Estimating long-term treatment effects in observational data: a comparison of the performance of different methods under real-world uncertainty

In the presence of time-dependent confounding there are several methods available to estimate treatment effects. With correctly specified models and appropriate structural assumptions any of these methods could provide consistent effect estimates, but with real-world data all models will be misspecified and it is difficult to know if assumptions are violated. In this paper, we investigate five methods: inverse probability weighting of marginal structural models, history-adjusted marginal structural models, sequential conditional mean models, g-computation formula, and g-estimation of structural nested models. This work is motivated by an investigation of the effects of treatments in cystic fibrosis using the UK Cystic Fibrosis Registry data focussing on two outcomes: lung function (continuous outcome) and annual number of days receiving intravenous antibiotics (count outcome). We identified five features of this data that may affect the performance of the methods: misspecification of the causal null, long-term treatment effects, effect modification by time-varying covariates, misspecification of the direction of causal pathways, and censoring. In simulation studies, under ideal settings all five methods provide consistent estimates of the treatment effect with little difference between methods. However, all methods performed poorly under some settings, highlighting the importance of using appropriate methods based on the data available. Furthermore, with the count outcome, the issue of non-collapsibility makes comparison between methods delivering marginal and conditional effects difficult. In many situations, we would recommend using more than one of the available methods for analysis, as if the effect estimates are very different this would indicate potential issues with the analyses