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 UniversityDepartment of Methodology and Statistics

Current situationOne 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

Current opinionsOne 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

Optimal designsOne 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

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:

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Premises

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. lj with lk’, with k ≠ k’, the block diagonal of the final covariance matrix V will be lost.

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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:

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Premises

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 = njc1 + nkSc2

Premises

Ceteris paribusAssumptions/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

Results

3 x 3 factorial experiment

Results

ξ* and ξI* - Two colourResults

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PERCENT

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The design measure ξ*

D-optimal design – main effects only

Results

One versus two??Subjects to groups allocation

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Results

How many subjects?

One versus two??Subjects to groups allocation

Results

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Efficiency comparison

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≠ N= I

Results

Cost comparison

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Results

Cost 1 – Cost 2!!!

Cost 1 – Cost 2

Cost comparison“adjusted for efficiency”

Results

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 remarksConclusion

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