A new type of parameter estimation algorithm for missing data problems

The expectation-maximization (EM) algorithm is often used in maximum likelihood (ML) estimation problems with missing data. However, EM can be rather slow to converge. In this communication we introduce a new algorithm for parameter estimation problems with missing data, which we call equalization-maximization (EqM) (for reasons to be explained later). We derive the EqM algorithm in a general context and illustrate its use in the specific case of Gaussian autoregressive time series with a varying amount of missing observations. In the presented examples, EqM outperforms EM in terms of computational speed, at a comparable estimation performance.Parameter estimation with missing data Maximum likelihood Expectation-maximization Cyclic maximization

Harmonization data of selected blood metabolites and IBS.

Harmonization data of selected blood metabolites and IBS.</p

The SNP-based heritability (h²) of the metabolites.

The SNP-based heritability (h2) of the metabolites.</p

Supplementary materials.

BackgroundIrritable bowel syndrome (IBS) is one of the most common functional bowel disorders and dysmetabolism plays an important role in the pathogenesis of disease. Nevertheless, there remains a lack of information regarding the causal relationship between circulating metabolites and IBS. A two-sample Mendelian randomization (MR) analysis was conducted in order to evaluate the causal relationship between genetically proxied 486 blood metabolites and IBS.MethodsA two-sample MR analysis was implemented to assess the causality of blood metabolites on IBS. The study utilized a genome-wide association study (GWAS) to examine 486 metabolites as the exposure variable while employing a GWAS study with 486,601 individuals of European descent as the outcome variable. The inverse-variance weighted (IVW) method was used to estimate the causal relationship of metabolites on IBS, while several methods were performed to eliminate the pleiotropy and heterogeneity. Another GWAS data was used for replication and meta-analysis. In addition, reverse MR and linkage disequilibrium score regression (LDSC) were employed for additional assessment. Multivariable MR analysis was conducted in order to evaluate the direct impact of metabolites on IBS.ResultsThree known and two unknown metabolites were identified as being associated with the development of IBS. Higher levels of butyryl carnitine (OR(95%CI):1.10(1.02–1.18),p = 0.009) and tetradecanedioate (OR(95%CI):1.13(1.04–1.23),p = 0.003)increased susceptibility of IBS and higher levels of stearate(18:0)(OR(95%CI):0.72(0.58–0.89),p = 0.003) decreased susceptibility of IBS.ConclusionThe metabolites implicated in the pathogenesis of IBS possess potential as biomarkers and hold promise for elucidating the underlying biological mechanisms of this condition.</div

Scatterplot for the significant MR association between metabolites and IBS.

Scatterplot for the significant MR association between metabolites and IBS.</p

An overview of this Mendelian randomization analysis.

IVW, inverse variance weighted; WM, weighted median; LOO analysis, leave-one-out analysis; MVMR, multivariable Mendelian randomization analysis; SNPs, single nucleotide polymorphisms.</p

MR analyses of genetically predicted levels of blood metabolites and risk of IBS.

MR analyses of genetically predicted levels of blood metabolites and risk of IBS.</p