Presentation on theme: "Optimal designs for one and two-colour microarrays using mixed models"— Presentation transcript:
1 Optimal designs for one and two-colour microarrays using mixed models A comparative evaluation of their efficienciesLima Passos, Winkens, Tan and BergerDEMA 2008Maastricht UniversityDepartment of Methodology and Statistics
3 Current situation One versus two colour comparisons BackgroundWoo 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;
4 Current opinions One or Two? BackgroundHardiman, 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’;
5 Optimal designs One versus two? ObjectiveThe 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?
6 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;???
8 Covariance structurePremisesBlock diagonal, compound symmetric structure of V:Dye swap is made at the level of technical replication with identical sample pairs. If not, i.e. lj with lk’, with k ≠ k’, the block diagonal of the final covariance matrix V will be lost.
9 Further premisesPremisesContrasts - Θ* = CΘ (first order interactions or main effects)Optimality criteria:Sequential search yields an approximateExact designs: rounding up/down to the closest integer:Relative efficiency one versus two:
10 The cost function cost = njc1 + nkSc2 PremisesGiven the prohibitive costs, it is recommendable to have an estimation of the costs of different microarray designs for comparative purposes:cost = njc1 + nkSc2
11 Ceteris paribus Assumptions/limitations PremisesTo 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;
12 3 x 3 factorial experiment ResultsResults3 x 3 factorial experiment
19 ResultsCost comparison“adjusted for efficiency”
20 Final remarksConclusionOptimal 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.