On the Bayesness, minimaxity and admissibility of point estimators of allelic frequencies

The impact of imperfect screening tools on measuring the prevalence of epilepsy and headaches in Burkina Faso

BACKGROUND

Epilepsy and progressively worsening severe chronic headaches (WSCH) are the two most common clinical manifestations of neurocysticercosis, a form of cysticercosis. Most community-based studies in sub-Saharan Africa (SSA) use a two-step approach (questionnaire and confirmation) to estimate the prevalence of these neurological disorders and neurocysticercosis. Few validate the questionnaire in the field or account for the imperfect nature of the screening questionnaire and the fact that only those who screen positive have the opportunity to be confirmed. This study aims to obtain community-based validity estimates of a screening questionnaire, and to assess the impact of verification bias and misclassification error on prevalence estimates of epilepsy and WSCH.

METHODOLOGY/PRINCIPAL FINDINGS

Baseline screening questionnaire followed by neurological examination data from a cluster randomized controlled trial collected between February 2011 and January 2012 were used. Bayesian latent-class models were applied to obtain verification bias adjusted validity estimates for the screening questionnaire. These models were also used to compare the adjusted prevalence estimates of epilepsy and WSCH to those directly obtained from the data (i.e. unadjusted prevalence estimates). Different priors were used and their corresponding posterior inference was compared for both WSCH and epilepsy. Screening data were available for 4768 individuals. For epilepsy, posterior estimates for the sensitivity varied with the priors used but remained robust for the specificity, with the highest estimates at 66.1% (95%BCI: 56.4%;75.3%) for sensitivity and 88.9% (88.0%;89.8%) for specificity. For WSCH, the sensitivity and specificity estimates remained robust, with the highest at 59.6% (49.7%;69.1%) and 88.6% (87.6%;89.6%), respectively. The unadjusted prevalence estimates were consistently lower than the adjusted prevalence estimates for both epilepsy and WSCH.

CONCLUSIONS/SIGNIFICANCE

This study demonstrates that in some settings, the prevalence of epilepsy and WSCH can be considerably underestimated when using the two-step approach. We provide an analytic solution to obtain more valid prevalence estimates of these neurological disorders, although more community-based validity studies are needed to reduce the uncertainty of the estimates. Valid estimates of these two neurological disorders are essential to obtain accurate burden values for neglected tropical diseases such as neurocysticercosis that manifest as epilepsy or WSCH.

TRIAL REGISTRATION

ClinicalTrials.gov NCT03095339.

Allelic frequency estimation in presence of uncertain priors

In this paper, we assume that allele frequencies are random variables and follow certain statistical distributions. However, specifying an appropriate informative prior distribution with specific hyperparameters seems to be a major issue. Assuming that prior information varies over some classes of priors, we develop the concept of robust Bayes estimation into the context of allele frequency estimation. We first assume that the region of interest is a single locus and the prior information is represented in terms of a class of Beta distributions, and present explicit forms of the resulting Bayes and robust Bayes estimators. We then extend our results to biallelic k-loci and multi-allelic k-loci cases within the region of interest. We perform a simulation study to measure performance of the proposed robust Bayes estimators against some Bayes estimators associated with specific hyperparameters. The simulations reflect satisfactory performance of the proposed robust Bayes estimators when there is no evidence implying the actual prior distribution.

Joint genome-wide prediction in several populations accounting for randomness of genotypes: A hierarchical Bayes approach. I: Multivariate Gaussian priors for marker effects and derivation of the joint probability mass function of genotypes

It is important to consider heterogeneity of marker effects and allelic frequencies in across population genome-wide prediction studies. Moreover, all regression models used in genome-wide prediction overlook randomness of genotypes. In this study, a family of hierarchical Bayesian models to perform across population genome-wide prediction modeling genotypes as random variables and allowing population-specific effects for each marker was developed. Models shared a common structure and differed in the priors used and the assumption about residual variances (homogeneous or heterogeneous). Randomness of genotypes was accounted for by deriving the joint probability mass function of marker genotypes conditional on allelic frequencies and pedigree information. As a consequence, these models incorporated kinship and genotypic information that not only permitted to account for heterogeneity of allelic frequencies, but also to include individuals with missing genotypes at some or all loci without the need for previous imputation. This was possible because the non-observed fraction of the design matrix was treated as an unknown model parameter. For each model, a simpler version ignoring population structure, but still accounting for randomness of genotypes was proposed. Implementation of these models and computation of some criteria for model comparison were illustrated using two simulated datasets. Theoretical and computational issues along with possible applications, extensions and refinements were discussed. Some features of the models developed in this study make them promising for genome-wide prediction, the use of information contained in the probability distribution of genotypes is perhaps the most appealing. Further studies to assess the performance of the models proposed here and also to compare them with conventional models used in genome-wide prediction are needed.