Power for OLS moderation plus a covariate

You have a continuous outcome recovery_days, two continuous predictors dose and age whose interaction is the hypothesis, and a third continuous variable baseline_severity you want to hold constant. The moderation question — does the slope of dose change across levels of age? — is the same continuous-by-continuous interaction as before, but here you also adjust for baseline_severity so the interaction is estimated net of that control.

As an MCPower formula this is recovery_days ~ dose * age + baseline_severity, where * expands to the two main effects plus their product (dose + age + dose:age) and + baseline_severity adds the control term additively — it has no interaction with anything. The test that carries the moderation hypothesis is the interaction coefficient dose:age.

Variations

Score the whole model, not just the interaction. Swap target_test="dose:age" for target_test="all" to get power for each main effect, the covariate, the interaction, and the omnibus test in one run.
Weaker or stronger moderation. The interaction is the uncertain term — re-run with dose:age=0.10 (small) or dose:age=0.25 (medium) to watch how fast the required sample size moves once the product term shrinks.
A correlated covariate. Controls are rarely orthogonal to the predictors. Add set_correlations("corr(dose, baseline_severity)=0.3") to see how shared variance with the control erodes power for the interaction.
Find the N instead of the power. Replace the find_power call with find_sample_size(target_test="dose:age", from_size=120, to_size=600, by=25) to sweep for the smallest sample that reaches 80% power on the interaction.
Same design, other fields:
- Ecology: growth_rate ~ rainfall * temperature + soil_nitrogen — does the rainfall effect on growth rate depend on temperature, adjusting for soil nitrogen?
- Social science: wage ~ years_education * experience_years + tenure — does the education wage return depend on experience level, adjusting for tenure?

Not this setup?

If you'd rather have…

Continuous-by-continuous moderation (interaction) — Same continuous-by-continuous moderation without the extra additive covariate — the direct parent of this setup.
ANCOVA with treatment-by-covariate interaction (homogeneity of slopes) — Covariate adjustment combined with an interaction, but the interacting predictor is a group factor (ANCOVA with heterogeneous slopes).
ANCOVA: group effect adjusting for a baseline covariate — Adjust a group effect for a baseline covariate with no interaction — the additive ANCOVA analog of adding a covariate.
Two-predictor multiple regression — Plain additive multiple regression if you want covariate-style controls without any moderation term.
Three-way continuous interaction — Step up to a full three-way continuous interaction instead of one interaction plus an additive control.

Copy-paste setup

from mcpower import MCPower

# Continuous-by-continuous moderation with an additive control variable: does the
# effect of dose on recovery_days depend on age, after adjusting for baseline_severity?
# '*' expands dose * age to dose + age + dose:age; '+ baseline_severity' adds the control
# term only (no interaction with it). The full model is dose + age + dose:age + baseline_severity.
model = MCPower("recovery_days = dose * age + baseline_severity")

# Standardised effects (continuous benchmarks: 0.10 / 0.25 / 0.40).
#   dose=0.30, age=0.25    -> moderate main effects.
#   dose:age=0.15          -> the smaller moderation effect (the test of interest).
#   baseline_severity=0.25 -> a moderate control association we adjust for.
model.set_effects("dose=0.30, age=0.25, dose:age=0.15, baseline_severity=0.25")

# Power for the interaction term at N=220.
model.find_power(sample_size=220, target_test="dose:age")

suppressMessages(library(mcpower))

# Continuous-by-continuous moderation with an additive control variable: does the
# effect of dose on recovery_days depend on age, after adjusting for baseline_severity?
# '*' expands dose * age to dose + age + dose:age; '+ baseline_severity' adds the control
# term only (no interaction with it). The full model is dose + age + dose:age + baseline_severity.
model <- MCPower$new("recovery_days ~ dose * age + baseline_severity")

# Standardised effects (continuous benchmarks: 0.10 / 0.25 / 0.40).
#   dose=0.30, age=0.25    -> moderate main effects.
#   dose:age=0.15          -> the smaller moderation effect (the test of interest).
#   baseline_severity=0.25 -> a moderate control association we adjust for.
model$set_effects("dose=0.30, age=0.25, dose:age=0.15, baseline_severity=0.25")

# Power for the interaction term at N=220.
invisible(model$find_power(sample_size = 220, target_test = "dose:age"))