Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines. (English) Zbl 1288.62161

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

Ann. Appl. Stat. 7, No. 2, 823-845 (2013).

Summary: DNA copy numbers and mRNA expressions 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, we model their associations. We employ piecewise linear regression splines (PLRS), which combine good interpretation with sufficient flexibility to identify any plausible type of relationships. The specification of the model leads to estimation and model selection in a constrained, nonstandard setting. We provide methodology for testing the effects of DNA on mRNA and choosing an 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62J05	Linear regression; mixed models
92C50	Medical applications (general)
62F30	Parametric inference under constraints
65C60	Computational problems in statistics (MSC2010)

Software:

DR-Integrator; ic.infer; CGHcall

References:

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