Causal Inference
Causal inference is the name given to the the area of statistical methodology aimed at identifying and estimating effects of interventions. The reason we care about the effects of interventions is that generally in social science and epidemiology, we are actively interested in intervening. For example, we want to know if a particular social programme works because if it does, it might result in new policies -- new interventions. We want to know whether a drug works because we want to prescribe it -- i.e. intervene.
The big problem in causal inference is that most of our data do not involve interventions but rather passive observation (except clinical trials) and we have to go somehow extract information about interventions from them. Essentially it boils down to overcoming confounding.
There are number of approaches to causal inference, all involve enhancing (explicitly or implicitly) the language of statistics with ways of formalising interventions. The most common approaches use counterfactuals or potential responses. I prefer to use an approach which uses statistical decision theory to formalise interventions as decisions as counterfactuals don't really exist. My thesis was about exploring aspects of causal inference in the statistical decision model.

The regression discontinuity design in Public Health and Epidemiology
The RD design is a quasi-experiment which takes advantage of an imposed threshold resulting in a treatment (e.g. a drug prescription guideline) to identify the causal effects of the treatment. Together with collaborators from UCL (Gianluca Baio and members of the UCL Research Department of Primary Care and Population Health) we are estimating the effects of a number of drugs, notably Statins, in clinical practice at the population level. We have recently been awarded an MRC grant to do this.

Connections between causal inference estimators
I am also currently trying to formalise the relationships between different causal inference estimators across the disciplines that use them (statistics, econometircs, epidemiology).

Bayesian statistics
The Bayesian approaches appeal to me not only because they are often easier to implement and understand than straight frequentist approaches but especially because I espouse the philosphy of subjective probability. Bruno de Finetti said that "Probability does not exist" and I tend to agree.

Modelling bias
It is important to try and come up with models that will adjust for bias in observational studies. I am especially interested in structural biases such as confounding, mediator and selection bias. I am currently working on models to adjust for selection bias in case-control studies and have used the statistical decision model for causal inference to tackle mediator bias.

Evidence synthesis
Evidence synthesis is the rigorous statistical combination of data from different sources to adjust for bias and improve inference. Recently it has become increasingly feasible to merge information from large routinely collected data sets (e.g. Census) with data from small observational studies to adjust for biases in the latter. A single data source, e.g. a survey or a study, cannot fully answer questions of interest to policy makers as the participating individuals are not representative of the target population. However, combining small biased with large representative data sets can sometimes provide better answers. I am interested in developing evidence synthesis methods based principally on re-weighting techniques.