Comparison of statistical approaches dealing with time-dependent confounding in drug effectiveness studies

Genetic matching for time-dependent treatments: a longitudinal extension and simulation study

BACKGROUND

Longitudinal matching can mitigate confounding in observational, real-world studies of time-dependent treatments. To date, these methods have required iterative, manual re-specifications to achieve covariate balance. We propose a longitudinal extension of genetic matching, a machine learning approach that automates balancing of covariate histories. We examine performance by comparing the proposed extension against baseline propensity score matching and time-dependent propensity score matching.

METHODS

To evaluate comparative performance, we developed a Monte Carlo simulation framework that reflects a static treatment assigned at multiple time points. Data generation considers a treatment assignment model, a continuous outcome model, and underlying covariates. In simulation, we generated 1,000 datasets, each consisting of 1,000 subjects, and applied: (1) nearest neighbour matching on time-invariant, baseline propensity scores; (2) sequential risk set matching on time-dependent propensity scores; and (3) longitudinal genetic matching on time-dependent covariates. To measure comparative performance, we estimated covariate balance, efficiency, bias, and root mean squared error (RMSE) of treatment effect estimates. In scenario analysis, we varied underlying assumptions for assumed covariate distributions, correlations, treatment assignment models, and outcome models.

RESULTS

In all scenarios, baseline propensity score matching resulted in biased effect estimation in the presence of time-dependent confounding, with mean bias ranging from 29.7% to 37.2%. In contrast, time-dependent propensity score matching and longitudinal genetic matching achieved stronger covariate balance and yielded less biased estimation, with mean bias ranging from 0.7% to 13.7%. Across scenarios, longitudinal genetic matching achieved similar or better performance than time-dependent propensity score matching without requiring manual re-specifications or normality of covariates.

CONCLUSIONS

While the most appropriate longitudinal method will depend on research questions and underlying data patterns, our study can help guide these decisions. Simulation results demonstrate the validity of our longitudinal genetic matching approach for supporting future real-world assessments of treatments accessible at multiple time points.

Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models

Longitudinal observational data on patients can be used to investigate causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights (IPTW) (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, and involves creating a sequence of "trials" from new time origins and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment assignment at the start of each "trial" (initiator or noninitiator), which is accounted for using inverse probability of censoring weights. The analysis uses data combined across trials. We show that the sequential trials approach can estimate the parameters of a particular MSM. The causal estimand that we focus on is the marginal risk difference between the sustained treatment strategies of "always treat" vs "never treat." We compare how the sequential trials approach and MSM-IPTW estimate this estimand, and discuss their assumptions and how data are used differently. The performance of the two approaches is compared in a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at later time points and relies on modelling assumptions. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

On the Use of Covariate Supersets for Identification Conditions

The union of distinct covariate sets, or the superset, is often used in proofs for the identification or the statistical consistency of an estimator when multiple sources of bias are present. However, the use of a superset can obscure important nuances. Here, we provide two illustrative examples: one in the context of missing data on outcomes, and one in which the average causal effect is transported to another target population. As these examples demonstrate, the use of supersets may indicate a parameter is not identifiable when the parameter is indeed identified. Furthermore, a series of exchangeability conditions may lead to successively weaker conditions. Future work on approaches to address multiple biases can avoid these pitfalls by considering the more general case of nonoverlapping covariate sets.

Simulating longitudinal data from marginal structural models using the additive hazard model

Observational longitudinal data on treatments and covariates are increasingly used to investigate treatment effects, but are often subject to time-dependent confounding. Marginal structural models (MSMs), estimated using inverse probability of treatment weighting or the g-formula, are popular for handling this problem. With increasing development of advanced causal inference methods, it is important to be able to assess their performance in different scenarios to guide their application. Simulation studies are a key tool for this, but their use to evaluate causal inference methods has been limited. This paper focuses on the use of simulations for evaluations involving MSMs in studies with a time-to-event outcome. In a simulation, it is important to be able to generate the data in such a way that the correct forms of any models to be fitted to those data are known. However, this is not straightforward in the longitudinal setting because it is natural for data to be generated in a sequential conditional manner, whereas MSMs involve fitting marginal rather than conditional hazard models. We provide general results that enable the form of the correctly specified MSM to be derived based on a conditional data generating procedure, and show how the results can be applied when the conditional hazard model is an Aalen additive hazard or Cox model. Using conditional additive hazard models is advantageous because they imply additive MSMs that can be fitted using standard software. We describe and illustrate a simulation algorithm. Our results will help researchers to effectively evaluate causal inference methods via simulation.

Dealing With Treatment-Confounder Feedback and Sparse Follow-up in Longitudinal Studies: Application of a Marginal Structural Model in a Multiple Sclerosis Cohort

The beta-interferons are widely prescribed platform therapies for patients with multiple sclerosis (MS). We accessed a cohort of patients with relapsing-onset MS from British Columbia, Canada (1995-2013), to examine the potential survival advantage associated with beta-interferon exposure using a marginal structural model. Accounting for potential treatment-confounder feedback between comorbidity, MS disease progression, and beta-interferon exposure, we found an association between beta-interferon exposure of at least 6 contiguous months and improved survival (hazard ratio (HR) = 0.63, 95% confidence interval 0.47, 0.86). We also assessed potential effect modifications by sex, baseline age, or baseline disease duration, and found these factors to be important effect modifiers. Sparse follow-up due to variability in patient contact with the health system is one of the biggest challenges in longitudinal analyses. We considered several single-level and multilevel multiple imputation approaches to deal with sparse follow-up and disease progression information; both types of approach produced similar estimates. Compared to ad hoc imputation approaches, such as linear interpolation (HR = 0.63), and last observation carried forward (HR = 0.65), all multiple imputation approaches produced a smaller hazard ratio (HR = 0.53), although the direction of effect and conclusions drawn concerning the survival advantage remained the same.

Reflection on modern methods: trial emulation in the presence of immortal-time bias. Assessing the benefit of major surgery for elderly lung cancer patients using observational data

Acquiring real-world evidence is crucial to support health policy, but observational studies are prone to serious biases. An approach was recently proposed to overcome confounding and immortal-time biases within the emulated trial framework. This tutorial provides a step-by-step description of the design and analysis of emulated trials, as well as R and Stata code, to facilitate its use in practice. The steps consist in: (i) specifying the target trial and inclusion criteria; (ii) cloning patients; (iii) defining censoring and survival times; (iv) estimating the weights to account for informative censoring introduced by design; and (v) analysing these data. These steps are illustrated with observational data to assess the benefit of surgery among 70-89-year-old patients diagnosed with early-stage lung cancer. Because of the severe unbalance of the patient characteristics between treatment arms (surgery yes/no), a naïve Kaplan-Meier survival analysis of the initial cohort severely overestimated the benefit of surgery on 1-year survival (22% difference), as did a survival analysis of the cloned dataset when informative censoring was ignored (17% difference). By contrast, the estimated weights adequately removed the covariate imbalance. The weighted analysis still showed evidence of a benefit, though smaller (11% difference), of surgery among older lung cancer patients on 1-year survival. Complementing the CERBOT tool, this tutorial explains how to proceed to conduct emulated trials using observational data in the presence of immortal-time bias. The strength of this approach is its transparency and its principles that are easily understandable by non-specialists.

The population-attributable fraction for time-dependent exposures using dynamic prediction and landmarking

The public health impact of a harmful exposure can be quantified by the population-attributable fraction (PAF). The PAF describes the attributable risk due to an exposure and is often interpreted as the proportion of preventable cases if the exposure was extinct. Difficulties in the definition and interpretation of the PAF arise when the exposure of interest depends on time. Then, the definition of exposed and unexposed individuals is not straightforward. We propose dynamic prediction and landmarking to define and estimate a PAF in this data situation. Two estimands are discussed which are based on two hypothetical interventions that could prevent the exposure in different ways. Considering the first estimand, at each landmark the estimation problem is reduced to a time-independent setting. Then, estimation is simply performed by using a generalized-linear model accounting for the current exposure state and further (time-varying) covariates. The second estimand is based on counterfactual outcomes, estimation can be performed using pseudo-values or inverse-probability weights. The approach is explored in a simulation study and applied on two data examples. First, we study a large French database of intensive care unit patients to estimate the population-benefit of a pathogen-specific intervention that could prevent ventilator-associated pneumonia caused by the pathogen Pseudomonas aeruginosa. Moreover, we quantify the population-attributable burden of locoregional and distant recurrence in breast cancer patients.

Performance of the marginal structural cox model for estimating individual and joined effects of treatments given in combination

BACKGROUND

The Marginal Structural Cox Model (Cox-MSM), an alternative approach to handle time-dependent confounder, was introduced for survival analysis and applied to estimate the joint causal effect of two time-dependent nonrandomized treatments on survival among HIV-positive subjects. Nevertheless, Cox-MSM performance in the case of multiple treatments has not been fully explored under different degree of time-dependent confounding for treatments or in case of interaction between treatments. We aimed to evaluate and compare the performance of the marginal structural Cox model (Cox-MSM) to the standard Cox model in estimating the treatment effect in the case of multiple treatments under different scenarios of time-dependent confounding and when an interaction between treatment effects is present.

METHODS

We specified a Cox-MSM with two treatments including an interaction term for situations where an adverse event might be caused by two treatments taken simultaneously but not by each treatment taken alone. We simulated longitudinal data with two treatments and a time-dependent confounder affected by one or the two treatments. To fit the Cox-MSM, we used the inverse probability weighting method. We illustrated the method to evaluate the specific effect of protease inhibitors combined (or not) to other antiretroviral medications on the anal cancer risk in HIV-infected individuals, with CD4 cell count as time-dependent confounder.

RESULTS

Overall, Cox-MSM performed better than the standard Cox model. Furthermore, we showed that estimates were unbiased when an interaction term was included in the model.

CONCLUSION

Cox-MSM may be used for accurately estimating causal individual and joined treatment effects from a combination therapy in presence of time-dependent confounding provided that an interaction term is estimated.

SSEv: A New Small Samples Evaluator Based on Modified Survival Curves

Rare diseases, either of genetic or epigenetic origin, either proliferative or degenerative, are hard to be studied credibly, because of sparse prevalence, thus, small sampling. In addition, biological or translational experimentation either with animal models, or in vitro studies share small sampling-often due to lack of financial support or due to mannered and costly techniques. Pilot or feasibility studies been performed, before expensive clinical trials are decided, focus on small samples. Small Samples Evaluator (SSEv) is a useful tool based on a modification of survival curves. The technique can be applied to repeated measures, as well as to case-control or cross-sectional designed studies. A web-based application of SSEv is created and presented herein. The application is freely accessible at: https://ssev.eu .