Improved two-stage estimation to adjust for treatment switching in randomised trials:g-estimation to address time-dependent confounding

In oncology trials, control group patients often switch onto the experimental treatment during follow-up, usually after disease progression. In this case, an intention-to-treat analysis will not address the policy question of interest – that of whether the new treatment represents an effective and cost-effective use of health care resources, compared to the standard treatment. Rank preserving structural failure time models (RPSFTM), inverse probability of censoring weights (IPCW) and two-stage estimation (TSE) have often been used to adjust for switching to inform treatment reimbursement policy decisions. TSE has been applied using a simple approach (TSEsimp), assuming no time-dependent confounding between the time of disease progression and the time of switch. This is problematic if there is a delay between progression and switch. In this paper we introduce TSEgest, which uses structural nested models and g-estimation to account for time-dependent confounding, and compare it to TSEsimp, RPSFTM and IPCW. We simulated scenarios where control group patients could switch onto the experimental treatment with and without time-dependent confounding being present. We varied switching proportions, treatment effects and censoring proportions. We assessed adjustment methods according to their estimation of control group restricted mean survival times that would have been observed in the absence of switching. All methods performed well in scenarios with no time-dependent confounding. TSEgest and RPSFTM continued to perform well in scenarios with time-dependent confounding, but TSEsimp resulted in substantial bias. IPCW also performed well in scenarios with time-dependent confounding, except when inverse probability weights were high in relation to the size of the group being subjected to weighting, which occurred when there was a combination of modest sample size and high switching proportions. TSEgest represents a useful addition to the collection of methods that may be used to adjust for treatment switching in trials in order to address policy-relevant questions

Statistical modeling of causal effects in continuous time

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321--334, (1998b) Encyclopedia of Biostatistics 6 4372--4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372--4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000820 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models

In this paper we review an approach to estimating the causal effect of a time-varying treatment on time to some event of interest. This approach is designed for the situation where the treatment may have been repeatedly adapted to patient characteristics, which themselves may also be time-dependent. In this situation the effect of the treatment cannot simply be estimated by conditioning on the patient characteristics, as these may themselves be indicators of the treatment effect. This so-called time-dependent confounding is typical in observational studies. We discuss a new class of failure time models, structural nested failure time models, which can be used to estimate the causal effect of a time-varying treatment, and present methods for estimating and testing the parameters of these models

History-Adjusted Marginal Structural Models to Estimate Time-Varying Effect Modification

Much of epidemiology and clinical medicine is focused on the estimation of treatments or interventions administered over time. In such settings of longitudinal treatment, time-dependent confounding is often an important source of bias. Marginal structural models are a powerful tool for estimating the causal effect of a treatment using observational data, particularly when time-dependent confounding is present. Recent statistical work presented a generalization of marginal structural models, called history-adjusted marginal structural models. Unlike standard marginal structural models, history-adjusted marginal structural models can be used to estimate modification of treatment effects by time-varying covariates. Estimation of time-dependent causal effect modification is frequently of great practical relevance. For example, clinical researchers are often interested in how the prognostic significance of a biomarker for treatment response can change over time. This article provides a practical introduction to the implementation and interpretation of history-adjusted marginal structural models. The method is illustrated using a clinical question drawn from the treatment of HIV infection. Observational cohort data from San Francisco, California, collected between 2000 and 2004, are used to estimate the effect of time until switching antiretroviral therapy regimen among patients receiving a non-suppressive regimen, and how this effect differs depending on CD4 T cell count

Estimating the comparative effectiveness of feeding interventions in the paediatric intensive care unit : a demonstration of longitudinal targeted maximum likelihood estimation

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

The Effect of Inter-Municipal Cooperation on Local Business Development in German Municipalities

Does inter-municipal cooperation (IMC) enhance municipal economic performance? This study employs marginal structural models to address selection into treatment and time-dependent confounding to estimate the effectiveness of IMC in the field of local business development. I use data on municipalities in four West-German states, Lower Saxony, Hesse, Rhineland Palatinate, and Bavaria during the years 2008-2015. I find that, over time, IMC has a positive effect on local economic performance and local business development resources are spent more productively in cooperating municipalities