Changes in gene expression can correlate with poor disease outcomes in two ways: through changes in relative transcript levels or through alternative RNA splicing leading to changes in relative abundance of individual transcript isoforms. The objective of this research is to develop new statistical methods in detecting and analyzing both differentially expressed and spliced isoforms, which appropriately account for the dependence between isoforms and multiple testing corrections for the multi-dimensional structure of at both the gene- and isoform- level. We developed a linear mixed effects model-based approach for analyzing the complex alternative RNA splicing regulation patterns detected by whole-transcriptome RNA-sequencing technologies. This approach thoroughly characterizes and differentiates three types of genes related to alternative RNA splicing events with distinct differential expression/splicing patterns. We applied the concept of appropriately controlling for the gene-level overall false discovery rate (OFDR) in this multi-dimensional alternative RNA splicing analysis utilizing a two-step hierarchical hypothesis testing framework. In the initial screening test we identify genes that have differentially expressed or spliced isoforms; in the subsequent confirmatory testing stage we examine only the isoforms for genes that have passed the screening tests. Comparisons with other methods through application to a whole transcriptome RNA-Seq study of adenoid cystic carcinoma and extensive simulation studies have demonstrated the advantages and improved performances of our method. Our proposed method appropriately controls the gene-level OFDR, maintains statistical power, and is flexible to incorporate advanced experimental designs.