Table II Specification of the full model
Algebraic model termaVariable or factorEffect type and assumptionbSubscript range (main effects) or number of terms (interactions)Terms in the computational modelc
yghijlResponse variablelog10(MFI)
μMean MFI of phospho-Akt measurements from vehicle-treated samples1Intercept
vgVehicle main effectsFixedg = 1,2(ligand vehicle)d, dmso
khKit (analyte) main effectFixedh = 1–16(akt)d, erk, gsk, ikb, jnk, p38, p70, p90, cjun, creb, hsp27, irs, mek, p53, stat3, s6rp
(vk)ghVehicle × Kit interactionFixed15dmso × 15 kits
tiTreatment main and interaction effectsFixedi = 1–17Main: d, 6, L, N, G
2-way interactions: d×6, d×L, d×N, d×G, 6×L, 6×N, 6×G, N×G
3-way interactions: d×6×L, d×6×N, d×6×G, d×N×G
(kt)hiTreatment × Kit interactionsFixed17 treatment effects × 15 kits = 255Each treatment term × 15 kits
δjDay main effectRandomj = 1–3d1, d2, d3
d∼N(0,σd2)
(kδ)hjDay × Kit interactionRandom3 days × 16 kits = 48Each day term × each of the 16 Kit terms
(kd)∼N(0,σkd2)
(tδ)ijDay × Treatments (main effects only) interactionRandom3 days × 5 treatments × 2 levels of each treatment = 30Each day term × each of d, 6, L, N and G
(td)∼N(0,σtd2)
ωlWell (sample) effectsRandoml = 1–86Well addresses (e.g., A9, G12, etc.)
w∼N(0,σw2)
ϵghijlResidual errorRandom
e∼N(0,σ2)
  • a The algebraic equation is a compact representation of the mixed-effects model that must be translated into a computationally readable form. Although R can handle categorical variables specified in compact form (e.g., specifying a factor such as “Kit” and listing its constituents as levels in the data column), doing so precludes eliminating terms from within that factor during variable selection. We therefore explicitly specified each level of the factor as its own term in models subjected to variable selection. See the spreadsheet file in the Supplementary Information for more details.

  • b The random effects were assumed to be independent values of their respective variables that are normally distributed with mean of zero and variance as indicated.

  • c Legend: d = Dexamethasone, 6 = interleukin-6, L = interleukin-1α, n = tumor necrosis factor-α, G = transforming growth factor-α, d1 = Day 1, d2 = Day 2, d3 = Day 3.

  • d Terms listed in brackets did not have their own terms in the computational model but instead served to estimate the intercept, relative to which the effects of the remaining terms were computed.