Repeated Measurements on Distinct Scales With Censoring-A Bayesian Approach Applied to Microarray Analysis of Maize

Abstract

We analyze data collected in a somatic embryogenesis experiment carried out on Zea mays at Iowa State University. The main objective of the study was to identify the set of genes in maize that actively participate in embryo development. Embryo tissue was sampled and analyzed at various time periods and under different mediums and light conditions. As is the case in many microarray experiments, the operator scanned each slide multiple times to find the slide-specific 'optimal' laser and sensor settings. The multiple readings of each slide are repeated measurements on different scales with differing censoring; they cannot be considered to be replicate measurements in the traditional sense. Yet it has been shown that the choice of reading can have an impact on genetic inference. We propose a hierarchical modeling approach to estimating gene expression that combines all available readings on each spot and accounts for censoring in the observed values. We assess the statistical properties of the proposed expression estimates using a simulation experiment. As expected, combining all available scans using an approach with good statistical properties results in expression estimates with noticeably lower bias and root mean squared error relative to other approaches that have been proposed in the literature. Inferences drawn from the somatic embryogenesis experiment, which motivated this work changed drastically when data were analyzed using the standard approaches or using the methodology we propose.

Figure 1

The time course experiment for somatic embryogenesis in maize.

Figure 2

(a) Many spots are censored above in the higher reading. (b) Many spots are censored below in the lower reading.

Figure 3

Comparison of gene expression estimates from the naive method (one scan) and the hierarchical model (three scans). On the left, the values are compared for all three line pools for the first three time points. The individual estimates are very consistent for moderate values and more distinct for values in the extreme ranges of possible censoring. On the right, the values are compared for the fourth time point. The estimates for Line AB do not agree as well as the other lines for moderate expression values.

Figure 4

Comparison of gene expression estimates across the four technical replicates for time point 4 of line AB. On the left, the estimates are the ‘best’ scan values. On the right, the estimates are the values from the hierarchical model with three scans. The replicates generally agree with each other except for replicate 1 estimated with one scan. The estimates for replicate 1 using the hierarchical model are more in agreement with the other technical replicates.

Figure 5

Errorbar plots for two example genes from the 12 normalized replicate expression estimates for each time point. The red lines are estimates from one scan and the black lines use the hierarchical model for three scans. The first gene was censored below on three slides out of 60; the second gene was not censored. Average estimated expression across the 12 replicates does not change substantially except for censored genes. The errorbars from one scan are all larger than the errorbars from the hierarchical model with three scans for these two genes and 25% of the genes in the experiment.

Figure 6

The microarray double loop design with dye swap for the maize embryogenesis experiment.