The Annals of Applied Statistics

Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines

Gwenaël G. R. Leday, Aad W. van der Vaart, Wessel N. van Wieringen, and Mark A. van de Wiel

Full-text: Open access

Abstract

DNA copy number and mRNA expression are widely used data types in cancer studies, which combined provide more insight than separately. Whereas in existing literature the form of the relationship between these two types of markers is fixed a priori, in this paper we model their association. We employ piecewise linear regression splines (PLRS), which combine good interpretation with sufficient flexibility to identify any plausible type of relationship. The specification of the model leads to estimation and model selection in a constrained, nonstandard setting. We provide methodology for testing the effect of DNA on mRNA and choosing the appropriate model. Furthermore, we present a novel approach to obtain reliable confidence bands for constrained PLRS, which incorporates model uncertainty. The procedures are applied to colorectal and breast cancer data. Common assumptions are found to be potentially misleading for biologically relevant genes. More flexible models may bring more insight in the interaction between the two markers.

Article information

Source
Ann. Appl. Stat., Volume 7, Number 2 (2013), 823-845.

Dates
First available in Project Euclid: 27 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1372338469

Digital Object Identifier
doi:10.1214/12-AOAS605

Mathematical Reviews number (MathSciNet)
MR3112919

Zentralblatt MATH identifier
1288.62161

Keywords
DNA copy number mRNA expression regression splines constrained inference model selection confidence bands

Citation

Leday, Gwenaël G. R.; van der Vaart, Aad W.; van Wieringen, Wessel N.; van de Wiel, Mark A. Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines. Ann. Appl. Stat. 7 (2013), no. 2, 823--845. doi:10.1214/12-AOAS605. https://projecteuclid.org/euclid.aoas/1372338469


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Supplemental materials

  • Supplementary material: Complementary results and simulations. We present a simulation study which compares the performance of the PLRS testing procedure in detecting associations of various functional shapes with that of other procedures. Additionally, we provide an overlap comparison of model selection procedures, complementary results for the simulation on point estimation and a description of the simulation on the precision of knots.