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Optimal designs for one and two- colour microarrays using mixed models A comparative evaluation of their efficiencies Lima Passos, Winkens, Tan and Berger DEMA 2008 Maastricht University Department of Methodology and Statistics

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Current situation One versus two colour comparisons Woo et al, 2004: –We observed good concordance in both estimated expression levels and statistical significance of common genes. Smyth, 2005: –All four platforms reasonably precise (cDNA, oligo, Agilent, Affymetrix); –Broadly agree; –Disagreement due to sequence differences, not to noise. John Hopkins Press release, 2005: –Different microarray systems more alike than previously thought; Patterson et al., 2006 : –The quality of the data stemming from one and two-colour arrays are equivalent in terms of reproducibility, sensitivity, specificity and accuracy; –highly concordant results regarding detection of differentially expressed genes; Background

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Current opinions One or Two? Hardiman, 2004: –The choice of platform … should be guided by the content on that platform and the amount of RNA available for experimentation. Agilent technologies: –Both one and two colour have their places in scientific research: One provide much quicker analysis, more efficient method for analysing a large number of samples or those that span long time frames; Two provide the most accurate results, helping identify small incremental changes in sample to further specific investigations; Patterson et al. 2006; –The decision to used one or two will be determined by cost, experimental design considerations and personal preference; –Platform type should not be considered a primary factor ‘in decisions regarding experimental microarray design’; Background

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Optimal designs One versus two? The majority of papers addressing microarray design questions - fixed effects models; They are all specifically directed to two-colour microarrays; Design papers with mixed models (also two-colour) are less abundant (Cui and Churchill, 2003; Landgrebe et al., 2004; Tempelman, 2005; Bueno Filho et al., 2006 and Tsai et al., 2006); Is the choice of platform an important design issue? Main question: What is exactly the impact the choice of a platform can have on the precision of model parameters? –If any, which are the financial implications? Objective

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Design issues at stake Two colour: –which pair-samples (the design points) to distribute across the slides together with their label assignment? One colour: –design points consists of the groups themselves, and not their pair-wise combinations; ??? Design

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Mixed models One colour: Two colour: Premises

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Covariance structure Block diagonal, compound symmetric structure of V: –Dye swap is made at the level of technical replication with identical sample pairs. If not, i.e. l j with l k’, with k ≠ k’, the block diagonal of the final covariance matrix V will be lost. Premises

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Further premises Contrasts - Θ* = CΘ (first order interactions or main effects) Optimality criteria: Sequential search yields an approximate Exact designs: rounding up/down to the closest integer: Relative efficiency one versus two: Premises

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The cost function Given the prohibitive costs, it is recommendable to have an estimation of the costs of different microarray designs for comparative purposes: cost = n j c 1 + n k Sc 2 Premises

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Ceteris paribus Assumptions/limitations To warrant comparability and fair assessment between the two platforms: –model parameters and contrasts (common research questions) for the one and two-colour arrays are given on the same scale; –number of technical replicates was held constant (2), and the search of optimal designs focused on the distribution of biological replicates; –homogeneity of biological variances of experimental groups as well as independence and homogeneity of residual error variances were assumed to hold ; –Variance components were restricted to a random intercept model with compound symmetric, block-diagonal covariance matrix (dye-swap with identical sample pairs!); –subjects’ price was constant over all biological groups and the one- and two-colour arrays cost the same ; Premises

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Results 3 x 3 factorial experiment Results

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ξ * and ξ I * - Two colour Results

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xdxd wdwd PmfDirected graph xdxd wdwd The design measure ξ * D-optimal design – main effects only Results

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One versus two?? Subjects to groups allocation Results How many subjects?

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One versus two?? Subjects to groups allocation Results ~

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Efficiency comparison =N≠ I=N≠ I ≠ N = I Results

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Cost comparison =N≠ I=N≠ I ≠ N = I Results Cost 1 – Cost 2!!! Cost 1 – Cost 2

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Cost comparison “adjusted for efficiency” Results

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Optimal allocation of subjects to experimental groups is much concordant between the two platforms - Hence the choice of platform will not affect the subjects to groups’ optimal allocation; By varying number of subjects and arrays, while holding statistical precision of parameter estimates comparable, the choice of the one over the two-colour platform or vice-versa will be determined the subject to arrays cost ratio; On the grounds of statistical efficiency and under the condition that the acquisition of arrays outstrips that of subjects financially, two-colour arrays should be considered an efficient alternative over the one-colour, specifically for studies involving class comparisons. Final remarks Conclusion

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