A Bayesian Approach to Linking a Survey and a Census via Small Areas

We predict the finite population proportion of a small area when individual-level data are available from a survey and more extensive household-level (not individual-level) data (covariates but not responses) are available from a census. The census and the survey consist of the same strata and primary sampling units (PSU, or wards) that are matched, but the households are not matched. There are some common covariates at the household level in the survey and the census and these covariates are used to link the households within wards. There are also covariates at the ward level, and the wards are the same in the survey and the census. Using a two-stage procedure, we study the multinomial counts in the sampled households within the wards and a projection method to infer about the non-sampled wards. This is accommodated by a multinomial-Dirichlet–Dirichlet model, a three-stage hierarchical Bayesian model for multinomial counts, as it is necessary to account for heterogeneity among the households. The key theoretical contribution of this paper is to develop a computational algorithm to sample the joint posterior density of the multinomial-Dirichlet–Dirichlet model. Specifically, we obtain samples from the distributions of the proportions for each multinomial cell. The second key contribution is to use two projection procedures (parametric based on the nested error regression model and non-parametric based on iterative re-weighted least squares), on these proportions to link the survey to the census, thereby providing a copy of the census counts. We compare the multinomial-Dirichlet–Dirichlet (heterogeneous) model and the multinomial-Dirichlet (homogeneous) model without household effects via these two projection methods. An example of the second Nepal Living Standards Survey is presented.

A generalised Dickman distribution and the number of species in a negative binomial process model

We derive the large-sample distribution of the number of species in a version of Kingman’s Poisson–Dirichlet model constructed from an $\alpha$ -stable subordinator but with an underlying negative binomial process instead of a Poisson process. Thus it depends on parameters $\alpha\in (0,1)$ from the subordinator and $r>0$ from the negative binomial process. The large-sample distribution of the number of species is derived as sample size $n\to\infty$ . An important component in the derivation is the introduction of a two-parameter version of the Dickman distribution, generalising the existing one-parameter version. Our analysis adds to the range of Poisson–Dirichlet-related distributions available for modeling purposes.

ACTOR: a latent Dirichlet model to compare expressed isoform proportions to a reference panel

The relative proportion of RNA isoforms expressed for a given gene has been associated with disease states in cancer, retinal diseases, and neurological disorders. Examination of relative isoform proportions can help determine biological mechanisms, but such analyses often require a per-gene investigation of splicing patterns. Leveraging large public datasets produced by genomic consortia as a reference, one can compare splicing patterns in a dataset of interest with those of a reference panel in which samples are divided into distinct groups (tissue of origin, disease status, etc). We propose ACTOR, a latent Dirichlet model with Dirichlet Multinomial observations to compare expressed isoform proportions in a dataset to an independent reference panel. We use a variational Bayes procedure to estimate posterior distributions for the group membership of one or more samples. Using the Genotype-Tissue Expression (GTEx) project as a reference dataset, we evaluate ACTOR on simulated and real RNA-seq datasets to determine tissue-type classifications of genes. ACTOR is publicly available as an R package at https://github.com/mccabes292/actor.

From Individual to Population Preferences: Comparison of Discrete Choice and Dirichlet Models for Treatment Benefit-Risk Tradeoffs

Introduction. The Dirichlet distribution has been proposed for representing preference heterogeneity, but there is limited evidence on its suitability for modeling population preferences on treatment benefits and risks. Methods. We conducted a simulation study to compare how the Dirichlet and standard discrete choice models (multinomial logit [MNL] and mixed logit [MXL]) differ in their convergence to stable estimates of population benefit-risk preferences. The source data consisted of individual-level tradeoffs from an existing 3-attribute patient preference study ( N = 560). The Dirichlet population model was fit directly to the attribute weights in the source data. The MNL and MXL population models were fit to the outcomes of a simulated discrete choice experiment in the same sample of 560 patients. Convergence to the parameter values of the Dirichlet and MNL population models was assessed with sample sizes ranging from 20 to 500 (100 simulations per sample size). Model variability was also assessed with coefficient P values. Results. Population preference estimates of all models were very close to the sample mean, and the MNL and MXL models had good fit (McFadden’s adjusted R2 = 0.12 and 0.13). The Dirichlet model converged reliably to within 0.05 distance of the population preference estimates with a sample size of 100, where the MNL model required a sample size of 240 for this. The MNL model produced consistently significant coefficient estimates with sample sizes of 100 and higher. Conclusion. The Dirichlet model is likely to have smaller sample size requirements than standard discrete choice models in modeling population preferences for treatment benefit-risk tradeoffs and is a useful addition to health preference analyst’s toolbox.