Figure 4: Parameter estimates with varying n for all selected variables.
Each of the four panels was obtained with a specific sample size with n={100;
200; 400; 1000}. Whatever the panel, the following distributions were plotted:
1-distribution of the estimates for the ΩR sets over 200 identification sets parameters
(histogram with horizontal hatching). 2-distribution of the estimates
of the ΩR sets over 200*50 validation datasets (histogram with diagonal hatching).
The vertical dotted line indicates the mean of the latter distribution. The
vertical continuous line indicates 0.2.
The R selected variables are a mixture of False Positives (V) and True
Positives (S) that respectively corresponds to the left and the right mode of the
distributions of ΩR estimates. When increasing the sample size, S increases
at the cost of a decrease of V, thus modifying the shape of the distribution of
the estimates for the ΩR variables. When n=1000, there are fewer FP and the
estimates for TP are no longer over-estimated. This shows the consequence
of the regression to the mean phenomenon in terms of confirmation of the
selected candidate biomarkers. |
