I previously wrote a post about the meaning of missing at random for longitudinal data in clinical trials, stemming from an earlier question from someone. Somebody recently asked an excellent question in the comments to this post, which here I’ll follow-up on using directed acyclic graphs (DAGs). The idea of using DAGs to under missingness assumptions has been written about by a number of authors, including Daniel et al and Thoemmes and Mohan.
Jonathan Bartlett
3 year post-doc in Bath – Clinical trial estimands – from definition to estimation
Applications are open now for 3 year post-doc Research Associate position at the University of Bath. The position is funded by a UK Medical Research Council grant ‘Clinical Trial Estimands – from definition to estimation’.
The context
Clinical trials represent the gold standard for evaluating the effects of treatments or interventions. Nevertheless, many trials are complicated by a variety of issues which renders their design and analysis more complicated. Examples include patients discontinuing their randomised treatment or taking additional rescue medications. In other settings, such as cancer studies, where quality of life endpoints are important secondary outcomes, a non-trivial proportion of patients may die before the quality of life endpoint can be measured, leading to ‘missingness due to death’. In cardiovascular trials, primary interest may be in estimating the treatments’ effects on incidence of cardiovascular events, but patients may die from other causes during follow-up, leading to so called competing risks.
In recent years there has been a growing recognition that such issues need careful consideration at both the design and analysis stages of a randomised trial. Within the world of pharmaceutical trials, this recognition has led to the publication of the ICH E9 estimand addendum. The addendum gives welcome focus to these issues and offers a framework for the definition of a clinical trial estimand in the presence of these issues (so called intercurrent events). It does not however say very much about which statistical methods ought to be used to estimate different estimands from clinical trial data. Moreover, the addendum does not explicitly discuss causal inference concepts, although these are sitting there in among the document (e.g. the principal stratification method, which is mentioned).
The project and post-doc
The grant funding this post-doc position aims to address the question of how statistical methods can be used to estimate a variety of estimands in the presence of so called intercurrent events. In particular, it seeks to exploit the many developments made in the field of modern casual inference to the problem. These methods were mostly developed with the analysis of non-randomised observational studies in mind. In randomised trials, although treatment group is randomly assigned, the post baseline intercurrent events that take place are not randomly assigned. As such the randomised trial becomes like an observational study, with the special property that the initial assignment to treatment was random.
The 3 year position will be based at the Department of Mathematical Sciences at the University of Bath. The post holder will be supervised by myself and Dr Rhian Daniel, Cardiff University, an expert in causal inference methods. The project will also benefit from regular input from the statisticians at the pharmaceutical company AstraZeneca.
For further details about the position and how to apply, please go to the University of Bath jobs page. For informal enquiries about the position, please email me at j.w.bartlett@bath.ac.uk
The mean of residuals in linear regression is always zero
In an introductory course on linear regression one learns about various diagnostics which might be used to assess whether the model is correctly specified. One of the assumptions of linear regression is that the errors have mean zero, conditional on the covariates. This implies that the unconditional or marginal mean of the errors have mean zero.