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Power & sample size for epidemiological designs

Design the study before you run it. StatsPAI's power family already covers econometric designs (RCT, DiD, RD, IV, cluster RCT, OLS); this guide covers the three sample-size questions epidemiologists and clinical trialists ask most: a binary outcome compared across two arms, a time-to-event (log-rank) comparison, and an unmatched case-control study.

Every function returns a PowerResult (with .power, .n, .summary()), accepts a scalar or an array for the sample-size argument (for power curves), and solves for the required sample size when you pass power_target= instead of n.

These calculators are validated by Monte-Carlo agreement with the test they approximate and against the closed-form Schoenfeld events requirement (see tests/test_power_study_designs.py).

1. Two proportions (cohort / RCT with a binary outcome)

import statspai as sp

# Power for a fixed sample size
r = sp.power_two_proportions(n=200, p1=0.30, p2=0.50)
print(r.power)            # ≈ 0.84

# Solve for the total sample size that gives 80% power
r = sp.power_two_proportions(p1=0.30, p2=0.50, power_target=0.80)
print(r.n)                # smallest n with power >= 0.80

# Unequal allocation (twice as many controls) and a power curve
import numpy as np
curve = sp.power_two_proportions(n=np.arange(50, 500, 50),
                                 p1=0.30, p2=0.50, ratio=2.0)
print(curve.power)

p1 is the reference (control) outcome probability, p2 the comparison arm; ratio = n2/n1.

2. Survival / log-rank (Schoenfeld)

Power for a time-to-event comparison depends on the number of events, not just the sample size, so you supply the hazard ratio and the overall probability that a subject is observed to have the event:

import statspai as sp

# 80% power to detect HR = 0.5 needs ~66 events (Schoenfeld 1983)
r = sp.power_logrank(hazard_ratio=0.5, prob_event=1.0, power_target=0.80)
print(r.params["n_events"])     # ≈ 66

# If only 60% of subjects are expected to have the event during follow-up:
r = sp.power_logrank(hazard_ratio=0.7, prob_event=0.6, power_target=0.80)
print(r.n)                       # total sample size (= events / prob_event)

3. Unmatched case-control

Parameterised the way case-control studies are actually planned — by the exposure odds ratio to detect and the exposure prevalence among controls — with ratio controls per case:

import statspai as sp

# Power with 150 cases, 1:1 controls, OR = 2, 30% control exposure
r = sp.power_case_control(n_cases=150, odds_ratio=2.0,
                          exposure_prevalence=0.30)
print(r.power)

# Number of cases for 80% power with 2 controls per case
r = sp.power_case_control(odds_ratio=2.0, exposure_prevalence=0.30,
                          ratio=2.0, power_target=0.80)
print(r.n)                       # required number of cases

The odds ratio and control exposure prevalence imply the case exposure prevalence p1 = OR·p0 / (1 + p0(OR−1)), and power is computed as a two-proportion comparison between cases and controls.

Notes & limitations

  • All three use the normal approximation; for very small samples or very rare outcomes, prefer an exact calculation and treat these as planning approximations.
  • Stepped-wedge and other cluster-period designs are not yet covered here (cluster RCTs are available via sp.power_cluster_rct).

Where to next

  • Competing risks
  • Survival analysis (sp.cox, sp.kaplan_meier, sp.survreg) — see the survival reference page.