Equal Aliquot Sample Clauses

Equal Aliquot. Volumes Consider the MLR model: Yij = xijβ + ϵij, j = 1 . . . ki, i = 1 . . . n, where Yij is the outcome and xij = (1, xij1, . . . , xijP ) the row vector of covariates for the jth subject in the ith pool, β is the column vector of coefficients, ki is the number of specimens in pool i (i.e. pool size), and ϵij is the error term with mean 0 and variance σ2. Furthermore, i=1 let N = Σn ki denote the total sample size. In practice, each specimen might have a different volume, depending on the amount initially collected, or the remaining volume after portions were taken for use in other studies. These differing aliquot volumes form a pooled measurement that is a weighted average of the value of each specimen included in the pool, requiring a slight variation in the regression formulation. We will first describe the simpler situation, when all aliquot volumes are assumed to be equal. Except where otherwise noted, we assume that the same aliquot volume is contributed by each member of a pool for the remainder of this study. When all specimens contribute equal aliquot volumes to the pool, we assume that the lab assay applied to a pooled sample yields the mean concentration from the individual specimens comprising the pool. The MLR model for the ith pool then becomes: Yi = xiβ + ϵi, i = 1 . . . n, ki j=1 ki