Integrated Likelihood for Phylogenomics under a No-Common-Mechanism Model

The availability of genome-wide sequence data from a large number of species as well as data from multiple individuals within a species has ushered in the era of phylogenomics. In this era, species phylogeny inference is based on models of sequence evolution on gene trees as well as models of gene tree evolution within the branches of species phylogenies. Parsimony, likelihood, Bayesian, and distance methods have been introduced for species phylogeny inference based on such models. All methods, except for the parsimony ones, assume a common mechanism across all loci as captured by a single value of each branch length of the species phylogeny. In this paper, we propose a ``no common mechanism" (NCM) model, where every gene tree evolves according to its own parameters of the species phylogeny. An analogous model was proposed and explored, both mathematically and experimentally, for sites, or characters, in a sequence alignment in the context of the classical phylogeny problem. For example, a famous equivalence between the maximum parsimony and maximum likelihood phylogeny estimates was established under certain NCM models by Tuffley and Steel. Here we derive an analytically integrated likelihood of both species trees and networks given the gene trees of multiple loci under an NCM model. We demonstrate the performance of inference under this integrated likelihood on both simulated and biological data. The model presented here will afford opportunities for exploring connections among various methods for estimating species phylogenies from multiple, independent loci.

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PIE: A prior knowledge guided integrated likelihood estimation method for bias reduction in association studies using electronic health records data

Objectives This study proposes a novelPrior knowledge guidedIntegrated likelihoodEstimation (PIE) method to correct bias in estimations of associations due to misclassification of electronic health record (EHR)-derived binary phenotypes, and evaluates the performance of the proposed method by comparing it to 2 methods in common practice. Methods We conducted simulation studies and data analysis of real EHR-derived data on diabetes from Kaiser Permanente Washington to compare the estimation bias of associations using the proposed method, the method ignoring phenotyping errors, the maximum likelihood method with misspecified sensitivity and specificity, and the maximum likelihood method with correctly specified sensitivity and specificity (gold standard). The proposed method effectively leverages available information on phenotyping accuracy to construct a prior distribution for sensitivity and specificity, and incorporates this prior information through the integrated likelihood for bias reduction. Results Our simulation studies and real data application demonstrated that the proposed method effectively reduces the estimation bias compared to the 2 current methods. It performed almost as well as the gold standard method when the prior had highest density around true sensitivity and specificity. The analysis of EHR data from Kaiser Permanente Washington showed that the estimated associations from PIE were very close to the estimates from the gold standard method and reduced bias by 60%–100% compared to the 2 commonly used methods in current practice for EHR data. Conclusions This study demonstrates that the proposed method can effectively reduce estimation bias caused by imperfect phenotyping in EHR-derived data by incorporating prior information through integrated likelihood.