Microplate assays analysis

Code for the analysis of our paper "Design and analysis of a microplate assay in the presence of multiple restrictions in the randomization"

Code files

R scripts

• 1_data_processing.R: Read the raw data provided by Mimetas, tidy it and save it as data/fibrosity.rda. Also exports the data table as output/data_table.csv for the additional material of the paper.

• 2_error_structure.R: Read the excel file containing the error structure of the experiment and save it as data/fibrosity_error.rda.

• 3_active_effects.R: Run the full linear model with 31 terms, corresponding to the 31 estimable factorial effects, and compute a robust estimate of the standard error in each error stratum. For each stratum, define the active effects based on the PSE(50) critical value at 10%, computed from the robust standard error estimate. Save the effect sizes, thresholds, and robust error estimates as data/active_effects.rda.

• 4_position_plot.R: Plot the fitted means for each column and row position, using the data from the mixed model, exported from Genstat. Both plots are saved in the output/ folder as column_effect.pdf and row_effect.pdf, respectively.

• 5_interaction_plot.R: Generate the interaction plots for the three two-factor interaction that are active in the final model. All three plots are saved in the output/figures/ folder as interaction_plot_*.pdf.

• alternative_scenarios.R: Generate the design files for the 4 alternative scenarios mentioned in the paper. They are stored in the ouput/tables/ folder and named alternative_scenario_*_designs.xlsx. Also generate a table summarizing the structure of the experiment under each scenario (similar to Figure 2 in the paper), saved as output/tables/alternative_scenarios_structure.xlsx. Finally, create a table with the words used for the weeks, plates, tubes and column positions, for the four scenarios, saved as output/tables/alternative_scenarios_summary.xlsx.

Genstat scripts

The only genstat script is the file genstat/fibrosity_mixed_model.gen that runs the mixed model presented in the paper on the full data set. In case you are unable to run genstat, the file can be opened with a text editor, and the output of the script is given in output/output_fibrosity_mixed_model.rtf.

Python scripts

Design generation

All files related to the generation of the design for the experiment. In these files, we first start with a $8^12^6$ regular design in 32 runs generated using JMP, that uses the $2^{6-1}$ design with $f=abcde$ and the $W_1$-optimal blocking scheme of Mee (2009) to generate the 8 blocks.

• 1_txt2oa.py: Convert the original $8^12^6$ design from JMP to an array object from the OApackage python package.

• 2_extend_OA.py: Extend in all possible ways the $8^12^6$ to a $8^14^12^6$ by adding a four-level factor to the design.

• 3_regular_filter.py: Filter all the $8^14^12^6$ designs generated previously to only keep the ones with regular aliasing among the factors.

• 4_aliasing.py: Compute the aliasing between the 6 factors $a$ to $f$ (main effects, two-factor interactions and three-factor interactions) and the four-level factor defining the plates and the eight-level factor defining the 8 blocks for the column positions.

After generating the aliasing patterns of the three regular designs, we choose the best one as the design for the experiment.

Aliasing

All files related to the computation of the aliasing of factors and the error structure of the design

• column_position_pseudo_factor_aliasing.py: Compute the aliasing of the 7 column position pseudo-factors $p_i$, with $i=1,\ldots,7$, that represents the 8 block over the columns of a plate, with the 6 main effects, 15 two-factor interactions and 20 three-factor interactions between the 6 factors $a$ to $f$. No file output.

• g_h_aliasing.py: Compute the aliasing of the two whole plot factors ($g$ and $h$), with the with the 6 main effects, 15 two-factor interactions and 20 three-factor interactions between the 6 other factors of the design ($a$ to $f$). No file output.

• column_position_definition.py: Print a table that shows how, for each plate, the 8 column positions on a plate, are defined by the three independent pseudo-factors $p1$, $p2$ and $p_3$. No file output.

MATLAB scripts

The matlab folder contains four scripts that compute the repartition of the factorial effects into the different error strata, and the aliasing of the different factorial effects, for the base scenario and scenario 1, 3 and 4, since scenario 2 is quite similar to the base scenario in terms of aliasing.