Abstract
We propose a general class of 2-phase epidemiologic study designs for quantitative, longitudinal data that are useful when phase 1 longitudinal outcome and covariate data are available but data on the exposure (e.g., a biomarker) can only be collected on a subset of subjects during phase 2. To conduct a study using a design in the class, one first summarizes the longitudinal outcomes by fitting a simple linear regression of the response on a time-varying covariate for each subject. Sampling strata are defined by splitting the estimated regression intercept or slope distributions into distinct (low, medium, and high) regions. Stratified sampling is then conducted from strata defined by the intercepts, by the slopes, or from a mixture. In general, samples selected with extreme intercept values will yield low variances for associations of time-fixed exposures with the outcome and samples enriched with extreme slope values will yield low variances for associations of time-varying exposures with the outcome (including interactions with time-varying exposures). We describe ascertainment-corrected maximum likelihood and multiple-imputation estimation procedures that permit valid and efficient inferences. We embed all methodological developments within the framework of conducting a substudy that seeks to examine genetic associations with lung function among continuous smokers in the Lung Health Study (United States and Canada, 1986–1994).
Blow-ups of caloric measure in time varying domains and applications to two-phase problems