Cellular functions of living organisms are carried out through complex systems of interacting components. Including such interactions in the analysis, and considering sub-systems defined by biological pathways instead of individual components (e.g. genes), can lead to new findings about complex biological mechanisms. Networks are often used to capture such interactions and can be incorporated in models to improve the efficiency in estimation and inference. In this paper, we propose a model for incorporating external information about interactions among genes (proteins/metabolites) in differential analysis of gene sets. We exploit the framework of mixed linear models and propose a flexible inference procedure for analysis of changes in biological pathways. The proposed method facilitates the analysis of complex experiments, including multiple experimental conditions and temporal correlations among observations. We propose an efficient iterative algorithm for estimation of the model parameters and show that the proposed framework is asymptotically robust to the presence of noise in the network information. The performance of the proposed model is illustrated through the analysis of gene expression data for environmental stress response (ESR) in yeast, as well as simulated data sets.