Relative Belief Inferences from Decision Theory.

Relative belief inferences are shown to arise as Bayes rules or limiting Bayes rules. These inferences are invariant under reparameterizations and possess a number of optimal properties. In particular, relative belief inferences are based on a direct measure of statistical evidence.

The impact of statistical properties of incremental monetary net benefit and incremental cost-effectiveness ratio on health economic modeling choices.

INTRODUCTION: There is controversy on whether to use incremental monetary net benefit (INMB) or incremental cost-effectiveness ratio (ICER) in health economic evaluations alongside randomized controlled trials. We studied the impact of restricted mean survival time (RMST) on the long-term projection of INMB and ICER. METHODS: We analyzed the unbiasedness and efficiency of ICER and INMB by (1) deriving the metrics' expected values and variances based on theoretical probability distributions, (2) simulating their 15-year post-trial projections based on between-arm-RMST-gained through a 2 × 4 × 2 factorial experiment of Markov 2-state microsimulations. Simulations and comparison were run on the data from the Cardiovascular Outcomes for People Using Anticoagulation Strategies Study (COMPASS). RESULTS: Our simulation findings using RMST showed that ICER was more efficient than INMB, regardless of disease populations, time horizon, modeling choices, and underlying probability distributions of incremental mean cost and effect. ICER had a small variance and thus showed its robustness to the choices of models. CONCLUSION: INMB's variance varies with a willingness-to-pay (WTP) threshold quadratically while ICER's variance with a WTP threshold value quadratically while ICER's variance with incremental-mean-cost quadratically. A simple and naïve model can sufficiently estimate ICER. Future metrics are expected to be health-economic-meaningful, unambiguous, unbiased, efficient, and statistical-inference-friendly.

An unbiased kinship estimation method for genetic data analysis.

Accurate estimate of relatedness is important for genetic data analyses, such as heritability estimation and association mapping based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to biased heritability estimations and spurious associations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce kinship estimation bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to compare UKin with scGRM and three other kinship estimating methods: rGRM, tsGRM, and KING. Our results demonstrate that both bias and root mean square error in kinship coefficient estimation could be reduced by using UKin. We further investigated the performance of UKin, KING, and three GRM-based methods in calculating the SNP-based heritability, and show that UKin can improve estimation accuracy for heritability regardless of the scale of SNP panel.

Variance Estimation and Confidence Intervals from Genome-wide Association Studies Through High-dimensional Misspecified Mixed Model Analysis.

We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) in misspecified mixed model analysis. Previous studies have shown that, in spite of the model misspecification, certain quantities of genetic interests are consistently estimable, and consistent estimators of these quantities can be obtained using the restricted maximum likelihood (REML) method under a misspecified linear mixed model. However, the asymptotic variance of such a REML estimator is complicated and not ready to be implemented for practical use. In this paper, we develop practical and computationally convenient methods for estimating such asymptotic variances and constructing the associated confidence intervals. Performance of the proposed methods is evaluated empirically based on Monte-Carlo simulations and real-data application.

FUNCTIONAL SUFFICIENT DIMENSION REDUCTION THROUGH AVERAGE FRÉCHET DERIVATIVES.

Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Fréchet derivative estimator, which extends the gradient of the regression function to the operator level and enables us to develop estimators for our functional dimension reduction spaces. We show the resulting functional SDR estimators are unbiased and exhaustive, and more importantly, without imposing any distributional assumptions such as the linearity or the constant variance conditions that are commonly imposed by all existing functional SDR methods. We establish the uniform convergence of the estimators for the functional dimension reduction spaces, while allowing both the number of Karhunen-Loève expansions and the intrinsic dimension to diverge with the sample size. We demonstrate the efficacy of the proposed methods through both simulations and two real data examples.

Design-Based Approach for Analysing Survey Data in Veterinary Research.

Sample surveys are an essential approach used in veterinary research and investigation. A sample obtained from a well-designed sampling process along with robust data analysis can provide valuable insight into the attributes of the target population. Two approaches, design-based or model-based, can be used as inferential frameworks for analysing survey data. Compared to the model-based approach, the design-based approach is usually more straightforward and directly makes inferences about the finite target population (such as the dairy cows in a herd or dogs in a region) rather than an infinite superpopulation. In this paper, the concept of probability sampling and the design-based approach is briefly reviewed, followed by a discussion of the estimations and their justifications in the context of several different elementary sampling methods, including simple random sampling, stratified random sampling, and one-stage cluster sampling. Finally, a concrete example of a complex survey design (involving multistage sampling and stratification) is demonstrated, illustrating how finding unbiased estimators and their corresponding variance formulas for a complex survey builds on the techniques used in elementary sampling methods.

Distributed estimation of principal eigenspaces.

Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distributed algorithms for PCA are thus needed. This paper proposes and studies a distributed PCA algorithm: each node machine computes the top K eigenvectors and transmits them to the central server; the central server then aggregates the information from all the node machines and conducts a PCA based on the aggregated information. We investigate the bias and variance for the resulting distributed estimator of the top K eigenvectors. In particular, we show that for distributions with symmetric innovation, the empirical top eigenspaces are unbiased and hence the distributed PCA is "unbiased". We derive the rate of convergence for distributed PCA estimators, which depends explicitly on the effective rank of covariance, eigen-gap, and the number of machines. We show that when the number of machines is not unreasonably large, the distributed PCA performs as well as the whole sample PCA, even without full access of whole data. The theoretical results are verified by an extensive simulation study. We also extend our analysis to the heterogeneous case where the population covariance matrices are different across local machines but share similar top eigen-structures.