Bayesian Inference under Cluster Sampling with Probability Proportional to Size

Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to cluster size, and then units are randomly sampled inside selected clusters. Challenges arise when the sizes of nonsampled cluster are unknown. We propose nonparametric and parametric Bayesian approaches for predicting the unknown cluster sizes, with this inference performed simultaneously with the model for survey outcome. Simulation studies show that the integrated Bayesian approach outperforms classical methods with efficiency gains. We use Stan for computing and apply the proposal to the Fragile Families and Child Wellbeing study as an illustration of complex survey inference in health surveys

Covariate-adaptive randomization inference in matched designs

It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via covariate-adaptive randomization inference, which modifies the permutation probabilities to vary with estimated propensity score discrepancies and avoids requirements to exclude matched pairs or model an outcome variable. We show that the test achieves type I error control arbitrarily close to the nominal level when large samples are available for propensity score estimation. We characterize the large-sample behavior of the new randomization test for a difference-in-means estimator of a constant additive effect. We also show that existing methods of sensitivity analysis generalize effectively to covariate-adaptive randomization inference. Finally, we evaluate the empirical value of covariate-adaptive randomization procedures via comparisons to traditional uniform inference in matched designs with and without propensity score calipers and regression adjustment using simulations and analyses of genetic damage among welders and right-heart catheterization in surgical patients.Comment: 41 pages, 8 figure

Replication : an approach to the analysis of data from complex surveys

Development and evaluation of a replication technique for estimating variance.[By Philip J. McCarthy].Public Health Service publication, no. 1000-Series 2, no. 14.Bibliography: p. 31-32.196