Exact and approximate p-values for some extreme cases.

<p>m, the number of genes in the gene set. Total number of genes is set as 10,000.</p

Effect of local statistics on the comparison of the two approximation methods.

<p>The plot are of negative base 10 logarithm of the p-value from normal approximation versus that of the p-value from uniform approximation when using fold change (microarray) and log likelihood ratio (RNA-Seq) as local statistics. Panels (a) and (b) are two different microarray datasets. Panels (c) and (d) are the RNA-seq datasets with Poisson assumption. Panels (e) and (f) are the RNA-seq datasets with Negative Binomial assumption.</p

False positive rates comparison between uniform and normal approximations to WRS test.

<p>Results are the mean of false positive rate from 50 rounds of simulations. m, number of genes in gene set.</p

Comparison of p values obtained from normal and uniform approximations.

<p>The p values (negative base 10 logarithm) from the normal approximation are plotted against those from the uniform approximation. The red line is the identity line and the two blue lines represent the cut-off p value of 0.05 with Bonferroni correction. Panels (a) and (c) are for the two microarray datasets. Panels (b) and (d) are for the two RNA-Seq datasets.</p

Flowchart for the analysis of real data.

<p>The location for null distribution approximation is highlighted with grey background.</p

The distributions of the sizes of GO terms in the microarray and RNA-seq datasets analyzed in this paper.

<p>Most GO terms are small.</p

Linear relationship between the absorbance summation (AS) and estimated point of maximum growth (PMG).

<p>For observations with an estimated PMG within the observable concentrations, the AS and the PMG have a clear negative correlation. The straight line is the regression line.</p

Relationship between the three proxies and simulated PMG.

<p>Sigmoidal curves are simulated with different point of maximum growth (PMG). Each estimated proxy is plotted against the simulatied PMG. The estimated PMG works well for values where there is more data surrounding the PMG, but variance increases when the available data are not near the PMG. The endpoint titer method results in discrete values and has a weaker relationship with the actual PMG. The absorbance summation has a strong relationship with the true PMG.</p

Absorbance summation: A novel approach for analyzing high-throughput ELISA data in the absence of a standard

<div><p>We have developed a very simple method, termed absorbance summation (AS), for comparing protein concentrations between samples in ELISA assays without a standard. This method sums the observed absorbance values from all dilutions to obtain one data point for each sample to be used for comparison. AS is less computationally intensive than fitting sigmoidal curves, and it avoids the difficulty of parameter estimation for samples with absorbance values lying primarily at the lower tail of the curve. Our simulation studies showed that it performs much better than the sigmoidal curve fitting method and the conventional endpoint titer method. The power of this simple method is as high as the formal curve fitting followed by the estimation of area under the curve (AUC).</p></div

Statistical power comparison among the three methods.

<p>Statistical power is plotted against the PMG differences between the two comparing groups. Sigmoidal curves are simulated with different PMG, which range from within (-16.0959 and -15.0959) to outside of the measurements (-13.0959 and -11.5959), as shown in the panel columns. The error variance is either constant or changing along the curve with a linear or quadratic relationship with the values on the curve, which are shown in different panel rows. Statistical power is calculated based on the two group t test. Var, variance.</p