¹Department of Mathematics and Statistics, Rolf Nevanlinna Institute, University of Helsinki, Helsinki, Finland

Correspondence: Dr MJ Sillanpää, Department of Mathematics and Statistics, Rolf Nevanlinna Institute, P.O. Box 68, FIN-00014, University of Helsinki, Helsinki, Finland. E-mail: mjs@rolf.helsinki.fi

Received 13 December 2007; Revised 13 May 2008; Accepted 23 May 2008; Published online 23 July 2008.

Abstract

Previous articles have presented clinical quantitative trait locus (cQTL) models, where the information provided by quantitative/qualitative phenotypes, molecular markers and gene expressions (transcription levels) were combined and analyzed simultaneously. Because of financial constraints, marker data may be available for much larger group of individuals than expression data. However, it is desirable to use all the available information. We therefore extend such approaches by presenting a reliable missing data model for the case when marker data is more complete (that is, has many fewer missing entries). In the suggested hierarchical model, an expression QTL (eQTL) model (which is essentially our missing data model) is part of the larger cQTL model and it represents a Bayesian model-based method for estimating cis- and trans-acting regulatory effects for multiple (typically hundreds of) expression phenotypes simultaneously. The modeling dependence between transcripts in the eQTL model is also considered. The method is based on presenting data in the form of marker gene pairs, for which the presence of regulatory effect (link) can be hypothesized. These marker gene pairs can be obtained from oligonucleotide arrays or created using information available on known pathways or previous eQTL/allelic expression studies. The estimation of the model parameters (such as presence/absence of regulation, eQTL/cQTL effects and proportion of eQTLs and cQTLs among the set of marker gene pairs) as well as the handling of missing data is performed using Markov Chain Monte Carlo (MCMC) sampling. The method is illustrated using both simulated and real data.