Post-selection inference and trajectory analysis

? DESCRIPTION (provided by applicant): This is a project to develop new methods of post-selection inference and trajectory analysis directed towards important public health applications in genomics and epidemiology. The broad objective of the project is to provide new methods of post-selection inference for detecting the presence of signi?cant predictors in high- dimensional screening. These methods will be developed with a view to applications in several areas: drug resistance studies, personalized medicine, growth trajectories, and survival outcomes. Screening large numbers of predictors and assessing their utility in treatment decisions is a challenging problem. Among other things, the project will provide a more powerful alternative to the popular (yet conservative) Bonferroni method of controlling familywise error rates that are a crucial concern for these applications. Work on this topic was initiated in the principal investigator's current R01 grant, but was con?ned to linear regression settings. The signi?canc of the new application is that it will greatly expand the scope of these methods to allow for their much broader application. High-dimensional screening is especially relevant for extracting predictive features of growth trajectories. In addition, the project will develop new screening tests speci?cally for the purpose of comparing survival functions. This will be done in terms of nonparametric tests for stochastic ordering and hazard rate ordering under various censoring and biased sampling scenarios. An empirical likelihood approach (more powerful than the Wald approach) will be used. Post- selection inference issues to be addressed in this setting involve devising a way to calibrate maximally selected empirical likelihood-based test statistics over the follow-up period, and in screening for the presence of signi?cant orderings among multiple groups of subjects. A further objective is to develop new methods for reconstructing growth trajectories from sparse temporal data for use as predictors of health outcomes. This work was also initiated in the principal investigator's current R01 grant, and recently used by the principa investigator to study of the association between autism and dynamical features of growth during early infancy. The renewal will focus on improving these trajectory analysis methods by adjusting for measurement error and prior knowledge about the shape and boundedness of growth trajectories, with a view to applications in two new areas: 1) biosignatures in Finnish prenatal studies of schizophrenia, bipolar disorder and related psychotic disorders, and 2) pregnancy weight gain and long term maternal and child health outcomes.