In many studies, the goal is to estimate the effect of a longitudinal treatment on an outcome. Often, these treatment regimes are given in non-randomized fashions; in particular, intermediate outcomes may be used to guide treatment choices. Data arising in such a study must be analyzed carefully to address the longitudinal nature of the treatment, and the severe bias as well as variability that can arise in estimates due to the large dimension of the problem.
In other scenarios, the insufficient measurement of confounders makes inference even more difficult. Instrumental variables allow for estimation of causal effects in the context of unmeasured confounding. In particular, Mendelian randomization studies are observational studies in which one studies the effect of an exposure on an outcome using genetic variables as instruments. As the cost of measuring genetic variables is relatively high, epidemiologists often use efficient sampling designs such as the nested case-control study and the case-cohort study to answer questions relating to genetics.
Our interest is in the application of these instrumental variables techniques to data arising from studies with more complex design. In collaboration with Constantine Frangakis (Johns Hopkins), we have shown that standard techniques are not directly applicable to the composite design setting, and we developed methodology for estimating causal effects in this scenario.