Batch effects matter

Here’s an example of plate effect. Here both top and bottom rows of the plate are used as controls.

This is the experiment design:

These are the readouts:

Due to the plate effect, the control rows are affected differently. It is virtually impossible to normalize readouts in a meaningful way.

Go fully random?

• Could it be sufficient to randomly distribute samples across batches?
• Not necessarily!
  • Often sample sizes are too small to avoid grouping by change
  • Experimental constraints might not allow for a fully random layout

Gone wrong: Random distribution of 31 grouped subjects into 3 batches turns out unbalanced:

“Block what you can and randomize what you cannot.” (G. Box, 1978)

designit

• Data structure: BatchContainer class
  • R6 object storing:
    • Experiment dimensions (cages, plates…)
    • Sample annotation
    • Scoring functions for sample distribution
• Main function: optimize_design()
  • Optimizes the layout with user defined
    • Scores for sample distribution
    • Optimization protocols
    • Sample shuffling functions
  • Returns improved design and optimization trace

Setup

• Assign 31 samples to 3 equally sized batches
• Balance by:
  • treatment group (higher priority)
  • sex (lower priority)

bc <- BatchContainer$new(
  dimensions = list("batch" = 3, "location" = 11)
) |>
  assign_random(subject_data)

Batch composition before optimization

bc$get_samples()

Optimization

• Assign 31 samples to 3 equally sized batches
• Balance by:
  • treatment group (higher priority)
  • sex (lower priority)

bc <- optimize_design(
  bc,
  scoring = list(
    group = osat_score_generator(
      batch_vars = "batch",
      feature_vars = "Group"
    ),
    sex = osat_score_generator(
      batch_vars = "batch",
      feature_vars = "Sex"
    )
  ),
  n_shuffle = 1,
  acceptance_func =
    ~ accept_leftmost_improvement(..., tolerance = 0.01),
  max_iter = 150,
  quiet = TRUE
)

Batch composition after optimization

Continuous confounding

Assays are often performed in well plates (24, 96, 384)

Observed effects

• Edge effects (bad plate sealing)
• Gradients (non-equal temperature distribution)
• Row / column effects (pipetting issues)

Since plate effects often cannot be avoided, we aim to distribute sample groups of interest evenly across the plate and adjust for the effect computationally.

Setup

• Assume previous batches are 24-well plates
• Within plate optimization & across plate blocking
• Balanced by:
  • treatment group (higher priority)
  • sex (lower priority)

set.seed(4)

bc <- BatchContainer$new(
  dimensions = list("plate" = 3, "row" = 4, "col" = 6)
) |>
  assign_in_order(dat)

plot_plate(bc,
  plate = plate, row = row, column = col,
  .color = Group, title = "Initial layout by Group"
)
plot_plate(bc,
  plate = plate, row = row, column = col,
  .color = Sex, title = "Initial layout by Sex"
)

2-step optimization

bc1 <- optimize_design(
  bc,
  scoring = list(
    group = osat_score_generator(
      batch_vars = "plate",
      feature_vars = "Group"
    ),
    sex = osat_score_generator(
      batch_vars = "plate",
      feature_vars = "Sex"
    )
  ),
  n_shuffle = 1,
  acceptance_func =
    ~ accept_leftmost_improvement(..., tolerance = 0.01),
  max_iter = 150,
  quiet = TRUE
)

bc2 <- optimize_design(
  bc1,
  scoring = mk_plate_scoring_functions(
    bc1,
    plate = "plate", row = "row", column = "col",
    group = "Group"
  ),
  shuffle_proposal_func = shuffle_with_constraints(dst = plate == .src$plate),
  max_iter = 150,
  quiet = TRUE
)

2-step optimization multi_plate_layout()

We are performing the same optimization as before, but using the multi_plate_layout() function to combine the two steps.

bc <- optimize_multi_plate_design(
  bc,
  across_plates_variables = c("Group", "Sex"),
  within_plate_variables = c("Group"),
  plate = "plate", row = "row", column = "col",
  n_shuffle = 2,
  max_iter = 500 # 2000
)
#> 1 ... 2 ... 3 ...

#> Warning: Removed 4509 rows containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 4509 rows containing missing values or values outside the scale range
#> (`geom_point()`).