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The Proportion of True Null Hypotheses in Microarray Gene Expression Data Open Access

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Microarray technology is extensively used today in many applications. One of its uses is discovering sets of genes that are most likely to be related to cancer. Typically, based on microarray data, a statistical test is conducted for each of thousands of genes simultaneously. In a two-group comparative microarray experiment, an important parameter for controlling the rate of false positives and also for determining the appropriate sample size is the proportion of true null hypotheses (π0). To obtain an improved estimation method for π0, we modify an existing simple method by introducing artificial censoring to p-values. The model is a two-component mixture of a censored Uniform(0,1) and a censored Beta(α,1) distribution. The model fitting is achieved through the Expectation Maximization algorithm. In a comprehensive simulation study and applications to experimental data sets, we illustrate the benefits of using our method by comparing its performance to other existing methods. Furthermore, we develop and study the properties of a likelihood ratio test for π0 at different combinations of sample size, number of genes, and H0 value of π0. Maximization of the restricted likelihood is achieved by incorporating a linear constraint of the parameters into the Expectation Maximization algorithm. The p<\italic>-value of the test is based on a parametric bootstrap approach. We illustrate the usefulness of the test through applications to experimental datasets.

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