Statistical entropy is derived from the negative binomial distribution where an experiment with two equally likely outcomes, labeled success or failure, is considered.
The predictive accuracy for the samples with nine poor outcome labels was only 45% for DMFS and 36% for BCSS (see Figure 4 and Additional data file 4).
Furthermore, while we used 'death' as the outcome variable for the prognosis prediction described above, we find that it is robust to using other variables as outcome labels (Additional file 2: Supplementary Notes).
To control for this, the data were re-analysed 999 times using random permutations of the patient outcome labels to generate true (permuted) P-values for each gene set.
We found significant enrichment for univariate association with recurrence in these 138 genes (see Additional file 8, Figure S1 for comparison of the distribution of nominal p-values with a null distribution empirically determined by permutation of the outcome labels).
We now only consider the subset of SNPs X ˜ obtained from L after neglecting all irrelevant SNPs and use a measure correlation function χ2 X ˜, Y) to test the association between the outcome label and each SNP X j.
The assumption of sample independence is violated in cross-validated predictions, so following Simon et al. (2011), we also assessed significance for the Elastic Net model by permuting the outcome labels 500 times.
Through the repeated permutation of clinical outcome labels and the re-computation of mutual information values, a threshold θ is defined as the maximum of the average mutual information values for each gene pair.
Attribute importance was assessed by means of RF, calculating the average re-scaled (i.e. divided by its standard error) decrease in accuracy by variable randomization (repeated for 1000 times), and comparing it against a null distribution obtained by shuffling outcome labels, calculating p-values according to the method of Altmann et al.[ 42] and previous works[ 43, 44].
This narrative review reveals several linked knowledge gaps and recommended areas for future research: First, more research is needed on the effectiveness of food label interventions to better understand how consumers across different demographics use labels in real-world settings and the long-term health outcomes of labelling.
