Statistical methods in experimental design and analysis of microarray data

In this thesis, we concentrate on statistical methods in identifying differentially expressed genes and providing experimental designs for cDNA microarray experiments.; Identifying differentially expressed genes for different conditions is one of the main objectives in eDNA microarray experiments. Many current statistical models cannot be used for insufficient replicated arrays. In Chapter 3, we propose a, new method to solve this problem, when a single array data are available. If the log-transformed ratios for the expressed genes as well as unexpressed genes have equal variances, we use a Hadamard matrix to construct a t test from a single array data. Basically, we test whether each doubtful gene has significantly differential expression compared to the unexpressed genes. We form some new random variables corresponding to the rows of a Hadamard matrix using the algebraic sum of gene expressions. A one-sample t test is constructed and the p-value is calculated for each doubtful gene based on these random variables. By using any method for multiple testing, adjusted p-values could be obtained from original p-values and significance of doubtful genes can be determined. When the variance of expressed genes differs from the variance of unexpressed genes, we construct a confidence interval for the difference in the log expression levels and using this interval, we determine differentially expressed genes. In Chapter 4, we generalize the results of Chapter 3 by considering fewer replications of arrays. We use data from doubtfully expressed genes and unexpressed genes to construct a t test, using Satterthwaite's degrees of freedom to identify differentially expressed genes for both direct and indirect designs.; A good statistical design is important to get valid inferences in microarray experiments. Sonic optimal designs have been proposed in the literature, but they are not widely applicable. In Chapter 5, we discuss designing 2 m factorial cDNA mieroarray experiments using Hadamard matrices. We balance the levels of the factors on the disease conditions and construct orthogonal factorial experiments, in general. These designs orthogonally estimate the effects of interest. In Chapter 6, we extend our work to construct new factorial designs with 3 levels for each factor.