Title: Design of observational longitudinal studies
Description: This dissertation investigates several aspects of study design for longitudinal studies with a continuous outcome and a binary exposure, with special focus on observational studies. Chapter 1 focuses on studies where the exposure is time-invariant. It covers a wide range of topics in study design. Formulas for power, sample size, number of repeated measurements, and the optimal combination of number of participants and number of repeated measures which maximize power for a given budget, or which minimize the total cost of the study while achieving a specific power are derived. The effect of all parameters on these quantities is studied. Some of the difficulties investigators need to address when the study is not randomized are discussed. Chapter 2 provides design formulas for studies where interest is in the main effect of a time-varying exposure. In observational studies, several exposure patterns are observed, they are often severely imbalanced, and the design matrix is unknown a priori. The prevalence and the intraclass correlation of exposure, which is a measure of within-subject variation in exposure, are additional parameters needed to compute study design quantities when the response has compound symmetry covariance. For other covariance structures, these parameters allow the computation of reasonable approximations. It is shown that, in most situations, having a time-varying instead of a time-invariant exposure produces gains in efficiency, which can be substantial in studies with several repeated measurements.

Chapter 3 provides study design formulas for studies that compare rates of change as a function of a time-varying exposure. Formulas are derived for models that assume an acute or a cumulative effect of exposure, and for models that do and do not separate the within- and between-subject effects. Exact formulas as a function of the exposure prevalence and intraclass correlation can be derived for a few simple cases, while for the others reasonable approximations are obtained. For the cumulative effect model, efficiency is lost in most cases when having a time-varying exposure, while for the acute effect model both gains and losses in efficiency are observed. User-friendly software, which handles all scenarios described above, is publicly available at http://www.hsph.harvard.edu/faculty/spiegelman/optitxs.html.