Select the weak-component weight from a pair of response counts — egidi_select_weak_weight

The binomial counterpart of egidi_select_weak_weight(). The component tables are fixed, so the scan is over candidate weights alone.

Usage

egidi_select_weak_weight_binomial(
  table_informative,
  table_weak,
  y_control,
  y_treatment,
  alpha_pc = 0.05,
  weight_grid_step = 0.001,
  tolerance = 1e-09
)

Arguments

table_informative, table_weak: Component tables.
y_control, y_treatment: Observed responder counts.
alpha_pc: Conflict threshold.
weight_grid_step: Resolution of the weight scan.
tolerance: Relative tolerance for comparing probabilities.

Value

A one-row data frame shaped like egidi_select_weak_weight()'s.

Details

As in the normal case both ends are evaluated first and decide the common cases, and the scan runs upwards for the first crossing because the conflict p-value need not be monotone in the weight. The p-value is a step function of the weight here, since the conflict set can only change when a cell crosses the observed cell's probability, so the crossing is reported at the grid resolution rather than refined further.