Adeleke, Mariam Olaide; (2021) Extensions to the Regression Discontinuity Design with Applications in Biostatistics. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The regression discontinuity (RD) design is a method for estimating a treatment effect in an observational study where there is a treatment allocation guideline that can be linked to the value of a continuous assignment variable and a pre-determined threshold. Typically, treatment is offered to patients whose assignment variable values lie above (or below) the threshold. Patients whose assignment variable values lie close to the threshold can be seen as exchangeable and typically, treatment effect estimation in an RD design involves comparing patients above and below the threshold. For a continuous outcome, estimating a treatment effect usually entails fitting local linear regression models for patients above and below the threshold. We propose the use of the thin plate regression spline to fit flexible regression models for patients above and below the threshold. Limited research has been done on an RD design for binary and time-to-event outcomes. For the binary outcome, we focused on the estimation of the risk ratio. The Wald and multiplicative structural mean models are approaches for estimating the risk ratio that can be applied to an RD design, however, they require additional assumptions. In this thesis, we have proposed an alternative approach for the estimation of the risk ratio that is based on the assumptions of the RD design. For the time-to-event outcome, the accelerated failure time (AFT) model was considered because it has some desirable properties in terms of interpreting causal effects. We propose an estimator of the acceleration factor that is based on the assumptions of an RD design. In addition to this, the structural AFT, a common approach for estimating the acceleration factor in observation studies, was discussed. Simulation studies were carried out to compare the proposed approaches with the existing ones, the results show that the proposed approaches compete favourably with, and in some cases, perform better than the existing methods. In addition, we have provided Bayesian alternatives to the three proposed approaches. Finally, we demonstrated these methods by applying them to real datasets on statin and metformin prescriptions.

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