESULTS

Among 1,491 patients, 100 (6.7%) received antifungal treatment for a suspected infection. Patients treated with antifungals were more severely ill than untreated patients. Within the 30-day follow-up period, 363 (24.3%) patients died, and 22 (1.5%) exhibited documented invasive candidiasis. After adjustment on baseline and time-dependent confounders (underlying illness, severity, invasive procedures, Candida colonization), and using a marginal structural model for longitudinal data, treatment was not associated with a decreased risk of mortality or of occurrence of invasive candidiasis (hazard ratio, 1.05; 95% confidence interval, 0.56-1.96; P = 0.91).

CONCLUSIONS

This study failed to show outcome benefits for empirical systemic antifungal therapy in the sickest critically ill, nonneutropenic, nontransplanted patients. The post hoc power did not allow us to conclude to an absence of treatment effect especially for specific subgroups. Studies to refine indications for empirical treatment based on surrogate markers of invasive candidiasis are warranted.

Impact of paliperidone palmitate versus oral atypical antipsychotics on healthcare outcomes in schizophrenia patients

AIM

To assess impact of initial treatment and time-dependent treatment with paliperidone palmitate (PP) versus oral atypical antipsychotics (OAAs) on healthcare resource utilization and costs.

PATIENTS & METHODS

A retrospective longitudinal study was conducted among Medicaid beneficiaries with schizophrenia. Inverse probability treatment weighting method and marginal structural models were used to estimate the impact of treatment on healthcare resource utilization and costs, respectively.

RESULTS

Compared to OAAs, PP was associated with lower medical costs (mean monthly cost difference [MMCD] = -US$256; p = 0.008), which offset the higher pharmacy expense (MMCD = US$122; p < 0.001) resulting in nonsignificant cost savings associated with PP (MMCD = -US$91; p = 0.689).

CONCLUSION

PP was associated with comparable overall costs to OAAs, but with significantly lower medical costs, particularly attributable to reduced inpatient visits and long-term care admissions.

Changes in Depressive Symptoms and Incidence of First Stroke Among Middle-Aged and Older US Adults

Background

Although research has demonstrated that depressive symptoms predict stroke incidence, depressive symptoms are dynamic. It is unclear whether stroke risk persists if depressive symptoms remit.

Methods and Results

Health and Retirement Study participants (n=16 178, stroke free and noninstitutionalized at baseline) were interviewed biennially from 1998 to 2010. Stroke and depressive symptoms were assessed through self-report of doctors’ diagnoses and a modified Center for Epidemiologic Studies - Depression scale (high was ≥3 symptoms), respectively. We examined whether depressive symptom patterns, characterized across 2 successive interviews (stable low/no, onset, remitted, or stable high depressive symptoms) predicted incident stroke (1192 events) during the subsequent 2 years. We used marginal structural Cox proportional hazards models adjusted for demographics, health behaviors, chronic conditions, and attrition. We also estimated effects stratified by age (≥65 years), race or ethnicity (non-Hispanic white, non-Hispanic black, Hispanic), and sex. Stroke hazard was elevated among participants with stable high (adjusted hazard ratio 2.14, 95% CI 1.69 to 2.71) or remitted (adjusted hazard ratio 1.66, 95% CI 1.22 to 2.26) depressive symptoms compared with participants with stable low/no depressive symptoms. Stable high depressive symptom predicted stroke among all subgroups. Remitted depressive symptoms predicted increased stroke hazard among women (adjusted hazard ratio 1.86, 95% CI 1.30 to 2.66) and non-Hispanic white participants (adjusted hazard ratio 1.66, 95% CI 1.18 to 2.33) and was marginally associated among Hispanics (adjusted hazard ratio 2.36, 95% CI 0.98 to 5.67).

Conclusions

In this cohort, persistently high depressive symptoms were associated with increased stroke risk. Risk remained elevated even if depressive symptoms remitted over a 2-year period, suggesting cumulative etiologic mechanisms linking depression and stroke.

Effect on child cognitive function of increasing household expenditure in Indonesia: application of a marginal structural model and simulation of a cash transfer programme

BACKGROUND

Parental investments in children are an important determinant of human capability formation. We investigated the causal effect of household expenditure on Indonesian children's cognitive function between 2000 and 2007. We also investigated the effect of change in mean cognitive function from a simulation of a hypothetical cash transfer intervention.

METHODS

A longitudinal analysis using data from the Indonesian Family Life Survey (IFLS) was conducted including 6136 children aged 7 to 14 years in 2000 and still alive in 2007. We used the inverse probability of treatment weighting of a marginal structural model to estimate the causal effect of household expenditure on children's cognitive function.

RESULTS

Cumulative household expenditure was positively associated with cognitive function z-score. From the marginal structural model, a 74534 rupiah/month (about US$9) increase in household expenditure resulted in a 0.03 increase in cognitive function z-score [β=0.32, 95% confidence interval (CI) 0.30-0.35] Based on our simulations, among children in the poorest households in 2000 an additional ≈ US$6-10 of cash transfer resulted in a 0.01 unit increase in cognitive function z-score, equivalent to about 6% increase from the mean z-score prior to cash transfer. In contrast, children in the poorest household in 2007 did not benefit from an additional ≈ US$10 cash transfer. We found no overall effect of cash transfers at the total population level.

CONCLUSIONS

Greater household expenditure had a small causal effect on children's cognitive function. Although cash transfer interventions had a positive effect for poor children, this effect was quite small. Multi-faceted interventions that combine nutrition, cash transfer, improved living conditions and women's education are required to benefit children's cognitive development in Indonesia.

High-dimensional propensity score algorithm in comparative effectiveness research with time-varying interventions

The high-dimensional propensity score (hdPS) algorithm was proposed for automation of confounding adjustment in problems involving large healthcare databases. It has been evaluated in comparative effectiveness research (CER) with point treatments to handle baseline confounding through matching or covariance adjustment on the hdPS. In observational studies with time-varying interventions, such hdPS approaches are often inadequate to handle time-dependent confounding and selection bias. Inverse probability weighting (IPW) estimation to fit marginal structural models can adequately handle these biases under the fundamental assumption of no unmeasured confounders. Upholding of this assumption relies on the selection of an adequate set of covariates for bias adjustment. We describe the application and performance of the hdPS algorithm to improve covariate selection in CER with time-varying interventions based on IPW estimation and explore stabilization of the resulting estimates using Super Learning. The evaluation is based on both the analysis of electronic health records data in a real-world CER study of adults with type 2 diabetes and a simulation study. This report (i) establishes the feasibility of IPW estimation with the hdPS algorithm based on large electronic health records databases, (ii) demonstrates little impact on inferences when supplementing the set of expert-selected covariates using the hdPS algorithm in a setting with extensive background knowledge, (iii) supports the application of the hdPS algorithm in discovery settings with little background knowledge or limited data availability, and (iv) motivates the application of Super Learning to stabilize effect estimates based on the hdPS algorithm.

Ensemble learning of inverse probability weights for marginal structural modeling in large observational datasets

Inverse probability weights used to fit marginal structural models are typically estimated using logistic regression. However, a data-adaptive procedure may be able to better exploit information available in measured covariates. By combining predictions from multiple algorithms, ensemble learning offers an alternative to logistic regression modeling to further reduce bias in estimated marginal structural model parameters. We describe the application of two ensemble learning approaches to estimating stabilized weights: super learning (SL), an ensemble machine learning approach that relies on V-fold cross validation, and an ensemble learner (EL) that creates a single partition of the data into training and validation sets. Longitudinal data from two multicenter cohort studies in Spain (CoRIS and CoRIS-MD) were analyzed to estimate the mortality hazard ratio for initiation versus no initiation of combined antiretroviral therapy among HIV positive subjects. Both ensemble approaches produced hazard ratio estimates further away from the null, and with tighter confidence intervals, than logistic regression modeling. Computation time for EL was less than half that of SL. We conclude that ensemble learning using a library of diverse candidate algorithms offers an alternative to parametric modeling of inverse probability weights when fitting marginal structural models. With large datasets, EL provides a rich search over the solution space in less time than SL with comparable results.

Impact of a pharmacy benefit change on new use of mail order pharmacy among diabetes patients: the Diabetes Study of Northern California (DISTANCE)

OBJECTIVE

To assess the impact of a pharmacy benefit change on mail order pharmacy (MOP) uptake.

DATA SOURCES/STUDY SETTING

Race-stratified, random sample of diabetes patients in an integrated health care delivery system.

STUDY DESIGN

In this natural experiment, we studied the impact of a pharmacy benefit change that conditionally discounted medications if patients used MOP and prepaid two copayments. We compared MOP uptake among those exposed to the benefit change (n = 2,442) and the reference group with no benefit change (n = 8,148), and estimated differential MOP uptake across social strata using a difference-in-differences framework.

DATA COLLECTION/EXTRACTION METHODS

Ascertained MOP uptake (initiation among previous nonusers).

PRINCIPAL FINDINGS

Thirty percent of patients started using MOP after receiving the benefit change versus 9 percent uptake among the reference group (p < .0001). After adjustment, there was a 26 percentage point greater MOP uptake (benefit change effect). This benefit change effect was significantly smaller among patients with inadequate health literacy (15 percent less), limited English proficiency (14 percent less), and among Latinos and Asians (24 and 16 percent less compared to Caucasians).

CONCLUSIONS

Conditionally discounting medications delivered by MOP effectively stimulated MOP uptake overall, but it unintentionally widened previously existing social gaps in MOP use because it stimulated less MOP uptake in vulnerable populations.

Change in physical activity after smoking cessation: the Coronary Artery Risk Development in Young Adults (CARDIA) study

AIMS

To estimate physical activity trajectories for people who quit smoking, and compare them to what would have been expected had smoking continued.

DESIGN, SETTING AND PARTICIPANTS

A total of 5115 participants in the Coronary Artery Risk Development in Young Adults Study (CARDIA) study, a population-based study of African American and European American people recruited at age 18-30 years in 1985/6 and followed over 25 years.

MEASUREMENTS

Physical activity was self-reported during clinical examinations at baseline (1985/6) and at years 2, 5, 7, 10, 15, 20 and 25 (2010/11); smoking status was reported each year (at examinations or by telephone, and imputed where missing). We used mixed linear models to estimate trajectories of physical activity under varying smoking conditions, with adjustment for participant characteristics and secular trends.

FINDINGS

We found significant interactions by race/sex (P = 0.02 for the interaction with cumulative years of smoking), hence we investigated the subgroups separately. Increasing years of smoking were associated with a decline in physical activity in black and white women and black men [e.g. coefficient for 10 years of smoking: -0.14; 95% confidence interval (CI) = -0.20 to -0.07, P < 0.001 for white women]. An increase in physical activity was associated with years since smoking cessation in white men (coefficient 0.06; 95% CI = 0 to 0.13, P = 0.05). The physical activity trajectory for people who quit diverged progressively towards higher physical activity from the expected trajectory had smoking continued. For example, physical activity was 34% higher (95% CI = 18 to 52%; P < 0.001) for white women 10 years after stopping compared with continuing smoking for those 10 years (P = 0.21 for race/sex differences).

CONCLUSIONS

Smokers who quit have progressively higher levels of physical activity in the years after quitting compared with continuing smokers.

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.

Antiretroviral therapy reduces the rate of hepatic decompensation among HIV- and hepatitis C virus-coinfected veterans

BACKGROUND

 Human immunodeficiency virus (HIV) coinfection accelerates the rate of liver disease outcomes in individuals chronically infected with hepatitis C virus (HCV). It remains unclear to what degree combination antiretroviral therapy (ART) protects against HCV-associated liver failure.

METHODS

 We evaluated 10 090 HIV/HCV-coinfected males from the Veterans Aging Cohort Study Virtual Cohort, who had not initiated ART at entry, for incident hepatic decompensation between 1996 and 2010. We defined ART initiation as the first pharmacy fill date of a qualifying ART regimen of ≥3 drugs from ≥2 classes. Hepatic decompensation was defined as the first occurrence of 1 hospital discharge diagnosis or 2 outpatient diagnoses for ascites, spontaneous bacterial peritonitis, or esophageal variceal hemorrhage. To account for potential confounding by indication, marginal structural models were used to estimate hazard ratios (HRs) of hepatic decompensation, comparing initiation of ART to noninitiation.

RESULTS

 We observed 645 hepatic decompensation events in 46 444 person-years of follow-up (incidence rate, 1.4/100 person-years). Coinfected patients who initiated ART had a significantly reduced rate of hepatic decompensation relative to noninitiators (HR = 0.72; 95% confidence interval [CI], .54-.94). When we removed individuals with HIV RNA ≤400 copies/mL at baseline from the analysis (assuming that they may have received undocumented ART at entry), the hazard ratio became more pronounced (HR = 0.59; 95% CI, .43-.82).

CONCLUSIONS

 Initiation of ART significantly reduced the rate of hepatic decompensation by 28%-41% on average. These results suggest that ART should be administered to HIV/HCV-coinfected patients to lower the risk of end-stage liver disease.

An analytic framework for aligning observational and randomized trial data: Application to postmenopausal hormone therapy and coronary heart disease

We describe a conceptual analytic framework for aligning observational and randomized controlled trial (RCT) data. The framework allows one to 1) use observational data to estimate treatment effects comparable to their RCT counterparts, 2) properly include early events that occur soon after treatment initiation in the analysis of observational data, 3) estimate various treatment effects that are of clinical and scientific relevance while appropriately adjusting for time-varying confounders in both the RCT and observational analyses, 4) assess the generalizability of RCT findings in the more diverse populations generally found in the observational data, and 5) combine both types of data to study associations that cannot be addressed by one study or a single dataset. We describe the theoretical application of this framework to the Women's Health Initiative data to examine the relation between postmenopausal hormone therapy and coronary heart disease. The analytic framework can be tailored to specific exposure-outcome associations and data sources, and may be refined as more is learned about its strengths and limitations.

Diagnosing and responding to violations in the positivity assumption

The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural working model, restriction of the sample, and modification of the target intervention. All of these approaches can be understood as trading off proximity to the initial target of inference for identifiability; we advocate approaching this tradeoff systematically.

Antihypertensive medication use and change in kidney function in elderly adults: a marginal structural model analysis

BACKGROUND

The evidence for the effectiveness of antihypertensive medication use for slowing decline in kidney function in older persons is sparse. We addressed this research question by the application of novel methods in a marginal structural model.

METHODS

Change in kidney function was measured by two or more measures of cystatin C in 1,576 hypertensive participants in the Cardiovascular Health Study over 7 years of follow-up (1989-1997 in four U.S. communities). The exposure of interest was antihypertensive medication use. We used a novel estimator in a marginal structural model to account for bias due to confounding and informative censoring.

RESULTS

The mean annual decline in eGFR was 2.41 ± 4.91 mL/min/1.73 m(2). In unadjusted analysis, antihypertensive medication use was not associated with annual change in kidney function. Traditional multivariable regression did not substantially change these estimates. Based on a marginal structural analysis, persons on antihypertensives had slower declines in kidney function; participants had an estimated 0.88 (0.13, 1.63) ml/min/1.73 m(2) per year slower decline in eGFR compared with persons on no treatment. In a model that also accounted for bias due to informative censoring, the estimate for the treatment effect was 2.23 (-0.13, 4.59) ml/min/1.73 m(2) per year slower decline in eGFR.

CONCLUSION

In summary, estimates from a marginal structural model suggested that antihypertensive therapy was associated with preserved kidney function in hypertensive elderly adults. Confirmatory studies may provide power to determine the strength and validity of the findings.

Collaborative double robust targeted maximum likelihood estimation

Collaborative double robust targeted maximum likelihood estimators represent a fundamental further advance over standard targeted maximum likelihood estimators of a pathwise differentiable parameter of a data generating distribution in a semiparametric model, introduced in van der Laan, Rubin (2006). The targeted maximum likelihood approach involves fluctuating an initial estimate of a relevant factor (Q) of the density of the observed data, in order to make a bias/variance tradeoff targeted towards the parameter of interest. The fluctuation involves estimation of a nuisance parameter portion of the likelihood, g. TMLE has been shown to be consistent and asymptotically normally distributed (CAN) under regularity conditions, when either one of these two factors of the likelihood of the data is correctly specified, and it is semiparametric efficient if both are correctly specified. In this article we provide a template for applying collaborative targeted maximum likelihood estimation (C-TMLE) to the estimation of pathwise differentiable parameters in semi-parametric models. The procedure creates a sequence of candidate targeted maximum likelihood estimators based on an initial estimate for Q coupled with a succession of increasingly non-parametric estimates for g. In a departure from current state of the art nuisance parameter estimation, C-TMLE estimates of g are constructed based on a loss function for the targeted maximum likelihood estimator of the relevant factor Q that uses the nuisance parameter to carry out the fluctuation, instead of a loss function for the nuisance parameter itself. Likelihood-based cross-validation is used to select the best estimator among all candidate TMLE estimators of Q(0) in this sequence. A penalized-likelihood loss function for Q is suggested when the parameter of interest is borderline-identifiable. We present theoretical results for "collaborative double robustness," demonstrating that the collaborative targeted maximum likelihood estimator is CAN even when Q and g are both mis-specified, providing that g solves a specified score equation implied by the difference between the Q and the true Q(0). This marks an improvement over the current definition of double robustness in the estimating equation literature. We also establish an asymptotic linearity theorem for the C-DR-TMLE of the target parameter, showing that the C-DR-TMLE is more adaptive to the truth, and, as a consequence, can even be super efficient if the first stage density estimator does an excellent job itself with respect to the target parameter. This research provides a template for targeted efficient and robust loss-based learning of a particular target feature of the probability distribution of the data within large (infinite dimensional) semi-parametric models, while still providing statistical inference in terms of confidence intervals and p-values. This research also breaks with a taboo (e.g., in the propensity score literature in the field of causal inference) on using the relevant part of likelihood to fine-tune the fitting of the nuisance parameter/censoring mechanism/treatment mechanism.

Targeted maximum likelihood estimation of the parameter of a marginal structural model

Targeted maximum likelihood estimation is a versatile tool for estimating parameters in semiparametric and nonparametric models. We work through an example applying targeted maximum likelihood methodology to estimate the parameter of a marginal structural model. In the case we consider, we show how this can be easily done by clever use of standard statistical software. We point out differences between targeted maximum likelihood estimation and other approaches (including estimating function based methods). The application we consider is to estimate the effect of adherence to antiretroviral medications on virologic failure in HIV positive individuals.

Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, Part II: proofs of results

In this companion article to "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content" [Orellana, Rotnitzky and Robins (2010), IJB, Vol. 6, Iss. 2, Art. 7] we present (i) proofs of the claims in that paper, (ii) a proposal for the computation of a confidence set for the optimal index when this lies in a finite set, and (iii) an example to aid the interpretation of the positivity assumption.