Presence Of Time-dependent Confounders Research Articles

Marginal structural models for multilevel clustered data.

Marginal structural models (MSMs), which adopt inverse probability treatment weighting in the estimating equations, are powerful tools to estimate the causal effects of time-varying exposures in the presence of time-dependent confounders. Motivated by the Conservation of Hearing Study (CHEARS) Audiology Assessment Arm (AAA) where repeated hearing measurements were clustered by study participants, time, and testing sites, we propose two methods to account for the multilevel correlation structure when fitting the MSMs. The first method directly models the covariance of the repeated outcomes when solving the weighted generalized estimating equations for MSMs, while the second two-stage analysis approach fits cluster-specific MSMs first and then combines the estimated parameters using mixed-effects meta-analysis. Finite sample simulation results suggest that our methods can obtain less biased and more efficient estimates of the parameters by accounting for the multilevel correlation. Moreover, we explore the effects of using fixed- or mixed-effects model to estimate the treatment probability on the parameter estimates of the MSMs in the presence of unmeasured cluster-level confounders. Lastly, we apply our methods to the CHEARS AAA data set, to estimate the causal effects of aspirin use on hearing loss.

Application of Causal Inference Methods in the Analysis of Observational Neurosurgical Data: G-Formula and Marginal Structural Model

When using observational data to estimate the causal effects of a treatment on clinical outcomes, we need to adjust for confounding. In the presence of time-dependent confounders that are affected by previous treatment, adjustments cannot be made via the conventional regression approach or propensity score-based methods, but requires sophisticated methods called g-methods. We aimed to introduce g-methods to estimate the causal effects of treatment strategies defined by treatment at multiple time points, such as treat 2 days versus treat only day 1 versus never-treat. Two g-methods were introduced: the g-formula and inverse probability-weighted marginal structural models. Under exchangeability, consistency, and positivity assumptions, they provide a consistent estimate of the causal effects of the treatment strategy. Using a numeric example that mimics the observational study data, we presented how the g-formula and inverse probability-weighted marginal structural models can estimate the effect of the treatment strategy. Both g-formula and inverse probability-weighted marginal structural models can correctly estimate the effect of the treatment strategy under 3 identifiability assumptions, which conventional regression analysis cannot. G-methods may assist in estimating the effect of treatment strategy defined by treatment at multiple time points.

Antihypertensive medication adherence and cardiovascular disease risk: A longitudinal cohort study

Background and aimsFew studies estimated the impact of antihypertensive adherence on cardiovascular diseases (CVD) in a longitudinal cohort with presence of time-dependent confounders. This study aims to assess the association between antihypertensive adherence and CVD using marginal structural Cox model (MSM-Cox) and to characterize blood pressure (BP) trajectories of patients with different adherence. MethodsThis longitudinal study included 16,896 hypertensive patients receiving antihypertensive medication. The median follow-up time was 3.5 years (25th to 75th, 1.75–4.75 years). BP and medication adherence were measured four times every year. We used MSM-Cox and Cox model to assess association between antihypertensive adherence and CVD events. The linear mixed-effects model was used to characterize BP trajectories of patients with different adherence, and the area under curves (AUC) was calculated as BP burden. ResultsWe documented 4735 CVD events, crude incidence of CVD was 80.8 (95% CI, 78.1–83.4) and 112.6 (95% CI, 107.2–118.0) per 1000 person-years for baseline high-adherence and low-adherence, respectively. Compared with high adherence, the adjusted hazard ratio (HR) for association between low adherence with CVD was 1.75 (95%CI, 1.62–1.89) and 1.34 (95%CI, 1.26–1.42) based on the MSM-Cox and the Cox model, respectively. The BP burden and fluctuation range of BP trajectory in low-adherence patients were larger than those of high-adherence patients. Patients with high adherence got 28% greater reduction of BP burden than low-adherence patients. ConclusionsAntihypertensive adherence was more strongly associated with the risk of CVD than conventional regression analyses based on a single adherence measurement.

Impact of loop diuretics on critically ill patients with a positive fluid balance.

The impact of the use of loop diuretics to prevent cumulative fluid balance in non-oliguric patients is uncertain. This is a retrospective study to estimate the association of time-averaging loop diuretic exposure in a large population of non-cardiac, critically ill patients with a positive fluid balance (>5% of body weight). The exposure was loop diuretic and the main outcomes were 28-day mortality, severe acute kidney injury and successful mechanical ventilation weaning. Time-fixed and daily time-varying variables were evaluated with a marginal structural Cox model, adjusting bias for time-varying exposure and the presence of time-dependent confounders. A total of 14,896 patients were included. Patients receiving loop diuretics had better survival (unadjusted hazard ratio 0.56, 95%CI 0.39-0.81 and baseline variables adjusted hazard ratio 0.53, 95%CI 0.45-0.62); after full adjusting, loop diuretics had no association with 28-day mortality (full adjusted hazard ratio 1.07, 95%CI 0.74-1.54) or with reducing severe acute kidney injury occurrence during intensive care unit stay - hazard ratio 1.05 (95%CI 0.78-1.42). However, we identified an association with prolonged mechanical ventilation (hazard ratio 1.59, 95%CI 1.35-1.89). The main results were consistent in the sub-group analysis for sepsis, oliguria and the study period (2002-2007 vs. 2008-2012). Also, equivalent doses of up to 80 mg per day of furosemide had no significant association with mortality. After adjusting for time-varying variables, the time average of loop diuretic exposure in non-cardiac, critically ill patients has no association with overall mortality or severe acute kidney injury; however, prolonged mechanical ventilation is a concern.

Optimal probability weights for estimating causal effects of time-varying treatments with marginal structural Cox models.

Marginal structural Cox models have been used to estimate the causal effect of a time-varying treatment on a survival outcome in the presence of time-dependent confounders. These methods rely on the positivity assumption, which states that the propensity scores are bounded away from zero and one. Practical violations of this assumption are common in longitudinal studies, resulting in extreme weights that may yield erroneous inferences. Truncation, which consists of replacing outlying weights with less extreme ones, is the most common approach to control for extreme weights to date. While truncation reduces the variability in the weights and the consequent sampling variability of the estimator, it can also introduce bias. Instead of truncated weights, we propose using optimal probability weights, defined as those that have a specified variance and the smallest Euclidean distance from the original, untruncated weights. The set of optimal weights is obtained by solving a constrained quadratic optimization problem. The proposed weights are evaluated in a simulation study and applied to the assessment of the effect of treatment on time to death among people in Sweden who live with human immunodeficiency virus and inject drugs.

Confounding time dependent or not: introspection

Longitudinal studies, where data are repeatedly collected on one subject over a period, are common in medical research. When effect of a time-varying exposure on an outcome of interest is measured at different time points, standard statistical methods fail to give robust estimate in the presence of time-dependent confounders. There is alternative method avoid, that is, inverse probability weighted estimation of marginal structural models the problems associated with standard approaches.

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.

The Effect of Going Public on Innovative Productivity and Exploratory Search

This paper investigates whether and how going public affects firm innovation. I propose that initial public offerings (IPOs) fundamentally reshape core organizational structures and processes, and I consider implications for firms' overall innovative productivity and their exploratory search strategies. Using longitudinal data on U.S. medical device firms funded by venture capital and inverse probability of treatment weights to account for self-selection into IPOs and the presence of time-dependent confounders, I find that a firm's overall innovative productivity increases after the firm goes public. Going public also decreases the proportion of innovation search that explores new and recently developed knowledge and increases the proportion of exploratory search building on scientific knowledge. Estimates represent population average treatment effects.

Targeted maximum likelihood estimation for marginal time-dependent treatment effects under density misspecification

Targeted maximum likelihood methods have been proposed to estimate treatment effects for longitudinal data in the presence of time-dependent confounders. This class of methods has been mathematically proven to be doubly robust and to optimize the asymptotic estimating efficiency among the class of regular, semi-parametric estimators when all estimated density components are correctly specified. We show that methods previously proposed to build a one-step estimator with a logistic loss function generalize to a generalized linear loss function, and so may be applied naturally to an outcome that can be described by any exponential family member. We evaluate several methods for estimating unstructured marginal treatment effects for data with two time intervals in a simulation study, showing that these estimators have competitively low bias and variance in an array of misspecified situations, and can be made to perform well under near-positivity violations. We apply the methods to the PROmotion of Breastfeeding Intervention Trial data, demonstrating that longer term breastfeeding can protect infants from gastrointestinal infection.

Analysis of individual drug use as a time-varying determinant of exposure in prospective population-based cohort studies

In pharmaco-epidemiology, the use of drugs is the determinant of interest when studying exposure-outcome associations. The increased availability of computerized information about drug use on an individual basis has greatly facilitated analyses of drug effects on a population-based scale. It seems likely that many negative findings in the early days of pharmaco-epidemiology can be explained by non-differential misclassification because of too simple (yes/no) exposure measures. In this paper, the authors discuss the importance of an adequate definition of drug exposure in pharmaco-epidemiological research and how this time-varying determinant can be analyzed in cohort studies. To reduce the risk of non-differential misclassification, a precise definition of exposure is mandatory and it is important to distinguish the complete follow-up period of a population into mutually exclusive episodes of non-use, past use and current use for each individual. By analyzing exposure to drugs as a time-dependent variable in a Cox regression model, cohort studies with complete coverage of all filled prescriptions can provide us with valid and precise risk estimates of drug-outcome associations. However, such estimates may be biased in the presence of time-dependent confounders which are themselves affected by prior exposure.

Relation between three classes of structural models for the effect of a time-varying exposure on survival

Standard methods for estimating the effect of a time-varying exposure on survival may be biased in the presence of time-dependent confounders themselves affected by prior exposure. This problem can be overcome by inverse probability weighted estimation of Marginal Structural Cox Models (Cox MSM), g-estimation of Structural Nested Accelerated Failure Time Models (SNAFTM) and g-estimation of Structural Nested Cumulative Failure Time Models (SNCFTM). In this paper, we describe a data generation mechanism that approximately satisfies a Cox MSM, an SNAFTM and an SNCFTM. Besides providing a procedure for data simulation, our formal description of a data generation mechanism that satisfies all three models allows one to assess the relative advantages and disadvantages of each modeling approach. A simulation study is also presented to compare effect estimates across the three models.

Analysis of longitudinal marginal structural models

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.

Analysis of longitudinal marginal structural models.

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.