Systematic error detection in experimental high-throughput screening

BMC Bioinformatics

Table 1 Five types of HTS datasets containing different kinds of systematic and/or random error generated and tested in this study

Error type	Generation of error-affected measurements
A. Datasets with both column and row systematic errors which are constant across all assay plates.	${x^{'}}_{i j p} = x_{i j p} + r_{i} + c_{j} + R a n d_{i j p}$ , 1 ≤ i ≤ 8, 1 ≤ j ≤ 12, 1 ≤ p ≤ 1250.
B. Datasets with the column systematic error only which is constant across all plates.	${x^{'}}_{i j p} = x_{i j p} + c_{j} + R a n d_{i j p}$ , 1 ≤ i ≤ 8, 1 ≤ j ≤ 12, 1 ≤ p ≤ 1250.
C. Datasets with the well systematic error which is constant across all plates.	${x^{'}}_{i j p} = x_{i j p} + w_{i j} + R a n d_{i j p}$ , 1 ≤ i ≤ 8, 1 ≤ j ≤ 12, 1 ≤ p ≤ 1250.
D. Datasets with the variable column and row systematic error which are different for each plate.	${x^{'}}_{i j p} = x_{i j p} + r_{i p} + c_{j p} + R a n d_{i j p}$ , 1 ≤ i ≤ 8, 1 ≤ j ≤ 12, 1 ≤ p ≤ 1250.
E. Datasets with the random error only (i.e., systematic error was absent).	${x^{'}}_{i j p} = x_{i j p} + R a n d_{i j p}$ , 1 ≤ i ≤ 8, 1 ≤ j ≤ 12, 1 ≤ p ≤ 1250.

where: ${x^{'}}_{i j p}$ is the error-affected value in well i,j (row i, column j) of plate p.
x_ijp is the original value in well i,j of plate p in the error-free dataset.
r_i is the systematic error in row i (constant over all plates); it had a normal distribution with the parameters ~N(0, C).
x_j is the systematic error in column j (constant over all plates); it had a normal distribution with the parameters ~N(0, C).
w_ij is the systematic error that affects well i,j (row i, column j) and is the same for all plates; it had a normal distribution with the parameters ~N(0, C).
r_ip is the systematic error in row i of plate p; it had a normal distribution with the parameters ~N(0, C).
c_jp is the systematic error in column i of plate p; it had a normal distribution with the parameters ~N(0, C).
Rand_ijp is the random error affecting well i,j (row i, column j) of plate p; it had a normal distribution with the parameters ~N(0, 0.3×SD).
Datasets for C = 0, 0.6×SD, 1.2×SD, 1.8×SD, 2.4×SD and 3×SD were generated and tested, where μ is the mean and SD is the standard deviation of the error-free dataset.

ISSN: 1471-2105