Optimal designs for one and two-colour microarrays using mixed models

1. 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

3. Current situationOne versus two colour comparisons Background • 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;

4. Current opinionsOne or Two? Background • 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’;

5. Optimal designsOne versus two? Objective • 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?

6. Design issues at stake Design 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; • ???

7. Mixed models Premises • One colour: • Two colour:

8. Covariance structure Premises • 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. lj with lk’, with k ≠ k’, the block diagonal of the final covariance matrix V will be lost.

9. Further premises 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:

10. The cost function Premises • Given 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 paribusAssumptions/limitations Premises • 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;

12. Results Results 3 x 3factorial experiment

13. ξ* and ξI* - Two colour Results

14. 11 33 12 13 32 21 31 23 22 The design measure ξ* D-optimal design – main effects only Results Pmf Directed graph wd xd wd xd

15. One versus two?? Subjects to groups allocation Results How many subjects? 11 8 5 12

16. One versus two?? Subjects to groups allocation Results ~

17. Results Efficiency comparison =N ≠I ≠ N =I

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

19. Results Cost comparison “adjusted for efficiency”

20. Final remarks Conclusion 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.