Sample size determination for the parallel model in a survey with sensitive questions

Recently, a new non-randomized parallel design is proposed by Tian (2013) for surveys with sensitive topics. However, the sample size formulae associated with testing hypotheses for the parallel model are not yet available. As a crucial component in surveys, the sample size formulae with the parallel design are developed in this paper by using the power analysis method for both the one- and two-sample problems. We consider both the one- and two-sample problems. The asymptotic power functions and the corresponding sample size formulae for both the one- and two-sided tests based on the large-sample normal approximation are derived. The performance is assessed through comparing the asymptotic power with the exact power and reporting the ratio of the sample sizes with the parallel model and the design of direct questioning. We numerically compare the sample sizes needed for the parallel design with those required for the crosswise and triangular models. Two theoretical justifications are also provided. An example from a survey on ‘sexual practices’ in San Francisco, Las Vegas and Portland is used to illustrate the proposed methods.postprin

A noniterative sampling method for computing posteriors in the structure of EM-type algorithms

We propose a noniterative sampling approach by combining the inverse Bayes formulae (IBF), sampling/importance resampling and posterior mode estimates from the Expectation/Maximization (EM) algorithm to obtain an i.i.d. sample approximately from the posterior distribution for problems where the EM-type algorithms apply. The IBF shows that the posterior is proportional to the ratio of two conditional distributions and its numerator provides a natural class of built-in importance sampling functions (ISFs) directly from the model specification. Given that the posterior mode by an EM-type algorithm is relatively easy to obtain, a best ISF can be identified by using that posterior mode, which results in a large overlap area under the target density and the ISF. We show why this procedure works theoretically. Therefore, the proposed method provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. We first illustrate the method with a proof-of-principle example and then apply the method to hierarchical (or mixed-effects) models for longitudinal data. We conclude with a discussion.published_or_final_versio

Bayesian computation for contingency tables with incomplete cell-counts

This article studies Bayesian analysis of contingency tables (or multinomial data) where the cell counts are not fully observed due to reasons such as nonresponse and misclassification, and derives the posterior distributions of the unknown cell probabilities in terms of various types of generalized Dirichlet distributions. For some special situations such as grouped and nested Dirichlet distributions, the posterior means of the unknown cell probabilities can be obtained in closed form by using inverse Bayes formulae and/or stochastic representation. When closed-form expressions do not exist, we suggest using importance sampling with a feasible proposal density to approximately compute the posterior quantities, and propose a procedure for choosing an effective proposal density. Applications are illustrated by sample surveys with nonresponse, crime survey data, death penalty attitude data, and misclassified multinomial data.published_or_final_versio

The nested dirichlet distribution and incomplete categorical data analysis

The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirichlet distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computationally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated with simulated and real data.published_or_final_versio

A fast em algorithm for quadratic optimization subject to Convex constraints

Convex constraints (CCs) such as box constraints and linear inequality constraints appear frequently in statistical inference and in applications. The problems of quadratic optimization (QO) subject to CCs occur in isotonic regression, shape-restricted non-parametric regression, variable selection (via the lasso algorithm and bridge regression), limited dependent variables models, image reconstruction, and so on. Existing packages for QO are not generally applicable to CCs. Although EM-type algorithms may be applied to such problems (Tian, Ng and Tan (2005)), the convergence rate/speed of these algorithms is painfully slow, especially for high-dimensional data. This paper develops a fast EM algorithm for QO with CCs. We construct a class of data augmentation schemes indexed by a 'working parameter' r (r ε R), and then optimize r over R under several convergence criteria. In addition, we use Cholesky decomposition to reduce both the number of latent variables and the dimension, leading to further acceleration of the EM. Standard errors of the restricted estimators are calculated using a non-parametric bootstrapping procedure. Simulation and comparison are performed and a complex multinomial dataset is analyzed to illustrate the proposed methods.published_or_final_versio

Further properties and new applications of the nested Dirichlet distribution

Recently, Ng et al. (2009) studied a new family of distributions, namely the nested Dirichlet distributions. This family includes the traditional Dirichlet distribution as a special member and can be adopted to analyze incomplete categorical data. However, other important aspects of the family, such as marginal and conditional distributions and related properties are not yet available in the literature. Moreover, diverse applications of the family to the real world need to be further explored. In this paper, we first obtain the marginal and conditional distributions and other related properties of the nested Dirichlet distribution. We then present new applications of the family in fitting competing-risks model, analyzing incomplete categorical data and evaluating cancer diagnosis tests. Three real data involving failure times of radio transmitter receivers, attitude toward the death penalty and ultrasound ratings for breast cancer metastasis are provided. © 2009 Elsevier B.V. All rights reserved.postprin

Moderately elevated blood pressure during pregnancy and odds of hypertension later in life: the POUCHmoms longitudinal study

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/1/bjo14556-sup-0010-ICMJE7.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/2/bjo14556-sup-0007-ICMJE4.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/3/bjo14556.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/4/bjo14556-sup-0008-ICMJE5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/5/bjo14556-sup-0001-TableS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/6/bjo14556-sup-0002-TableS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/7/bjo14556-sup-0005-ICMJE2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/8/bjo14556-sup-0003-TableS3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/9/bjo14556-sup-0006-ICMJE3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/10/bjo14556-sup-0009-ICMJE6.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/11/bjo14556_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138364/12/bjo14556-sup-0004-ICMJE1.pd

Regulation of a rat VL30 element in human breast cancer cells in hypoxia and anoxia: role of HIF-1

Novel approaches to cancer gene therapy currently exploit tumour hypoxia to achieve transcriptional targeting using oxygen-regulated enhancer elements called hypoxia response elements. The activity of such elements in hypoxic cells is directly dependent on upregulation of the hypoxia-inducible transcription factor-1 However tumours also contain areas of anoxia, which may be considered a more tumour-selective transcriptional stimulus than hypoxia for targeting gene therapy to tumours. Another element, from the rat virus-like retrotransposon, VL30 (termed the ‘secondary anoxia response element’) has been reported to be more highly inducible in rat fibroblasts under anoxia than hypoxia. To investigate anoxia as a potential transcriptional target in human tumours, we have examined secondary anoxia response element inducibility in two human breast cancer cell lines, MCF-7 and T47D, under anoxia, hypoxia and normoxia. In both cell types, the trimerised secondary anoxia response element showed greater inducibility in anoxia than hypoxia (1% and 0.5% O2). The anoxic response of the secondary anoxia response element was shown to be dependent on hypoxia-inducible transcription factor-1 and the presence of a hypoxia-inducible transcription binding site consensus (5′-ACGTG-3′). Mutational analysis demonstrated that the base immediately 5′ to this modulates the anoxic/hypoxic induction of the secondary anoxia response element, such that TACGTG>GACGTG>>CACGTG. A similar correlation was found for erythropoietin, phosphoglycerate kinase 1, and aldolase hypoxia response elements, which contain these respective 5′ flanking bases