Design and analysis of two-phase studies with multivariate longitudinal data.

Two-phase studies are crucial when outcome and covariate data are available in a first-phase sample (e.g., a cohort study), but costs associated with retrospective ascertainment of a novel exposure limit the size of the second-phase sample, in whom the exposure is collected. For longitudinal outcomes, one class of two-phase studies stratifies subjects based on an outcome vector summary (e.g., an average or a slope over time) and oversamples subjects in the extreme value strata while undersampling subjects in the medium-value stratum. Based on the choice of the summary, two-phase studies for longitudinal data can increase efficiency of time-varying and/or time-fixed exposure parameter estimates. In this manuscript, we extend efficient, two-phase study designs to multivariate longitudinal continuous outcomes, and we detail two analysis approaches. The first approach is a multiple imputation analysis that combines complete data from subjects selected for phase two with the incomplete data from those not selected. The second approach is a conditional maximum likelihood analysis that is intended for applications where only data from subjects selected for phase two are available. Importantly, we show that both approaches can be applied to secondary analyses of previously conducted two-phase studies. We examine finite sample operating characteristics of the two approaches and use the Lung Health Study (Connett et al. (1993), Controlled Clinical Trials, 14, 3S-19S) to examine genetic associations with lung function decline over time.

Two-wave two-phase outcome-dependent sampling designs, with applications to longitudinal binary data.

Two-phase outcome-dependent sampling (ODS) designs are useful when resource constraints prohibit expensive exposure ascertainment on all study subjects. One class of ODS designs for longitudinal binary data stratifies subjects into three strata according to those who experience the event at none, some, or all follow-up times. For time-varying covariate effects, exclusively selecting subjects with response variation can yield highly efficient estimates. However, if interest lies in the association of a time-invariant covariate, or the joint associations of time-varying and time-invariant covariates with the outcome, then the optimal design is unknown. Therefore, we propose a class of two-wave two-phase ODS designs for longitudinal binary data. We split the second-phase sample selection into two waves, between which an interim design evaluation analysis is conducted. The interim design evaluation analysis uses first-wave data to conduct a simulation-based search for the optimal second-wave design that will improve the likelihood of study success. Although we focus on longitudinal binary response data, the proposed design is general and can be applied to other response distributions. We believe that the proposed designs can be useful in settings where (1) the expected second-phase sample size is fixed and one must tailor stratum-specific sampling probabilities to maximize estimation efficiency, or (2) relative sampling probabilities are fixed across sampling strata and one must tailor sample size to achieve a desired precision. We describe the class of designs, examine finite sampling operating characteristics, and apply the designs to an exemplar longitudinal cohort study, the Lung Health Study.