Simulating Class and Batch Effects in Omics Data

To simulate class-effect proportion (CEP), class effects are applied onto 0, 0.2, 0.5 and 0.8 of measured proteins (Fig. 2). The magnitude of applied effect sizes is randomly selected from 0.2, 0.5, 0.8, 1 and 2. The class effect is applied in one class, but not the other, and is a proportionate increment. For example, a 0.2 class-effect level means a 20% increment from the original value. When CEP is high, it leads to sample classes whose basal expression states are drastically different.Figure 2

Simulation strategies for data with simulated class and batch effects (A) and data with real batch effects, but simulated class effects (B).

Batch effects are simulated similarly, except the batch effects are inserted according to batch factors (the categorization of technical batches). In this simplistic scenario, we simply assign half of the samples of each class, to each batch.
Since the set of differential variables are known a priori, normalization performance across the five strategies may be evaluated by statistical feature selection (based on the two-sample t test; α = 0.05 significance level) and overall batch-effect correction based on the gPCA delta^{21 (link)} (see below).
For statistical feature selection, the precision, recall and their harmonic mean (the F-score) are used. These are expressed as: $$\begin{array}{cc}& \text{Precision}=\frac{\mathit{TP}}{TP+FP}\hfill \\ \hfill & \text{Recall}=\frac{\mathit{TP}}{TP+FN}\hfill \\ \hfill & \text{F-score}=2\times \frac{Precision\times Recall}{Precision+Recall}\hfill \\ \hfill \end{array}$$
where TP, FP and FN refer to true positives, false positives and false negatives, respectively. The efficacy of batch correction is evaluated using gPCA^{21 (link)}. The gPCA delta measures the proportion of variance due to batch effects in test data, and is bound between 0 and 1. Ideally, we want this to be as low as possible following normalization.