Marshall (1975) and Johnson and Kotz (1975) interpreted r i (x 1,x 2) as the conditional failure rate of X i evaluated at x i under condition that X j >x j for i=1,2, i≠j.
As shown in the analytical power derivations presented in Additional file 3, an improvement in power for M R gluc max, P m, relative to the power for K i, P k, occurs whenever the coefficient of variation (CV) in K i evaluated at the mean glucose level is less than 1.
The estimation of the continuous curves x i (t) from data points y i (t j ) is based on the measurement model (1) y i t j = x i t j + ϵ ij, where x i (t j ) is x i evaluated at time t j and ϵ ij ~ N 0, σ) is an error term.
The time-point expression patterns were modelled as follows, (2) y ij = μ i t j + ϵ ij where μ i t j = log 2 x ¯ D t j / x ¯ C t j is the population average time curve for gene i evaluated at time t j and where ϵ ij is the random deviation from this curve.
The wild-type data and the TF-knockout data were organized in different columns of the E matrix (expression data matrix where E ij corresponds to the log of gene expression ratio of gene i evaluated at experiment j, see Methods).
