Power for ANCOVA homogeneity-of-slopes test

You ran a two-group trial and measured each patient's blood pressure at baseline. Before trusting a single adjusted treatment effect, you want to know whether the treatment works differently depending on where a patient started — does the slope of blood_pressure on baseline_bp differ between the treatment and control arms? That is a group-by-covariate interaction, the homogeneity-of-slopes test that an ordinary ANCOVA assumes away.

As an MCPower formula this is blood_pressure = treatment * baseline_bp, where * expands to treatment + baseline_bp + treatment:baseline_bp. treatment is a two-level treatment factor and baseline_bp is a continuous covariate; the test of interest is the interaction term treatment:baseline_bp.

Variations

• Search for the N you need instead of scoring one design: swap find_power(sample_size=180, …) for find_sample_size(target_test="treatment:baseline_bp", from_size=80, to_size=400, by=20). Interactions need markedly more N than main effects, so widen the upper bound rather than guess.
• Test the adjusted main effect too by setting target_test="treatment" (or target_test="all" for every term plus the omnibus), if you also care about the average treatment effect, not only the slope difference.
• Stronger or weaker moderation: move treatment:baseline_bp between 0.10 (subtle slope difference) and 0.40 (the two arms respond very differently) to see how fast power for the homogeneity test collapses as the effect shrinks.
• A continuous treatment intensity instead of two arms: drop set_variable_type("treatment=binary") and keep treatment continuous — that turns the design into continuous-by-continuous moderation.
• Same design, other fields:
  • Ecology: plant_biomass ~ habitat * soil_nitrogen — does habitat moderate the soil-nitrogen slope on plant biomass?
  • Social science: wage ~ gender * experience_years — does gender moderate the experience-years wage slope?

Not this setup?

• ANCOVA: group effect adjusting for a baseline covariate
• Binary-by-continuous moderation
• Dummy-coded factor interacting with a continuous predictor

If you'd rather have…

• ANCOVA: group effect adjusting for a baseline covariate — Same ANCOVA design but parallel slopes — group effect adjusted for baseline, no group-by-covariate interaction (drop the homogeneity-of-slopes test).
• Binary-by-continuous moderation — Same binary-by-continuous moderation structure, framed as a predictor interaction (gender * experience_years) rather than a treatment-vs-covariate ANCOVA.
• Dummy-coded factor interacting with a continuous predictor — Interaction of a categorical predictor with a continuous one, but the factor has 3+ levels (habitat * rainfall) instead of a two-level treatment group.
• Continuous-by-continuous moderation (interaction) — Continuous-by-continuous moderation if your 'treatment' is actually a continuous predictor rather than a treatment factor.
• Continuous moderation with a covariate — Continuous moderation plus an additive covariate — useful if you want an interaction and a separate adjustment term.

Copy-paste setup

from mcpower import MCPower

# ANCOVA with a homogeneity-of-slopes test: does the treatment effect on
# blood_pressure depend on each patient's baseline_bp? '*' expands treatment * baseline_bp
# to treatment + baseline_bp + treatment:baseline_bp, so the interaction is fitted explicitly.
model = MCPower("blood_pressure = treatment * baseline_bp")

# treatment is a two-level treatment factor (0=control, 1=treatment); baseline_bp is a
# continuous covariate.
model.set_variable_type("treatment=binary")

# Effect sizes on the benchmark scale.
#   treatment=0.50             → medium treatment shift (binary benchmark).
#   baseline_bp=0.40           → strong baseline-outcome association (continuous benchmark).
#   treatment:baseline_bp=0.25 → moderate slope difference (the moderation effect).
model.set_effects("treatment=0.50, baseline_bp=0.40, treatment:baseline_bp=0.25")

model.set_seed(2137)

# Power for the homogeneity-of-slopes test (the interaction) at N=180.
model.find_power(sample_size=180, target_test="treatment:baseline_bp")

suppressMessages(library(mcpower))

# ANCOVA with a homogeneity-of-slopes test: does the treatment effect on
# blood_pressure depend on each patient's baseline_bp? '*' expands treatment * baseline_bp
# to treatment + baseline_bp + treatment:baseline_bp, so the interaction is fitted explicitly.
model <- MCPower$new("blood_pressure ~ treatment * baseline_bp")

# treatment is a two-level treatment factor (0=control, 1=treatment); baseline_bp is a
# continuous covariate.
model$set_variable_type("treatment=binary")

# Effect sizes on the benchmark scale.
#   treatment=0.50             -> medium treatment shift (binary benchmark).
#   baseline_bp=0.40           -> strong baseline-outcome association (continuous benchmark).
#   treatment:baseline_bp=0.25 -> moderate slope difference (the moderation effect).
model$set_effects("treatment=0.50, baseline_bp=0.40, treatment:baseline_bp=0.25")

model$set_seed(2137)

# Power for the homogeneity-of-slopes test (the interaction) at N=180.
invisible(model$find_power(sample_size = 180, target_test = "treatment:baseline_bp"))