| Pooled analyses integrate data from multiple studies and achieve a large sample size for enhanced statistical power. When heterogeneity exists in variables' effects on the outcome across studies (16), the simple pooling strategy fails to present a fair and complete picture of the effects of heterogeneous variables. Therefore, it is important to investigate the homogeneous and heterogeneous structure of variables in pooled studies. Another issue in large studies is measurement errors in covariates due to device error or within-subject variation. The measurement error causes bias in parameter estimation and adversely affects statistical inference. However, research of the measurement error in pooled studies is limited.;In this dissertation, we consider two problems. First, when there is no mea- surement error, we investigate the homogeneous and heterogeneous structure of variables in pooled studies. We treat each variable's effects across studies as a group, and formulate the heterogeneity problem in the framework of group variable selection. We propose a penalty regularized approach with adaptively weighted L1 and L1/ L2 penalties, which can characterize the variables as having homogeneous, heterogeneous or null effects, and estimate non-zero effects. Second, we explore the variables' effects and heterogeneity structure in pooled data with measurement errors in covariates. We propose a penalized least squares approach for linear models, and a penalized score function with one-step estimate for logistic models.;We implement our methods using the iterative shooting algorithm (17; 54), and establish asymptotic properties for our proposed estimators. The proposed methods are evaluated using extensive numerical studies and demonstrated using real data examples. |
