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Modeling skin and ageing phenotypes using latent variable models in Infer.NET

We demonstrate and compare three unsupervised Bayesian latent variable models implemented in Infer.NET [2] for biomedical data modeling of 42 skin and aging phenotypes measured on the 12,000 female twins in the Twins UK study [7]. We address various data modeling problems include high missingness, heterogeneous data, and repeat observations. We compare the proposed models in terms of their performance at predicting disease labels and symptoms from available explanatory variables, concluding that factor analysis type models have the strongest statistical performance in this setting. We show that such models can be combined with regression components for improved interpretability. This work is being performed in collaboration with the Department of Twin Research and Genetic Epidemiology (DTR) at King’s College London. The DTR manages the largest UK adult twin registry of around 12,000 female monozygotic and dizygotic twins, established in 1992 [7]. The data has characteristics common to many biomedical applications, each of which we our able to address using our modeling framework. 1. High missingness. Many variables have up to 80% missing, and the level of overlap between phenotypes varies considerably. This level of missingness motivates Bayesian methods which are able to naturally deal with missingness, rather than attempting crude imputation procedures. 2. Heterogeneous data. The data contains continuous, categorical (including binary), ordinal and count data. We show in simulation experiments that using appropriate likelihood functions for each of these data types improves statistical power. 3. Multiple observations. Often the same underlying phenotype is recorded as multiple measurements, and the measurements may not be consistent. Allowing the model to combine these measurements into a single phenotype aids interpretability, improves statistical power and helps deal with the missingness problem. 4. High dimensional. The Twins UK database contains over 6000 phenotype and exposure variables, measured at multiple time points. Modern healthcare records are of the same nature. For a subset of 800 individuals we have 10,000 gene expression measurements in three different tissues, and the genotype of 600k Single Nucleotide Polymorphisms (SNPs). Our modeling framework allows these issues to be straightforwardly and rigorously addressed, and provides an efficient inference platform using Variational Message Passing under the Infer.NET framework. Although the models we use all provide some form of dimensionality reduction, which is essential for the high dimensional nature of the data, we currently only analysis around 40 phenotypes of particular relevance to skin and aging. Scaling these models to handle the full dataset, including gene expression and genotype data, is ongoing research. An attribute of the data that we have not fully explored how to model at this stage is that it is time series data. Most individuals in the study group have made multiple visits to be medically