Collections > Electronic Theses and Dissertations > Inference about treatment effects using bounds, sensitivity analysis and instrumental variables
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This dissertation considers conducting inference about the effect of a treatment (or exposure) on an outcome of interest. In the ideal setting where treatment is assigned randomly, under certain assumptions the treatment effect is identifiable from the observable data and inference is straightforward. However, in many other settings observable data may only partially identify treatment effects or may identify treatment effects only for some subset of the population. In this case three approaches are often employed: (i) bounds are derived for the treatment effect under minimal assumptions, (ii) additional untestable assumptions are invoked that render the treatment effect identifiable and then sensitivity analysis is conducted to assess how inference changes as the untestable assumptions are varied, or (iii) instrumental variables are used to identify treatment effects for a subset of the population of interest. In this dissertation, first we review approaches (i) and (ii) in various settings, including assessing principal strata effects, direct and indirect effects, and effects of time-varying exposures. Methods for drawing formal inference about partially identified parameters are also discussed. Second, we derive the large sample properties of instrumental variable-based treatment effect estimators and test statistics when the outcome is subject to right censoring and competing risks. These results are applied to a real data example about the use of antiretroviral therapy to reduce mother to child transmission of HIV. Third, we derive identification results for direct, indirect and total effects of treatment in presence of interference (i.e., settings where the treatment of one individual may be affected by the treatment of other individuals). These results are applied to a real data example about rotavirus vaccination. All derived asymptotic results are supported by simulation studies.