Statistical Designs for 3D-tissue Microarrays
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1 Statistical Designs for 3D-tissue Microarrays Michael J Phelan Biostatistics Shared Resource Chao Family Comprehensive Cancer Center UC, Irvine School of Medicine October 9, 2012 MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
2 Outline 1 Background & Motivation 2 Statistical Designs 3 Linear Models and ANOVA 4 Summary MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
3 A Program Project Grant The Tumor Microenvironment in Human Colon Cancer Chris Hughes, Marian Waterman, Steve George, John Lowengrub Cellular cross-talk among tumor, stroma, and vasculature Wnts, HGF, TNF α signaling pathways, hypoxia Tumor progression, growth, angiogenesis, invasiveness A novel 3D-tumor model Advances in microfabrication, microfluidics, and microscopy 3D biological constructs for studying tissues and cells New kinds of experiments and measurements Bridging gaps to animal models...with translational potential MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
4 3D-perfused tissue microarrays MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
5 Microfluidic control MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
6 Tumor spheroids in 3D microchamber MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
7 3D-perfused tumor microarray: dual-layer design MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
8 Experimental units and treatments Experimental units a series of m chambers = angiostatic unit microarray = r c array of angiostatic units angiostatic unit = experimental unit Treatments angiostatic units under independent microfluidic control and conditions may be applied in complex combinations angiostatic units are nested within microarrays and some conditions may be applied to the whole array, only MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
9 Split-unit design: Example one Microtissue consists of co-cultures of fibrin, endothelial cells, stromal cells and tumor spheroids. There are two sources each of stromal cells and tumor spheroids. Of particular interest is the effects of concentrations of tumor cells, stromal cells and levels of Wnt signaling on a total vessel network length. Whole-unit treatments 2 2 -factorial: 2 stromal cells 2 tumor spheroids Split-unit treatments 3 3 -factorial: 3 levels of C tc 3 of C sc 3 of I wnt Note: there are 27 angiostatic units per array in these experiments. Sequential exploration of the (split-unit) factor space will be explored by response surface methods. The 3 3 -factorial may be replaced by a central composite design in only 15 runs, making reinforcements possible. MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
10 Split-unit design: Example two Microtissue consists of co-cultures of fibrin, endothelial cells, stromal cells and tumor spheroids. Here we add two conditions of hypoxia versus normoxia when treating microarrays. Of particular interest is the combined effects of phosphorylation ratios, lactate and VEGF on a total vessel network length. Whole-unit treatments 2 3 -factorial: 2 stromal 2 tumor 2 hypoxic conditions Split-unit treatments 3 3 -factorial: 3 levels of R ph 3 of C lac 3 of C vegf Note: there are again 27 angiostatic units per array in these experiments. Sequential exploration of the (split-unit) factor space will be explored by response surface methods. The 3 3 -factorial may again be replaced by a central composite design in only 15 runs, making reinforcements possible. MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
11 Randomization and ANOVA Randomization Step 1: Whole-unit treatments to 3D-tissue microarrays Step 2: Split-unit treatments to angiostatic units within an array Note: Replicate whole microarrays within whole-unit treatments. Source ANOVA df Whole-unit Trt t-1 Reps (in WU) t(r-1) Split-unit Trt g-1 SU Trt WU Trt (g-1)(t-1) SU Trt Reps (in WU) t(g-1)(r-1) Note: It is often desirable to partition the df s of treatment effects into those associated with particular contrasts. MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
12 Linear Models Split-unit designs have whole-unit treatments deliberately confounded with block effects. Like randomized blocks they involve restrictions on the randomization. The modeling is more about correlation. Standard linear model Y ijk = µ+τ i +A ij +γ k +(τγ) ik +ǫ ijk, where i = 1,...,t, j = 1,...,r, k = 1,...,g. Note 1 A ij N(0,σ a ) 2 ǫ ijk N(0,σ e ) 3 Corr(Y ijk,y ijk ) = σ2 a, k k σa 2+σ2 e MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
13 Summary Novel 3D tumor model for CRC 3D-perfused tissue microarray r c array of angiostatic units Split-unit designs Relegate important contrasts to split-unit treatments Replicate microarrays (in whole-unit treatments) to add DF s Future directions variance components analysis modeling correlation structure (across chambers) within angiostatic units design-based microscopy (stereology) MJ Phelan (UCIrvine) Designs for 3D-tissue microarrays October 9, / 13
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