Modeling single-cell multiplex immunofluorescence imaging data with parsimonious finite mixtures of Tukey g-and-h distributions

Oregon Convention Center 

A mixture of 4-parameter Tukey's g-&-h distributions is proposed for fitting finite mixtures with Gaussian and non-Gaussian components. Since the likelihood of the Tukey's g-&-h mixtures does not have a closed analytical form, we propose a Quantile Least Mahalanobis Distance (QLMD) estimator for parameters of such mixtures. QLMD is an indirect estimator minimizing the Mahalanobis distance between the sample and model-based quantiles, and its asymptotic properties follow from the general theory of indirect estimation. We have developed a stepwise algorithm to select a parsimonious Tukey's g-&-h mixture model and implemented all proposed methods in the R package QuantileGH available CRAN. A simulation study was conducted to evaluate performance of the Tukey's g-&-h mixtures and compare to performance of mixtures of skew-normal or skew-t distributions. The Tukey's g-&-h mixtures were applied to model cellular expressions of Cyclin D1 protein in breast cancer tissues, and resulting parameter estimates evaluated as predictors of progression-free survival.

Finite Mixtures

Tukey’s g-&-h distribution

Indirect Estimator

Quantile Least Mahalanobis Distance

Cellular Protein Level 

Section on Statistical Computing