Robust microarray experiments by design: a multiphase framework

1. Robust microarray experiments by design: a multiphase framework Chris Brien Phenomics & Bioinformatics Research Centre,University of South Australia http://chris.brien.name/multitier Chris.brien@unisa.edu.au

2. Outline The multiphase framework for microarray experiments. A sources-of-variability Affymetrix microarray experiment. Conclusions.

3. 1. The multiphase framework for microarray experiments • The framework is based on Brien et al. (2011). • We define a phase to be the period of time during which a set of units are engaged in producing a particular outcome. • The outcome can be material for processing in the next phase, or values for response variables, or both. • Only the final phase need have a response variable. • Also, one phase might overlap another phase. • Then, multiphase experiments consist of two or more such phases. • Generally, multiphase experiments randomize (randomly allocate) the outcomes from one phase to the next phase.

4. Physical phases in a microarray experiment Selection or production of biological material Sample acquisition & storage RNA extraction Labelling Hybridization, incl. post-washing Extracts Samples Organisms/Tissues Aliquots Scanning Measure-ments Hybridized arrays Arrays • Potentially a designed experiment at every phase (Speed & Yang with Smyth, 2008). Array production or purchase Design • Two-phase design (McIntyre, 1955; Kerr, 2003): • 1st phase can be an experiment or an observational (epidemiological) study; • 2nd phase is a laboratory phase (Brien et al., 2011). • Multiple randomizations (Brien & Bailey, 2006) in a seven-phase process. One list of phases, and their outcomes, that commonly occurs.

5. The components of the framework • Identify the set of phases involved. • Determine the design for each phase. • Produce factor-allocation description of the experiment. • Formulate the full mixed model. • Derive the ANOVA table and use it to • investigate design; and • obtain a mixed model of convenience.

6. II. Design for a phase: how to allocate one phase to the next • The basic principles used in single phase experiment are applied for each phase, along with others outlined by Brien et al. (2011): • Randomization to avoid bias. • Is it OK to process material from the same organism first in every phase, during operator or equipment warm-up in a phase? Randomization makes the experiment robust to such biases. • Minimizing variability. • Focusing on experimental design, an obvious way is to look to remove batch effects for batches built into the processes: • e.g. different acquisition times, processing days, operators, batches of reagent or sets of simultaneously-processed specimens.

7. 3. A sources-of-variability Affymetrix microarray experiment Production of biological material Sample acquisition & storage RNA extraction Labelling I. List of phases Hybridization, incl. post-washing Mammary gland sample Extract Rat 2 Aliquots Scanning Measure-ments 4 Hybridized arrays 4 Affymetrix arrays Array purchase Each aliquot halved for hybridization Extract halved for labelling • A modified version of a study to examine the variability of labelling and hybridization described by Zakharkin et al. (2005): • It involved 8 rats.

8. II. Assignment of factors for the sources-of-variability experiment • Suppose that: • Sampling of the rats is in a random order. • For each rat, the RNA is extracted immediately the tissue is obtained; i.e. RNA-extraction order from samples is not random. • In the labelling phase, the 2 half-extracts from an extract will be labelled consecutively. • In the hybridization phase, where washing occurs in batches of 16, one half-aliquot from all aliquots will be hybridized in one batch, and the remaining ones in a second batch. • This means all rats are included in a batch and that the estimate of hybridization variability includes batch variability. • In the scanning phase, the arrays will be scanned in a completely random order • If scanning is to be batched, Brien et al. (2011) would suggest batches in this phase line up with those in the hybridization phase. • Halving extracts and aliquots introduces technical replication, an example of laboratory replication (Brien et al., 2011).

9. III. Factor-allocation description 2 A1 Production of biological material Sample acquisition & storage RNA extraction Labelling Hybridization, incl. post-washing Mammary gland sample Extract Rat 2 Aliquots Scanning 2 AliquotHalvesin O,L Measure-ments 4 Hybridized arrays 2 HalfExtracts in E 4 Affymetrix arrays 16 half-extracts 32 Scans Array purchase 8 Extractions 8 Rats 8 Samplings 32 half-aliquots 32 scans Each aliquot halved for hybridization Extract halved for labelling 8 samples 8 rats 2 Labellings in O 8 Occasions Factor-allocation diagrams have a panel for a set of objects (here the set of outcomes of a phase); a panel lists the factors indexing a set. 32 hybridized arrays 2 Batches 16 Hybridizations in B 32 Chips Dashed arrow indicates systematic (Brien et al., 2011) Solid arrow indicates randomization 32 arrays

10. IV. Mixed model for experiment 2 AliquotHalvesin O,L 2 HalfExtracts in E 2 A1 16 half-extracts 32 Scans 8 Extractions 8 Rats 8 Samplings 32 half-aliquots 32 scans 8 samples 8 rats 2 Labellings in O 8 Occasions 32 hybridized arrays 2 Batches 16 Hybridizations in B 32 Chips • To get mixed model use Brien & Demétrio’s (2009) method: • In each panel, form terms as all combinations of the factors, subject to nesting restrictions; • For each term from each panel, add to either fixed or random model. • Mixed model: • Grand mean | Rats + Samplings + Extractions + ExtractionsHalfExtracts + Occasion + OccasionLabellings + OccasionLabellingsAliquotHalves + Batches + BatchesHybridizations + Chips + Scans 32 arrays

11. V. Mixed model of convenience 2 AliquotHalvesin O,L 2 HalfExtracts in E 2 A1 • Given confounding, can measure variability from: • Rats + Samplings + Extractions + Occasions; • ExtractionsHalfExtracts+ OccasionLabellings; • Batches • OccasionLabellingsAliquotHalves + BatchesHybridizations+ Chips + Scans. • Mixed model of convenience for fitting: • Grand mean | Rats + ExtractionsHalfExtracts+ Batches + BatchesHybridizations. • This model does not include all sources of variation. 16 half-extracts 32 Scans 8 Extractions 8 Rats 8 Samplings 32 half-aliquots 32 scans 8 samples 8 rats 2 Labellings in O 8 Occasions ANOVA useful for this 32 hybridized arrays 2 Batches 16 Hybridizations in B 32 Chips 32 arrays

12. Summary • Microarray experiments are multiphase: • One might employ an experimental design in every phase to randomize and block the processing order in the current phase. • Factor-allocation description can be used to formulate the analysis for an experiment, this analysis including terms from every phase. • The multiphase framework is flexible in that it can easily be adapted to another set of phases.

13. References http://chris.brien.name/multitier Brien, C.J., and Bailey, R.A. (2006) Multiple randomizations (with discussion). J. Roy. Statist. Soc., Ser. B, 68, 571–609. Brien, C.J. and Demétrio, C.G.B. (2009) Formulating mixed models for experiments, including longitudinal experiments. J. Agr. Biol. Env. Stat., 14, 253-80. Brien, C.J., Harch, B.D., Correll, R.L. and Bailey, R.A. (2011) Multiphase experiments with at least one later laboratory phase. I. Orthogonal designs. J. Agr. Biol. Env. Stat., 16(3): 422-450. Kerr, M. K. (2003) Design Considerations for Efficient and Effective Microarray Studies. Biometrics, 59(4), 822-828. McIntyre, G. A. (1955). Design and analysis of two phase experiments. Biometrics, 11, 324-334. Speed, T. P. and Yang, J. Y. H. with Smyth, G. (2008) Experimental design in genomics, proteomics and metabolomics: an overview. Advanced Topics in Design of Experiments. Workshop held at INI, Cambridge, U.K. Zakharkin, Stanislav O., et al. (2005) Sources of variation in Affymetrix microarray experiments. BMC Bioinformatics, 6, 214-11. Web address for Multitiered experiments site: